Watching with Woolsey

December 28th, 2010  ~  Bob Mackinnon  ~  No Comments 

Watching the Resinger Cup final on BBO was a real treat as it featured one of my favorite commentors, Kit Woolsey, who guided viewers through the action. We seldom encounter BAM scoring any more, which is a pity for every trick on every board counts. The IMPs game pales by comparison as an exciting and instructive contest of skill and a demonstration of card play, as there is none of this “next’ being called out after the opening lead, or yawns being expressed in print when the bidding stops at 1NT, a contract that should be one of the most exciting in bridge. My version of The Official Encyclopedia of Bridge states that BAM went out of favor largely because it is the most difficult contest for good players to overcome better players. That tells me that, contrary to some opinions, the luck factor is reduced to a minimum.

A British BBO commentator felt it was easier to sacrifice at BAM than at IMPs as the cost is limited, not like at IMPs where a large penalty risks a large carry-over. If the opponents can make a vulnerable game, a penalty of 800 translates to a loss of 5 IMPs, whereas a penalty of 500 represents a gain of 3 IMPs. Although at BAM scoring the gain and loss are equal, as Woolsey pointed out one shouldn’t be inclined to sacrifice at BAM if one can pass and tie the board without risk as a score of ½ is added to one’s running total. Sometimes sacrificing is 2:1 against the odds – if you are wrong and their contract does not make, you score a zero, whereas letting them play in their doubtful game or slam can have a positive outcome even if it is not theoretically optimal. In a previous blog we applied some mathematics to bidding decisions of this sort, so for clarification I decided to apply the same methodology to the situation to which Kit was referring.

The probability of making slam (or game) we denote as PM and the probability that the opponents at the other table will take the sacrifice is denoted as PB. If we do what the opponents do, the board is tied, the resultant score is ½ (on a scale of 1, ½, 0). There are 8 possibilities to be considered when we assume the sacrifice will cost less than the slam.

The advantage to not sacrificing is the difference: ½ – PM.

Clearly, if the slam has a better than 50% chance of making, on average it pays to sacrifice, regardless of what the opponents are doing. This implies that the decision rests solely with one’s expectations as to the lie of the cards. However, Woolsey points out that one may be making a poor bet to sacrifice when the opposition is not likely to do so. Let’s look at the conditions when we are certain they won’t sacrifice (PB=0).

Expected score for sacrificing = PM

Expected score for not sacrificing = ½

Thus, you are guaranteed an average score by not sacrificing. In order to make an even bet, where risk equals gain, slam must be a certainty. That was Woolsey’s point.

What’s Wrong with this Picture?

Here is a little story. Fred has just inherited $10,000, so he goes to his accountant to ask advice as to how to invest it.

‘Fred, this is your lucky day,’ the accountant says, ‘just this morning I read in the newspaper about this new sport franchise, Mexialleys, whose stock is predicted to rise 20% in the next year. It’s a terrific investment just waiting for someone like you.’

‘Tom,’ Fred says, ‘you mean I should put in $10,000 in order to gain $2000? Seems to me I would need 5:1 odds in order to justify such a gamble. Thanks, but I think I’ll just stuff the cash in my mattress and take out some extra fire insurance.’

Playing bridge is not akin to betting on a horse or putting all your money in one stock, it is like a mutual fund with many variable components, the sum of which serves on average to reduce the overall variability. Every hand is an investment for which there is a cost, a probable gain, and a probable loss. One will inevitably incur losses on some boards, the hope being that the cumulative gains will outweigh the losses by a sufficiently large margin so as to meet the aims set at the beginning. One’s strategy should depends on what wishes to achieve: scoring above average, or competing for a top finish.

Back to the Reisinger

In the qualifying stages there is evidence that indicates one should cautiously accept an average score. In the last 2 sessions the Jacobs team qualified for the final with scores of 52% and 53%. Non-qualifiers included Mahaffey at 35% and 65%, and Hampton at 42% and 61%. I am sure players on those teams wished they had scored a modest 45% on their first rounds, but it is difficult to control violent swings. Compensating for lows doesn’t mean you’ll get to keep the highs, as there is a different strategy involved. As 50% is not qualifying score one cannot be content with an average on every board. One should approach every hand with cautious optimism, not reckless abandon.

With regard to sacrificing against a slam, the even bet limit depends on the probability that the opponents will sacrifice. PB may not be independent of PM, as the more likely the slam is to make, the more likely the opponents will find the sacrifice. Nonetheless, the relationship between the 2 depends on the bidding. If one side opens 2NT at one table, say, it may not become obvious that a sacrifice is a good risk, whereas if the opening bid were a big club, a preemptive overcall could pave the way in that direction. In many cases it will be difficult to guess the auction at the other table. The situation in which one is maximally uncertain as to whether the opponents will sacrifice or not (PB = ½) constitutes a reasonable approach in unexceptional circumstances. Under this assumption, the expected scores are as follows:

Expected score for sacrificing = ½ PM + ¼ . Expected score for not = ¾ – ½ PM.

For PM=5/6 one has an even bet, the potential gain of 1/6 above average equals the potential loss below, but the expected score for not sacrificing is a lowly 1/3. One scores 2/3 on average by sacrificing, so it seems obvious to do so. There is something very wrong with the argument that one should act only when the gain is greater than the risk as only in 1 case out of 6 will it be wrong to sacrifice, and if you don’t sacrifice you are willing to accept a frequent poor score. So Fred may have doubts about Mexialleys, but it would not be reasonable to expect the shares to become worthless overnight. If he trusts the available information, it makes sense to invest for probable gains rather than take losses time after time, but the degree of risk depends on what Fred is trying to achieve.

Just reaching the Reisinger final may be good enough for some, but if one wishes to be near the top one needs to step it up. Here are some 2010 results w/o the carry-overs.

The top 2 teams were over 60% in first session and held on with slightly above average scores in the second. Rosenthal improved significantly by coming back with a 57% in the second session. Gordon’s recovery was more spectacular but their earlier session was too damaging. The Jacobus results are interesting; they scored well in the finals, but were handicapped by being 2.5 carry-over points behind the leaders after playing against the full field. So, scores in the low 50’s in the qualifying rounds will prove a handicap, however, just getting to the finals is worth 60 or more platinum masterpoints. For most players, being happy with average boards early in the going makes good sense.

If a top team had been capable of 2 final sessions of 57%, they would have won, but, of course, it doesn’t work that way – there will inevitably be random variability. If one’s target is 57% per session, one has developed the winning approach. Put yourself in the West seat in the 1st final session playing a board on which the 2 top finishers went face-to-face. Would you, as the front-runner, sacrifice in a nonvulnerable 5♦ or pass?

Dealer: West Vul: NS	North ♠ 8 6 4 ♥ A 7 5 2 ♦ A 9 6 ♣ A 10 7
West ♠ J 9 5 3 ♥ J ♦ 10 7 5 4 ♣ 9 8 4 3		East ♠ A 2 ♥ K 4 ♦ K Q J 8 3 2 ♣K Q J
	South ♠ K Q 10 7 ♥ Q 10 9 8 6 3 ♦ — ♣6 5 2

Would you as West pass or bid 5♦ ?

West for the eventual winning team, Michael Seamon, bid 5♦ on the hope that his partner, James Cayne, could hold the losses to 4 tricks, which he did. This was in keeping with the mathematical analysis given above which indicates that, regardless of the action at the other table, one should be inclined to sacrifice if the probability of their making is close to 1. Seamon thought so, undoubtedly influenced by the presence of the singleton ♥ J and the absence of anything else of much value. This action created a pickup against the second place team whose West took the conservative view of passing, scoring a zero for doing so when 4♥ by NS made easily. This was a swing of 1 full board and put Cayne in the lead. They barely held on in the second session, so this earlier board proved critical to the end result. The result indicates that one should be prepared to take one’s chances as they arise rather than hope to get them near the end after the situation has become desperate and one cannot be as selective in the choice of boards on which to swing.

The Matter of Frequency

December 15th, 2010  ~  Bob Mackinnon  ~  No Comments 

In a previous blog we considered the matter of frequency when choosing a partner to play in a matchpoint game that one wants particularly to win. We decided that in a single session event it is better to choose a partner who avoids tops and bottoms whereas in a longer event it is better to choose a partner whose tops exceed his bottoms. The reasoning behind that rested on the observation that with few opportunities for an appropriate swinging action, a bottom may be unrecoverable, whereas with many boards to come there are sufficient opportunities to a bottom (or two) near the beginning to be overcome. Over many boards the governing factor is not the number of bottoms expected but the probability of the difference between tops and bottoms. Mathematically, over a large number of boards the governing probability distribution function tends to be bell-shaped, symmetric about the median difference, whereas for a few number of boards the probability distribution function is skewed towards the number of bottoms.

What about scoring at Swiss Teams on a victory point scale? There are two differences to consider: the gains to be had from bidding vulnerable games, and the length of the matches. A few months ago I played in a Saturday night Swiss consisting of 4 7-board matches. In the second match before comparing scores with our teammates I knew our team had lost by a considerable margin because my score card showed three boards of -120, 2 of them on boards on which I expected our normally aggressive partners to be in vulnerable games going down. Those adverse swings pretty well ruled out our team’s chances of winning the event, but we finished respectably by winning the next two matches by a large margin. Our opponents’ only win was against us. My experience tells me that in order to win these events one has to bid close vulnerable games in an attempt to maximize one’s gain, even when the odds are against making it, but suppose one is playing for the event with just 7 boards left to play. Should we rein it in, try to avoid minus scores, and bid only those games that have a better than 50% chance of success? Jeff Rubens thinks so.

In the December issue of The Bridge World Editor Rubens has introduced the concept that one’s strategy should depend on the length of the match being played. He argues that with only a few boards remaining to be played, the best strategy is to win more boards than one loses, that is to say, the frequency of success outweighs the potential gain, just as it does throughout a Board-A-Match contest. He maintains that the long run odds in favor of bidding a vulnerable game are an exaggeration in a short match, where it is more important to be right rather than ‘have a good bet for an average result.’ Presumably he would aim to bid only to vulnerable games with at least a 50% chance of success. The idea is the same as for playing for tops and bottoms in a matchpoint game, namely, the odds are against recovering a loss, even when one gains 10 IMPs if a game is successful and loses 6 IMPs if it is not. The context of Rubens’ example is the final 7-board round of National Swiss scored on Victory Points where a 20 IMP victory will see his team place 3rd, and a 5 IMP victory will see them in 12th place.

We assume that a partnership decides before a match which strategy they will pursue. That may depend on what they assume the opponents will do in the same circumstances. Or not.: Rubens is silent on that aspect. Let’s suppose that the partners decide to play according to the long term odds and that they will bid all vulnerable games with at least a 37.5% chance of success, 3 chances out of 8. That means they are prepared to fail on 5 chances out of 8, because the opponents, following Rubens’ advice, have decided not to bid such games. If the game succeeds they gain 10 IMPs (G = 10), and it fails, they lose 6 IMPs (L = – 6 IMPs). Thus succeeding on just 3 deals balances the losses on 5 deals, and if the odds of making game are better than 37.5% a gain is expected in the long run. However, in a short match one will not encounter 8 such deals. Let’s look at the situation with only a few deals provide the opportunity to bid an inferior game with a 3 out of 8 chance of success, the lower limit usually recommended for bidding vulnerable games.

So one will lose IMPs 5 times for every 3 times one gains.

Here one gains IMPs 61% of the time and loses 39% of the time, which is highly encouraging for bidders. In terms of the frequency of gaining the advantage, there is a large difference between making just one decision and having the opportunity to decide twice under similar circumstances. This is not the case when G equals L, as in Board-A-Match, where the aggressive bidders will suffer 25 loses for every 9 victories.

The most frequent result is a loss of 2 IMPs. This may not matter much in the final victory point tabulation. The significant swings are more frequently to the plus side, 162 versus 125, 56%, for an average gain of 1.5 IMPs on those selected boards. Between gaining 14 IMPs (52% of the time) and losing 18 IMPs, there is an expected net loss of 1.4 IMPs over the long run, but overall there is a 5% chance of scoring 30 IMPs. Thus, with 3 opportunities the bidders will occasionally gain a very large margin of victory at a relatively low cost, as well as gaining significantly more times than losing significantly.

We consider 8 IMPs to be a significant amount, so one loses on 52% of the significant deals when 4 decisions are made. In that sense, one approaches a 50-50 split on a frequency basis between gain boards and loss boards. The conclusion is that with close decisions one should bid games, as frequency of failure will not be a major concern.

Next we consider bidding games on hands where there is a 50% chance of success. First assume we face ultra conservative opponents who will avoid such games.

Clearly it does not pay to be ultra conservative. With multiple decisions there are more plus boards than minus boards got by bidding.

Let’s assume that the opponents will bid 50% games 50% of the time. Whether the game makes or not is maximally uncertain, as is whether they will bid it or not. Maximum uncertainty implies that success or failure depends on the how the cards were dealt, an unpredictably random process, not on the accuracy of the bidding or on the skill of the declarer. Half the time when, they bid game, they will tie those who always bid game. Otherwise, they lose 10 IMPs a quarter of the time and gain 6 IMPs a quarter of the time, for the net loss of 1 IMP. Does it make sense to play to lose 1 IMP rather than to tie? No.

Let’s suppose both teams are neutrally selective, bidding half of their 50% games. Assume the choices are random and independent and the results are random. Half the time both teams make the same decision, so there is no resultant advantage. On one-quarter of the deals, one team gains 4 IMPs and on another quarter, the other team gains 4 IMPs. Perfect balance has been achieved. The greater the likelihood that one team will bid its 50% games, the greater its advantage over a neutrally selective team. Finally, if ideally one always bid games that have a probability of success greater than 50%, under those conditions one can only match those simple souls who blast away and bid some bad (37.5%) games along with all the good (50%) games. Note that bidding systems are based on probable outcomes and seldom provide enough information for a player to estimate the probability of success with great accuracy. So bidding a 50% game or not is more a matter of inclination rather than science which gets you to the point of decision but doesn’t tell you with certainty which way to go on any particular hand. That is the beauty of bridge as a game. We’ll discuss bidding methods further at the end of this article.

The Expected Number of Decisions

We consider the example of 8-board matches within which one’s side is vulnerable on 4 boards. On half of those boards our side holds the advantage. We assume (without detailed numerical evidence) that the chance of having to make a close decision as to whether to bid game is 1 in 4, an exciting proposition. How many such decisions are expected over 1 match, 2 matches, or 3 matches? That can be calculated using the binominal probability distribution function. Let P(n) represent the probability of n boards requiring a close decision. P(0) indicates the probability of not having to decide.

Over an 8-board match the greatest expectation is for one decision (42%). The probability having to make 2 decisions is half the maximum (21%). The probability of no decisions is 32%, resulting in a skew towards the lower number, characteristic of a few numbers of possibilities. Over 2 matches the greatest expectation is for 2 decisions, and over 3 matches, for 3 decisions. Over 24 boards the probability of having to make 2, 3, or 4 decisions is 78%. At the beginning of the session it makes sense to assume an attitude of bidding all close vulnerable games. The same applies over 16 boards.

The situation similar to that considered by Rubens is that where 8 boards remain to be played, and your team is in contention for an honorable placing, but out of contention for the top spot. The chances are 2:1 that your partnership will have to make one close decision rather than two. If early in the last match you bid game and lose 6 IMPs, that loss may drop your team from 16th place to oblivion as there is little hope of a second chance. If you bid the game and gain 10 IMPs, you reach the dizzying heights of 5th place, and if you get another chance, you may actually gain another 10 IMPs and attain 3rd place, although the odds are well against being so lucky. So what kind of player are you – the one who strives for excellence, or the one who is afraid of dropping out of the money?

Like the ill-fated Icarus of Greek mythology my preference is to rise as high as possible without fear of precipitously losing elevation. So I adopt the strategy of bidding close games, regardless of the point in the match at which they occur. With victory point scoring each board regardless of the order in which it is played contributes to the end result. Many games are pitifully lost when near the end the leading team grows cautious and attempts to sit on their lead. It is a common occurrence in competitive sports that the eventual winners come from behind at the end by vigorously striving to maximize their gains rather than passively waiting the leader to make mistakes. (This weekend the golfer Graeme McDowell demonstrated how to overcome errors and come from behind.)

Consider a 4-match victory point game at our local club. The winning score is usually slightly greater than 60 out of 80. One may attain 60 by the route 15-15-15-15, but that would be unusual as the last match will be against a team that has been playing with luck on their side. If both teams play with caution one’s scores may turn out to be 15-15-15-10, which gives a respectable total, but not one short of a winning total. So to win the event one must try to win the last match by at least 10 IMPs, attaining a sequence of 15-15-15-15. A vulnerable game in the last match is a god-given opportunity to pick up the margin of victory on one board.

Two swings of 6 IMPs each got by not bidding close vulnerable games will also achieve a victory point margin of 10, but the odds against 2 such swings are low. First, one may not get two chances, and second, the chances of gaining 6 IMPs on both is low, being the product of probabilities. Consider the case of a lower limit chance of success.

So it is reasonable when going into a final match to attempt to swing for 10 IMPs if the opportunity arises, rather than hope for 2 chances to gain 6 IMPs by keeping out of close vulnerable games aggressive opposition may bid. One hopes for at least one chance to bid a close vulnerable game and get it right. The first wish has a probability of 68%; the second wish is in the lap of the gods. I look at it this way: if there are no close decisions encountered in a match, my chances of winning the event are reduced.

Judgement and Bidding Systems

Here is the problem Rubens presents: holding ♠ J6432 ♥ AQ85 ♦ 2 ♣ Q96, do you raise to 3♠ after the sequence 1♦ – 1♠ ; 2♠ – ? He judges one should not and gives these hands to illustrate his point.

Less than 30% chance of no trump loser on a bad day, only 8 tricks

Whether by HCP evaluation or by losing trick count, the evaluation is that 9 tricks are available, but not 10. So normally one would not bid game. However, we know these are merely approximations, and there must be some probability associated with the claims of the total tricks available. Bidding systems are based on such criteria, so we can expect that these indicators represent a 50% chance of making the specified number of tricks. How can we then arrive at the 37.5% limit for 10 tricks?

Exact statistics would help, but lacking these we have to make a guess. With the losing trick count, we might estimate a deficit of a quarter of a loser, represented by the absence of a well-placed jack. With HCPs we would guess about 24 HCP would represent the normal requirement without shortages. Trump quality is the key. Judgment plays a part as well as the information revealed by the bidding process.

Generally when one raises from 2♠ to 3♠ , the proposition put to partner is, ‘if you have something extra for your bid, please bid game.’ Because no specific information is provided, this calls for a blind evaluation with particular attention paid to the trump situation. On point count opener has shown something between 12 and 14 HCP, so in the example shown above, opener may judge he has the extra required, and bid game. This is what Rubens fears, so he passes. It is bad bidding practice when one cannot invite safely. I would not raise to 4♠ on just 3 trumps without the possibility of trumping effectively in the short-trump hand. I avoid punishing an enterprising partner who is looking at 5 trumps in an 8-loser hand. Both shouldn’t stretch because of the vulnerability alone.

The losing trick count evaluation works better as a blind indicator. Opener is expected to have 7 losers. He has 7 losers, so he does not raise. Yes, the ♦ J may appear to be the little bit extra that is needed, but opener does not hold 4 trumps, as expected in a good system, such as Precision. So even under Precision methods opener should not raise to game even with a near maximum 14 HCP.

Normally with 4 trumps and 6 losers opener will give a jump raise to 3♠ , so responder knows immediately to raise to game with an 8-loser hand. So on a raise from 2♠ to 3♠ one’s best hope is to find opener with a good 7-loser hand, as shown below.

In this case opener has fewer HCPs than in the previous example, and the ♠ K has been demoted to the ♠ Q, yet the chances of making game are much greater due to the fact that a 9-card trump fit has been uncovered. A vulnerable game can be bid with justification. Rubens chooses to play ‘safely’ in 2♠ , and that decision might win 6 IMPs. Non-experts who count points and fear an aggressive partner might do the same.

Probability, Information, and Bidding

November 24th, 2010  ~  Bob Mackinnon  ~  2 Comments 

In a previous blog we gave a mathematical treatment, complete with numerical charts, of the contrasting bidding strategies of maximizing the gain when one guesses right and minimizing the loss when one guesses wrong in terms of 2 parameters, the probability of making a higher scoring contract (PM) and the probability that the field will bid that contract (PB). It is now time to flesh out the skeleton with some examples that support our assertion that generally the best strategy is to attempt to maximize one’s potential gains. That strategy entails bidding to higher scoring contracts that have a high probability of making and a low probability of being bid by the field. Most contracts of this type will involve distributional hands that are not efficiently handled by those players who depend greatly on HCP evaluations.

The circumstances of a deal that fit this description and prompted criticism from my partner were described in the previous blog. Here are the hands again.

At the time my jump to 6♠ was a quick, straightforward decision based largely on the losing trick count given that partner had limited his hand while promising support in the required areas. On the club lead I played low from dummy and the RHO nearsightedly put up the ♣ A which provided for a discard of my losing diamond. 12 tricks were made.

Accuracy is most easily achieved if one player is able to describe his holding within a limited context. This allows his partner to make an evaluation of their combined assets, hence a calculated guess of their overall potential. Thus, after I opened 1♠ , responder’s most descriptive bid is 3♠ when holding: ♠ AT84 ♥ 95 ♦ J6 ♣ K7652, showing 4 spade, 3+ controls, and 8 losers. The losing trick count is an important part of the definition with particular relevance to slam bidding in spades. The total HCPs is not. With this information my hand can be reassessed as a 4-loser hand, and a slam try can be made.

A later examination of the scores revealed that making just 650 would be worth only 33% of the matchpoints, that is, 4 out of 12. Making 680 was worth 8 out of 12. Obviously 4♠ was a contract that was hard to defend with double dummy accuracy. A conservative argument might run as follows: ‘I go with the field and stay in game. If I make 12 tricks I score 8 MP. If I bid slam I can score 12 MP, a gain of 4 MP, but if it goes down, I score a zero, so I am gambling a gain of 4 MP against a loss of 8 MP. Therefore, I need 2:1 favorable odds to bid the slam.’ This incomplete argument describes a strategy of minimizing the loss. Taking a wider view, one may calculate the expected scores for bidding a slam and for staying in game when the chance of taking 12 tricks is less than 2 out of 3, let’s say 5/8, which allows for some diminution from the evidence of the deal.

On the evidence of the actual results produced, it is clearly better on average to bid this slam in the environment in which it was played. Because the opposition faced was less likely than most to find the correct defence and hold declarer to 11 tricks, the argument for bidding slam is strengthened. Of course, many players would be afraid to bid the slam against strong defenders, thus failing to take advantage of a good opportunity.

Now we wish to study further the reasons behind my partner’s discontent. In the following deal the main feature is a long suit that will provide tricks opposite a limited, balanced hand, so the defence needs to be quick if slam is to be defeated. We have all felt the pressure to find the killing lead, so why not apply that pressure on an opponent?

A HCP evaluation indicates that a slam is not likely as the total of HCP will not reach the requirement of 33 HCP. So the true believer in HCP evaluation will bid 3NT although 2 suits are poorly held and leave it at that. A losing trick count evaluation indicates otherwise. Normally a 2NT opener will deliver 6 cover cards, and a 7-loser hand opposite will deliver enough winners to produce 12 tricks. The question to be answered is whether or not sufficient controls are present. An exchange of information might settle the matter, so that 6NT is bid when all is well, and not when the situation is unfavorable.

The losing trick total from the hands taken separately indicates that 12 tricks should normally be available. Taken together one sees that the defenders can cash the ♦ AK off the top, but they may not do so, so the probability of making a slam is not zero. If responder determines that slam is a fair contract unlikely to be bid by the field, he may reasonably decide to attempt to maximize his gains in the face of uncertainty. It is to his benefit to get to slam in an uninformative manner that will maximize his chances of gathering 12 tricks.

The brash approach of 2NT – 6♣ is not well conceived. Yes, in the face of failure it may not go down as much as 6NT, but that is not the proper way to maximize the score. The opening leader may decide to lead his ♦ A immediately and thereafter set 6♣ whereas against 6NT he would be reluctant to put down the ♦ A possibly to give away the contract.

The better approach, given responder is determined to bid slam, is to bid to 6NT under a seemingly normal circumstances. The chance of the ♦ A and ♦ K being in different hands is roughly 50%, and if the contract is 6NT one is unlikely to receive a lead away from an honor if the bidding indicates general strength. In fact, declarer might receive a passive club lead, ‘giving nothing away’. So, the calmer approach that goes through the motions of ace-asking always with the intention of bidding 6NT has the better chance of success.

To restate the obvious, the probability of making depends on more than where the cards lie, it depends also on the information made available to the defenders. Note that the above 2NT hand is not the best possible distribution of 20 HCPs, because of an overly qualified club suit. On the following more probable hand, 13 tricks might be available.

Responder begins with an estimate of normal expectation from a limited hand opposite and must decide how much information is enough information. Information comes at a cost, so responder must weigh a possible improvement in accuracy against the cost of perhaps steering the defence along the right path. The point is this: it is a matter of choice how much information responder decides to gather before making a final decision.

Let’s take an everyday situation where most responders are happy to jump to a normal conclusion without looking for possible flaws.

Despite a combined 28 HCP a 3NT contract is threatened on a black card lead. Responder may discover the spade flaw by initiating an informative auction as shown on the right. Opener’s 3♠ bid expresses doubt with regard to spades. Consequently responder bids the safer 4♣ . However, one would not expect applause for taking that approach, because almost every pair in the field will be taking the uninformative approach, in effect trading a slight risk against the potential cost of giving defenders information. Indeed, 3NT might make off the top if the opening leader underleads from ♠ AKxxx.

As the process here is the same as the process of bidding an optimistic slam, one must ask the question, why was my partner unduly upset by success? In bidding 1NT – 3NT one similarly may be bidding blindly to a helpless contract, but one is assured of company. That means one will not a score a zero. If one is wrong, the loss is minimized. If one is right in theory to bid 4♣ , some days one scores a top, some days one loses to everyone who makes 3NT on a normal but helpful lead. On average it will pay to bid 4♣ , but with regard to variability, there is less volatility in going with the field. Thus I conclude that my partner is greatly adverse to high volatility. He is content to go with the field on most hands, and await gifts on subsequent boards. ‘Count your HCPs and try to match the actions of the field,’ is appropriate advice for a beginner, but if one maintains this approach over the years, one’s bidding doesn’t progress much beyond the novice stage.

One’s primary aim should be to bid higher scoring contracts that make most of the time. If one bids 3NT without further ado, it is because this contract most likely will make, so there is little need to seek or give away further information. Because one is dealing with 2 balanced hands, the HCP evaluation is expected to produce an accurate prediction. However, when an unbalanced hand sits opposite a balanced hand, a HCP evaluation is an inaccurate indicator, so it is a mistake to persist in its use just because most will do so.

If both hands are unlimited, the captaincy is up for grabs. Here is an auction I encountered recently when facing a pair who were infrequent partners yet well experienced in use of the methods of a 2/1 system.

A start of 1♥ – 1♠ has proved notoriously troublesome, especially when a jump shift is wasted on showing weakness. Many pairs reached slam, but no one could find a way to reach the optimum 7♣ . Opener demonstrated a fear of being left to play in a part score by jumping to 3NT. If one is making a limited, descriptive bid, it helps immensely if partner can decode it accurately. Responder took 3NT to be ‘gambling’ in the modern sense with long hearts, and a scattering of minor suit honors, shortage in spades. Actually it was intended to show a hand with a strong preference for 3NT with strength in the minors and a weak heart suit, five to the ace, and shortage in spades, here the singleton ♠ K.

Responder was short in hearts, but felt he should make an encouraging move by introducing his second suit, clubs. Dangerously, both players had made bids that were subject to misinterpretation as 4♣ was taken to be RKC Gerber. 4♥ showed 3 key cards, but was taken as a sign-off. This horrible mix-up (worth 2 MPs, nonetheless) might have been avoided in several ways, but the fundamental difficulty was that the pair had quickly reached the lofty heights of 3NT without a sufficient exchange of information.

To overcome a need for openers to jump to show a strong hand, modern bidders allow themselves to beat around the bush in the early going, adopting the third- and fourth-suit forcing route: 1♥ – 1♠ ; 2♣ – 2♦ . Neither partner has yet provided a good description apart from not choosing a limited, descriptive bid on the second round. The aim is not to inform partner but to get through the round safely. Someone will have to come clean sooner or later…maybe. One can see this is a very different situation from the cases discussed above where one player limited his hand early, so that his partner could make a unilateral decision based on probability within the context of his partial knowledge.

My Candidate for the Best Bid Hand

When prizes are given for the best bid hands, the nod typically goes to a pair who have exchanged information through a long series of bids that ends in a cast iron slam. As Linda Lee asked in an earlier blog, why don’t we give prizes for a short auction? I know some of my best calls have been passes in the balancing seat. A quick decision, like 1NT – 7NT, is based on probability rather than actuality. If 13 tricks are taken on an exotic squeeze, one doesn’t expect to be praised for the bidding, only for the play. The best played hand of the year may derive from consideration of the probabilities of the distribution of the opponents’ cards where certainty is not guaranteed. The attitude is that declarer has made the best of the bad situation when placed in a doubtful contract that makes only on a particular lie of the cards. In order to qualify for the bidding prize the defenders must be seen to be helpless. This is not the usual situation in practice.

In reality the play of the cards is linked to the bidding that precedes it. Defenders and declarers operate in a realm of uncertainty where probabilities play a major role. So the best bid hand might be one in which the opening lead has been made more difficult by uninformative bidding, and a defender later makes a fatal discard as he is unaware that his apparently worthless jack-to-five is the key to the defence (as happened recently in the WBF Open Teams). So, the worse the bidding, the worse may be the defence.

Playing Perfecto Club, a 4-card majors system, responder bid 1♦ with the thought that on a heart lead 3NT might be better played from the other side. Opener’s jump was constructive, promising 4 diamonds and at least 4 controls. The following heart bids by responder were artificial asking bids that revealed opener held 6 controls in the minors, 2 queens and the ♣ J. Opener opted to play in the 4-4 diamond fit as his club suit would provide a discard for a potential losing trick in the majors. Beautiful, as 7♣ doesn’t make whereas 7♦ is cold even though diamonds split 4-1 and spades 6-2.

The best bid was not 7♦ , but what followed it – a double asking for a club lead. Fearing that a club ruff was imminent, responder corrected hopefully to 7NT, but down 1. Was the doubler void in clubs? No, they split 2-2. He deduced from the opponents’ skilful bidding that 7♦ was likely to make, so his side was doomed to a very poor score, because no other pair in the field could match its flawless perfection. The only hope was that 13 tricks would not be available in 7NT. It was a gamble that would cost little or nothing if it were wrong, but it was probably right for the opponents would have bid 7NT freely if they were confident of 13 tricks. Their long sequence was just too convincing. Perhaps perfection has its flaws and a little uncertainty is a good thing. So there you have it: a single bid wins the prize.

Bridge Laughter

November 17th, 2010  ~  Bob Mackinnon  ~  4 Comments 

Husbands, take note: wives know you better than they let on. Last week my wife let the veil slip when she commented, ‘you laugh a lot, but you seldom smile.’ It’s so true – I am not a great smiler; I don’t even like The Mona Lisa. But I do laugh a lot, usually at situations others don’t find at all funny. That becomes dangerous, if taken too far.

BBO is a good source of laughs as it provides a daily dosage of contrasts between harsh reality and failed expectations. Of course, at the table courtesy demands one keep a straight face. Just the other day after a hotly contested auction my RHO put down 3=5=5=0 dummy in 5♦* with the comment, ‘I’m only doing this because everyone else will be doing the same.’ Ha-Ha. He was entirely alone in his predicament, because as an occasional visitor, he had forgotten the wayward ways of our Seniors Day. No other pair our way was crazy enough to bid 4♠, which, as the cards lay, was makeable. When I laugh it is not personal, but in recognition of the handicaps that hamper us all, such being unable to see what’s just around the corner.

Politicians are taught to smile (or sob, as the soon-to-be Speaker of the House damply demonstrated), but laughter loses votes. Too much laughter reveals a lack of serious commitment to general principles, the true state of American politics with regard to the will of the people. As Shakespeare wrote, ‘one may smile and smile, and be a villain.’ Which brings us to the recent Copenhagen Invitational Pairs with HRH the Prince of Denmark (Henrik, not Hamlet) as Patron.

In a previous blog I pointed out some shortcomings in the bidding of 2 renowned Polish experts, the Krzysztofs, Jassem and Martens. I had suggested pusillanimous behavior as a reason for their collapse against the Nickell team in the 2010 WBF Open Teams. Well, when you come down it, what do I know? I only observe from afar, and I am always ready to change my views on the basis of fresh evidence. With regard to Jassem and Martens, in Copenhagen they finished third out of a field of 16 international experts, so I thought upon inspection of the deals I would find reason to alter my previous impression. Can supposed chicken bidders do well at IMP pairs? I would think not over 15 rounds against the best Europe has to offer. The following board caused me great amusement when it was played in the last round. Perhaps after this background you will see why.

Board 16

Dealer: West Vul: EW	North ♠ J 2 ♥ K Q J 5 4 ♦ 8 5 ♣ A K 5 3
West ♠ A Q 8 6 ♥ 10 8 7 6 ♦ — ♣ 9 8 7 6 2		East ♠ K 10 5 4 ♥ A 3 ♦ A K Q J 9 3 ♣ Q
	South ♠ 9 7 3 ♥ 9 2 ♦ 10 7 6 4 2 ♣ J 10 4

Seeing only the EW hands it is reasonable to reach 6♠ even after North has opened the bidding. Perhaps in the end it was the brashness of youth, or being raised under the Mediterranean sun, that caused Agustin Madala to bid the slam. What an ancient dame said to me on Seniors Day could be applied here, ‘you boys sure like to bid a lot.’ Boys!! The energetic Italians were to come in second just 8 IMPs above our heroes, Jassem and Martens. At the other table the bidding took an odd turn, again with boyish exuberance a factor.

Brogeland’s redouble is grand larceny at work, followed fearlessly with a second misdirection that could have proved suicidal. Jassem bid out his fine hand with mature discretion, and Martens had nothing to add. Erik Saelensminde was left to play in a totally hopeless contract without being doubled. Martens was not good enough to double, but too good to raise to 3♠ when 3♣ looked like going down. That’s how some think. What do you guess Jassem led against 3♣ ? Did you guess the ♣ Q?

It was the outcome that provided even more cause for laughter. Martens and Jassem picked up IMPs on this board, because Madala went down in 6♠ ! After a favorable, precipitous club lead (instead of a preparatory ♥ K) the brash declarer failed to provide for a bad split in diamonds by ruffing a diamond early. Negligently he started on trumps, thus establishing a heart loser for himself when the ♦ 10 didn’t fall in 4 rounds. He had slipped on a mental banana peel, going down 1, losing 5 IMPs instead of gaining 15. So, although the odds are against it, sometimes the chicken escapes the badger’s best efforts.

The Seniors Day deal that prompted the old dear’s misdirected comment presented my partner, Luke, and me with the following bidding problem:

At the time my jump to 6♠ was a quick, straightforward decision, given that partner might very well have underbid his first response holding a red king and the ace four times in spades. I suppose if one partner appears continually to stretch the HCP scale, upgrading as it’s called, a true believer learns to compensate, which makes the overbidder overbid even more. Dummy was a disappointment; the ♦ J appeared wasted, but at least it helped to prevent a fatal diamond lead. On the club lead I played low from dummy and the old lady on my right nearsightedly put up the ♣A. Well, that was my extra chance.

Driving home after another mediocre finish Luke began to complain, which I abhor, especially when in heavy traffic he is at the wheel making eye contact in the rear view mirror as I fret nervously in the back seat.

‘That slam you bid was filthy,’ he stated bitterly, hitting the brakes at a red light, ‘you’re lucky she covered with the ♠ K.’

‘Not so lucky,’ I replied, ‘any one-one trump split would have served as well. But please, Luke, if you must complain, choose a hand on which we scored a bottom, not one on which we scored a top. Making just 650 would be worth only 33%. The light has turned green by the way.’

You see, one never learns from undeserved tops, that’s why I refuse to discuss them. If the opportunity ever arises again in this lifetime, I fear the temptation to bid another makeable 19-point slam will be far too great to resist. I would have preferred to discuss all the losses we incur daily by not doubling part scores, something beneficial might be done there, but this was neither the time nor the place.

I more I play, the more I admire Rixi Markus, born 100 years ago last June 12. She gave some sage advice in her beautifully produced book, Play Better Bridge (1979), which I have just reread with great enjoyment. We can all do with some sage advice.

Bid Boldly, Play Safe, my friends.

The Anatomy of a Collapse

November 2nd, 2010  ~  Bob Mackinnon  ~  11 Comments 

With regard to playing Teams, a point of interest is to what extent one should be influenced by what one imagines may be happening at the other table. Zia has suggested that at the highest levels players should be informed of the current state of the match so they can adopt accordingly board-by-board without having to guess. The utopian view is that the beauty of bridge lies in revelation not competition, so each deal should be played on its own merits to achieve the par result regardless of the order of play. Reality lies somewhere between these two extreme views, as players always have a feel for how the match is proceeding and can hardly resist the temptation to compensate accordingly.

It is perhaps ironic that the Nickell team is known for its great comebacks, but that its leading member, Bob Hamman, is known for his unflappability, meaning that in the face of adversity he continues to play each hand on its own merits. Yet he participates in comebacks time and time again. That’s a clue that collapses may be due to psychological factors that affect teams that are leading. Do they bid too much, or too little? Does losing represent a weakness of character, and winning, a strength of resolve, or is it mostly randomness at work? In the recent WBF round of 16 the leading Martens team lost to Nickell by dropping 47 IMPs on the last 8 boards of a 56 board match. Do the events point to an optimum strategy that may help us avoid a similar collapse? Let’s see.

Gitelman Bids a Grand Slam

Before we consider the Martens-Nickell match, here is an amusing board from the WBF Open Teams final that illustrates the dangers of guessing what may be happening at the other table. The Diamond team had a healthy lead in the final stages of the match, so Fred Gitelman might well have imagined that Zia-Hamman at the other table would be swinging to pick up IMPs. The rest is speculation on my part, but the action illustrates the dangers of guessing what might have happened, even when seeing all 4 hands.

Dealer: West Vul: Both	North ♠ Q J 4 2 ♥ 8 3 ♦ Q 8 7 6 5 ♣ 9 8
West ♠ K 8 ♥ A 10 7 6 5 4 ♦ J 9 ♣ A 7 5		East ♠ A 6 3 ♥ K J ♦ A K 4 2 ♣ K 4 3 2
	South ♠ 10 9 7 5 ♥ Q 9 2 ♦ 10 3 ♣ Q J 10 6

Zia opened the bidding with 1♥ and the auction proceeded along natural lines as follows:

1♥ – 2♣ ; 2♥ – 2NT; 3♣ – 3♥ ; 4♥ – 6♥ ; all pass

Notable is Hamman’s restraint with his control-rich hand. There does not appear to be any attempt to swing a favorable result. The famously unrestrained Zia may have thought that the swinging result was to pass, his reputation for flair having preceded him. His play of the hand would have pleased his British fans in particular as he never led trumps but after the lead of the ♠ Q played along elimination lines, ruffing 2 diamonds and 2 spades in hand before exiting a low club to South leaving himself with ♥ AT7 and dummy with ♥ KJ ♣ 4, thus avoiding a guess in the trump suit, making 6 the Utopian way. Some with long memories could recall the great Belladonna once did the same thing, many years ago.

South had made the slight error earlier (pointed out by Mike Passell on BBO) of discarding a club rather than ruffing a diamond deceptively with the ♥ 9.

At the other table Fred Gitelman bid the bad grand slam that left the onlookers shaking their heads.

Gitelman may have thought Moss held better hearts, but his decision is nonetheless surprising opposite a partner who showed no slam ambitions. Maybe he felt that Zia might well bid 7♥ , so that he was taking out insurance against a possible swinging action. The amusing aspect of the hand is that Rodwell accepted Gitelman’s evaluation and led a trump, eliminating the trump guess Zia worked so hard to avoid. Now Moss made 13 tricks on a squeeze with the ♦ 4 a threat card against Rodwell and the ♣ 7 a threat card against Meckstroth, neither opponent being able to keep a guard in spades.

This hand shows once again that the bidding of a grand slam is not to be nervously avoided – there is always the chance of a favorable trump lead. If you are going to bid a risky contract, at least do it with confidence and the opponents may believe you and act make your assessment valid a posteriori. Laughter is a useful weapon. Also note that squeezing to get an extra trick is more profitable that doing all that’s possible to avoid a loser. The latter is an insurance policy, the former a speculative investment. One doesn’t get rich through buying insurance, which leads us to the aforementioned collapse.

Martens vs Nickell

The round of 16 in the WBF was played over 4 sessions of 14 boards each. At the end of the first session Martens led by 27 IMPs, and managed thereafter to maintain a lead. Session 3 was a bit of a chore, as the Nickell team gained 2 IMPs on 6 different boards, which must have been somewhat annoying. The young Czech player, Michal Kopecky, made an insightful play in 5♦ that gained 10 IMPs against the same contract played by Bob Hamman. Still, the Europeans knew they were being outplayed on most hands. The fourth session began with 4 game hands with no exchange of IMPs, so Martens still led by 17 IMPs, and they were about to gain 23 IMPs on the next 2 boards. Here is the scoreboard for the last 10 deals.

Superior card play was not a factor in the swings; it was all about bidding. The declaring side was the same in both rooms for all the boards, so there was no stealing involved. The large swings were due to the choice of level, the winning decision in 4 hands being to bid game rather than stop short in a partial. The lone exception was Bd 22 where the swing went to Zia-Hamman for staying out of game. First let’s examine whether system differences produced a swings on Boards 28 where the bidding was quite different.

The Krzysztofs, Jassem and Martens, are scholarly experts, the former having written a fine book on the Polish Club System, which contains the option of opening a limited Precision 2♣ with a 6 clubs and a 5-card major of poor quality. Rather than emphasizing the fine club suit, Jassem opted to start with a limited bid in his major suit, a common approach at matchpoints. Yes, a major suit game requires only 10 tricks, but here Jassem had a 4-loser hand and should have had higher ambitions. He showed a lack of foresight as well, for what might happen if the opposition competed strongly in spades? He ended up playing in clubs anyway, but at 3 levels too low when Martens sensibly passed 3♣ .

In the other room Rodwell opened the hand with a more descriptive Precision 2♣ , and the auction became competitive immediately when Kopecky doubled where Hamman had passed. Meckstroth could give a feeble raise to 3♣ , and with just that modicum of encouragement Rodwell bid 5♣ over 4♠ with some confidence. He was not unhappy about missing slam which makes because the ♣Q was dealt singleton in the North hand.

Board 25 was a costly 10 IMP loss when Jassem-Martens again pulled up short, playing in a club partial, but this time they missed a vulnerable game. As we discussed in a previous blog on the mathematics of bidding vulnerable games, one should bid them on the slightest excuse. Of course, Jassem knows that, but circumstances are different if one takes into account that the opponents may double the contract if one steps too far out of line. On the previous set Zia-Hamman had doubled Jasem-Martens 3 times, twice in part-scores, so a speculative penalty double was a live possibility. Zia, especially, has been known to compete deceptively then go for the throat. Here are the EW hands.

This was a first-class disaster as game is available in 3NT or 5♣ . At the time the Poles were aware that Board 21 had produced a great result when Zia had erred badly by choosing to play in a hopeless 3NT rather than an easy 4♠ . They must have felt well ahead at this point. This is not the time to let up, but the time to press on aggressively. The cuebid has become somewhat nebulous, showing general strength, so Jassem was hesitant to commit to 3NT on the expectation of quick tricks in his mediocre suit. He hedged with a nebulous 3♥ which must have puzzled Martens, who might have bid 3♠ , more nebulosity leaving 3NT an open possibility, as the status of a diamond stopper was still in question. Instead he bid 4♣ to show strength in the suit, but Jassem passed.

It is difficult to generate any sympathy for the Poles, who, after this exhibition of inhibition, well deserving of their loss. Here’s the action in the other room.

It looks easy, doesn’t it? Rodwell had no guarantee of a club fit, but he was willing to bet he could make 3NT holding at least one side entry. Clubs never came into the picture, so the purist might argue that this was bad bidding on his part. Still, when one is behind in a match, one takes chances, and if you are Rodwell and Meckstroth you take chances regardless, a factor that Jassem, in particular, might have acted upon. If it is to be done, ‘tis better it be done quickly, not so?

Another point concerning this hand is the opening bid. Kopecky chose 1NT when holding a 6-card minor, often thought to be a clever maneuver by those who like to bid for effect rather than for information. I was glad to see that it backfired, as it so often does when the opponents are not so easily cowed. Meckstroth’s double is good on points, bad on shape, but one has to start somehow. Kurka’s 2♠ bid didn’t strike fear into valiant hearts, but served only to increase the chance of club values in the doubler’s hand. Without the fear of a long diamond suit in the North hand, Rodwell simply bid what he hoped to make.

In competition, simple is best. Trying too hard can lead to big mistakes, such as happened to Kopecy-Kurka on Board 22. When they picked up their hands the Czechs had a 40 IMP lead with 8 boards to play. Could they have been aware of their sizable lead? From their perspective the deals had progressed normally. On Board 21 Kopecky had taken 12 tricks in a 4♠ contract gaining 13 IMPs, but he was unaware of the favorable turn of events. One can’t be entirely happy with taking 12 tricks in a game contract, but there was no need to over-react, as slam was not likely to be bid at the other table.

Board 22

Dealer: East Vul: EW	North ♠ A Q 9 4 ♥ A 10 8 7 ♦ A 5 ♣ Q 9 7
West ♠ 8 ♥ K 5 3 2 ♦ Q J 10 2 ♣ A K 5 2		East ♠ K 10 4 ♥ Q J 6 4 ♦ K 9 8 3 ♣ J 10
	South ♠ J 7 6 3 2 ♥ 9 ♦ 7 6 4 ♣ 8 6 4 3

Rodwell had shown a good limited bid and Meckstroth had shown values with his initial redouble. With 16 HCP of his own Michal Kopecky could expect his partner, Josef Kurka, to hold zilch. He was correct to double 4♥ for penalty insofar as that contract was doomed to be down 1, vulnerable. The question is this: was he wise to do so? Increasing the score from +100 to +200 doesn’t amount to much in terms of IMPs. Early in a match a fierce double might be an attempt to intimidate, but late in a match the psychological boundaries have been pissed upon already. When taking a risk it is the effect on partner one has to be most concerned about. In this case the pressure was too much to withstand, as Kurka made the fatal move of removing the double, thus changing +200 to -300, losing 10 IMPs for no particular good reason. Note that Kopecky might have overcalled the Precision 1♦ with 1NT. Now if he were to double 4♠ , Kurka could in good conscience pass. This, then, is another example of how making a simple descriptive bid can prove beneficial in a competitive auction.

So at last we come to consider Board 26, yet another 10 IMP loss for the Martens team. The approach of the popular historian is to make winning decisions appear rational, we’d all sleep better if that were so, but I believe in luck because I never win without it. The problem facing Hamman and Kopecky was this: both vulnerable, your partner opens 3♥ in second seat. Do you raise to game on ♠ Q6 ♥ A4 ♦ KT63 ♣ AT762? Find reasons.

Traditionally, second seat vulnerable preempts were expected to deliver a good suit, so holding the ♥ A points to being able to score 7 tricks in that suit. The ♣ A brings the total to 8, and a diamond lead would produce the required 9, so if one were considering a swinging action, 3NT would be a possibility. The silence of the lambs indicates partner may hold 3 spades to an honor, but one shouldn’t expect help in the minors. Otherwise, it is simply a matter of counting losers and deciding whether or not to bid 4♥ . If one places partner with 7 hearts and 3 spades, he is most likely to hold 2 diamonds and 1 club. On that reasoning game may depend solely on finding the •A with West. Here is the deal.

Dealer: East Vul: Both	North ♠ Q 6 ♥ A 4 ♦ K 10 6 3 ♣ A 10 7 6 2
West ♠ J 10 8 4 2 ♥ 10 7 ♦ A 9 7 5 ♣ K 8		East ♠ A 9 7 3 ♥ 9 6 ♦ Q 4 ♣ Q J 9 5 4
	South ♠ K 5 ♥ K Q J 8 5 3 2 ♦ J 8 2 ♣ 3

The old guy, Hamman, bid game, the young guy, Kopecky, didn’t. As one can see the opener has 2=7=3=1 shape, with the welcome presence of the ♦ J. The game depends on holding the diamond losers to 2. An underlead of the ♦ A would be brilliant, the kind of which nightmares are made. I am mentally prepared to submit to brilliance, but only after the occurrence, not before. At both tables the lead was the mundane ♠ J, and 10 tricks were easily harvested. A shame to have missed this one at the table.

Why didn’t Kopecky bid game? The reason may lie in his expectation of what constitutes a vulnerable 3♥ opening bid in second seat. The partnership style may be purely destructive so that by custom the South hand is too good for a preempt. Ha! Nevertheless, there should be various chances for a 10th trick, and to bid a vulnerable game, one is justified in clutching at straws, especially on a simple, noncompetitive auction.

How Not to Collapse: Stay calm. Keep it simple. Bid your vulnerable games. Expect what is normal. Put pressure on the opponents where it belongs, not on your partner.

Utopian Bridge – A Brief Escape from Reality

October 19th, 2010  ~  Bob Mackinnon  ~  9 Comments 

In 1516 Thomas More published a description of an ideal society he called Utopia in which everything was done in the best possible way. Greed was not a factor as there was no private property. All houses were built the same and all streets looked the same. There was no fashion, as everyone dressed in uniforms. There was religious freedom, universal health care, equality of the sexes, as men and women both worked 6 hours a day, each according to his abilities. If there was an abundance of goods, workers took a vacation (rather than going on strike) until the excess was used up. Some Christian societies hold similar ideals. We suggest a few modern updates:

-the country supports a trickle-up economy in which workers benefit first;

-managers get bonuses for maintaining production while improving working conditions;

-only individuals can make political contributions;

-there are no provisions for the wealthy to escape taxation;

-there is no such thing as an ‘official spokesperson’– those responsible report publicly;

-there are no freedom-of -nonsense laws, only freedom-from-nonsense laws;

-sports are participatory, not the basis of a government sponsored entertainment industry.

Bridge in Utopia

Let’s consider how bridge might be played in a modern Utopia. First, the emphasis is not on achieving high scores at the expense of others, but upon playing correctly in communal setting where the interests of the many surpass the interests of the few. In Utopia bridge is part of the mathematics curriculum starting in primary school, where children learn the 4-3-2-1 point count system. In middle school kids start playing standard bridge and are introduced to logical planning. In high school bridge is used to illustrate the principles of probability, statistics, and decision making in the face of uncertainty. Before graduation everyone has to pass tests on Utopian Sanctioned Systems, of which there are 5. Graduation Day features an evening of bridge playing with the elders followed by the traditional awarding of prizes for academic excellence, neatness, thrift, and outstanding service to the community. Everyone gets to bed safely by 11 o’clock that night.

Duplicate bridge comes under the jurisdiction of the Utopian Bridge Authority, a subdivision of the Ministry of Recreation. If one wishes to play a system different from SUC, the Standard Utopian Card, the agreement of all 4 players at the table is required. Each sanctioned system is restricted in the number of conventions that can be incorporated, and no deviations within the systems are allowed, as it is deemed that the ordinary player is not competent enough to make the choices that are in his best interests. The two most advanced systems are upgraded on New Year’s Day, a much anticipated event, on the basis of recommendations of experts and the head of the statistical analysis laboratory at Harmonia University, the aim being to produce the best possible mix within the overall framework. Complaints are dealt with in the customary manner – all players may suggest changes that will be given due consideration by the Systems Panel made up of elected members. Their recommendations for change are not binding, however.

The whole bridge scene is geared towards conformity where the process is more important than the outcome. Only duplicated hands from the Internet are used and scoring is done on a par basis by computers. A deal is played in a spirit of cooperation, although Undo’s are not allowed. The objective is to achieve a perfect result by both sides. Each bid and play is judged on the basis of correctness within the system being employed. One loses points for making bids, such as frivolous preempts, considered to be destructive rather than constructive, and those points are assigned to the victims. The player with the greatest accumulation of correctness points is declared the winner of the much coveted merit award. The pair with the greatest score are the winners of the results award, a lesser achievement. If a pair reaches an inferior contract that happens to make due to an opponent’s egregious error, say a vulnerable game that makes because a timid opponent leads a trump, their score is reduced proportionately, as it is felt no one should profit unduly from the folly and ignorance of others.

The Real World

Currently bridge operates in a state of confusion within which the Cult of Self is best served. Winning is all as no masterpoints are awarded for good conduct. Greed plays a dominant role in which the primary objective is to beat par by any means possible. The operative approach is that whatever is legal is justifiable, and we demand the right to split hairs to achieve our goals. Nonetheless, there are some traces of the Utopian ideals to be found. When we begin as session, we wish the opponents a good game, even though our aim is to see it doesn’t happen. Some thank partner for his efforts when he puts down the dummy. We may even praise an opponent for a fine play. These niceties go beyond mere courtesy. There is a feeling that as players we are cooperating in an endeavor for mutual satisfaction. Such communal attitudes are reflected in the articles in the ACBL Bulletins, and especially in the letters to the editor.

In September 2010 issue of the ACBL Bridge Bulletin, a letter writer, Jack Margid, describes the graciousness of an opponent in the face of a ‘fix’ caused by a successful bid of a grand slam most pairs would not have reached. He had apologized for breaking a ‘cardinal rule’ by cooperating in a grand slam try with poor trumps. Should he have done so? The upshot of Margid’s optimistic bidding was that his partner bid and made 7♠ missing Qxxx. The probability of bringing in this trump suit is 58%, so this result hardly qualifies as a fix. On theoretical grounds a 58% chance justifies bidding the grand slam although it may not be a common result. So the question becomes: to what extent should one e prepared to apologize to an opponent for scoring a top against them as a result of an abnormal action? This sounds very Utopian, doesn’t it?

I remember a regrettable occurrence from several decades ago when in a European tournament a prominent player reached a risky 6♣ . During the play the ♣ K fell singleton which allowed him to make his 12 tricks. Immediately he said, ‘I’m sorry’. The opponents called the director asserting his apology constituted a claim, thus restricting his choice of subsequent plays. Not being able to draw the rest of the trumps, he went down. That makes me wary of making comments during the play. I think it is foolish to say you are sorry, but also foolish to feel sorry in the first place. Here’s why.

Playing against the Odds

Consider the tossing of a coin. If I bet you that you will toss 2 heads in a row, and give you even odds, wouldn’t you be happy to take the bet? The probability of 2 heads in a row is 25%. If you proceed to toss 2 heads in a row, should I apologize for taking your money? That would be silly. In the same way if I were to bid a slam that requires 2 finesses, also a 25% chance, should I apologize for giving you such good odds for a top score? Any anti-percentage play favors the opposition. If it succeeds, they were unlucky in the placement of the cards, not in the execution. If it fails, as it is rated to do, they get a top without having done anything to earn it. In this case does one apologize to the rest of the field? In Utopia one should do so, but in a greedy world a player takes great satisfaction from big risks that profit from uncertainty and create favorable swings.

There is a lot of guessing involved in the bidding phase, as a result of the imperfections in the bidding systems. One should not apologize for a correct guess, even though better sequence would have got one to the same contract. Here is an example from a recent Sectional where my partner ‘fixed’ the opponents on the second deal of the afternoon.

In Precision, 2♣ promises 5+ clubs, usually a good suit. Partner is pretty sure the field will get to 6NT, but it costs nothing to ask concerning the quality of the club suit. Finding the ♦ A, and ♣ KQ+ he feels justified in bidding a grand slam when all pairs should reach a small slam, at least. A club is led, and the RHO shows out. Now the grand depends on spades splitting 3-3, which they do. We score 35.5 on a top of 37. Is this a fix? No, partner might even be complimented by the opponents on his fine judgment.

However, what actually happened was that partner was vaguely aware that 4NT was not RKCB, but was not sure that 4♦ was the substitute asking bid. So he guessed to jump to 7NT, thereby taking a great risk for the greatest return. If the ♣ J had been the ♥ J the opponents could very well have scored 37 unmerited matchpoints. So by guessing partner gave them a chance that the lie of the cards denied them. That’s normal.

Abnormal Bidding

Often a simple approach to bidding cannot achieve the optimum result, so one is left to guess. Sometimes improvement is obtained if one ‘invents’ a bid that does not conform to the standard definition. In the previous blog we showed a partner opening the bidding with an unorthodox 1♦ holding: ♠ KQJT  ♥ — ♦ Qxxxxx ♣ Jxx. It was the only way to reach 6♦ . This is a hand on which many would overcall and some would open in third seat, but not in first. It is not a question of playing strength but of definition within a system. Here is another situation where the playing strength of a hand cannot be revealed with standard bidding methods based primarily on HCPs.

Responder has an excellent 6-loser hand which should produce 12 tricks opposite a suitable 1NT opening bid. It is not good enough to complain, as many do, that one should never look for a perfect fit; if a perfect fit exists, try to find it. But how?

The first step in slam exploration is to establish the trump suit; the second to establish the degree of fit. Opposite a limited opening bid the aim is to get information rather than transmit it. It is useful to have the definition of the bid of a new minor at the 3-level to encompass the possibility of it being an advanced cue bid promising a control, not necessarily length, as in the case above. 3♣ need not be defined as a relay, but it serves the purpose. Once the opener agrees to spades as trumps, responder can take charge with 4NT as RKCB in spades. The sign-off in 5♠ suggests slam interest, and opener is well suited to accepting the invitation. Here is the full deal where some played in the inferior contract of 3NT. Slam needs some help. It can be made on a black suit lead, if a suspicious declarer avoids total reliance on the heart finesse and sees the advantage of playing on diamonds early – low towards the hidden ♦ K in order to gain a tempo.

Board 15

Dealer: South Vul: N/S	North ♠ A Q J 9 7 6 3 ♥ 5 3 ♦ Q 6 ♣ K 5
West ♠ 4 ♥ K J 9 6 2 ♦ J 10 8 ♣ Q 4 3 2		East ♠ 8 5 ♥ 10 8 4 ♦ A 5 4 3 ♣ J 10 9 7
	South ♠ K 10 2 ♥ A Q 7 ♦ K 9 7 2 ♣ A 8 6

With diamonds and clubs interchanged, the appropriate bid would be 3♦ which uses up more bidding space, but which is informative, ostensibly denying a club control. This treatment should be useful to the opponents as well as to partner, whereas a relay bid tends to benefit only the user. With that understanding in place, it is possible that a few swindlers would bid 3♦ just to keep in practice, intending always to gamble it out in slam if a spade fit is established. By misrepresenting the control situation they seek to increase the chances of a favorable lead, but a ♦ J lead would only help declarer find his way, as happened at our table. Ha! Deliberate attempts to mislead would not be allowed in Utopia. In this case it is obvious that a truly informative alternative is available.

Whatever else one might think of Utopia, the real world is a much more exciting, fractious, and dangerous place. As Harry Lime might comment disparagingly, ‘Utopia sounds too much like Switzerland.’ Orson Welles played the criminally inclined Harry Lime in the classic movie, The Third Man, and delivered the famous lines in which he mistakenly identifies the villainous Borgias as Godfathers to the Italian Renaissance while giving Switzerland credit only for the invention of the cuckoo clock. An American, he is weak on history. [Bertrand Russell observed that in his day the sins of Alexander VI could not be mentioned in the public schools of Boston or New York.] Peaceful, democratic Switzerland was born out of centuries of persecution fueled by imperialistic ambition and religious extremism. The Swiss found the middle way and have prospered greatly thereby. As for inventiveness, the cuckoo clock originated in Germany, whereas Albert Einstein made his greatest discoveries as a humble Swiss civil servant working in the patent office.

Two Gentlemen of Victoria

October 13th, 2010  ~  Bob Mackinnon  ~  6 Comments 

It was a thrill for me to watch on BBO two gentlemen of Victoria, Canada, outplay the several times the world champions from Italy in the qualifying round of this year’s world championships being held in Philadelphia. Based on their performance over 14 boards one would have to rank them amongst the world’s best partnerships. I know them very well, as we have played against them at the local clubs for over 3 decades, and can say that they are a great credit to their city, country, and to the game of bridge. They deserve whatever recognition that may come their way. Of course, playing over several days at the highest level may prove to be beyond their current capacity limited by a lack of training, but that does not detract from their accomplishment which must be the culmination of many years of devotion to one of the hardest games to master.

Critics have often found the organization of Canadian bridge to be lacking with regard to producing teams that can complete consistently for the world championship. That is true enough, but Canadian bridge is not about that. The top players are scattered about the country, and even in small bridge hotbeds like Victoria, the players are not inclined to get organized on a regular basis. As a result in any given year many teams have a chance to win the right to represent their country in international competition. It is not always the same players year after year. That is good for bridge, I believe. It’s democratic. Everyone can be inspired by talented amateurs like Mike and Jim, not even full-time partners, who can rise from relative obscurity to enjoy their brief time in the spotlight without turning themselves into full-time card sharks. Bridge is their game, not their life.

I can testify that both players are necessarily intense competitors who never fail to perform as gentlemen at the bridge table. I never resent a top they score against me because it is always well deserved. Any lucky tops I have scored against them have been gracefully accepted. A friendly but disciplined tone for Victoria players was set by the highly regarded ACBL director, Matt Smith, and is maintained by the top players and current club owners Debbie Wastle and her brother, Bill. The players are largely self-policing, and hair-splitting legal protests are not given much consideration. Over the years Jim on occasion has offered during play, when ‘I played too quickly’, to let me take my card back, saying, ‘surely you drew the wrong card, Bob, take it back’. That looks bad, but it is just Jim’s sense of humor at work. One of these years I shall say, ‘thanks, Jim, these cheap drugstore eyeglasses are murder’, just to see the look on his face.

Love blossoms at the bridge table which is a good reason as any for young and old to take up the game. Both Mike and Jim met their charming and accomplished wives, Debbie and Connie, at the bridge table. Mike, the more intense, a lawyer, puts great store in following the system to the letter, whereas Jim, a charted accountant, tends to more liberal interpretations on a case-by-case basis as circumstances allow. Both are firmly committed to a cooperative effort, and it is a lack of egotistic flights of fancy that preserves the strength of their partnership, no matter the opposition. Being amateurs they play only for the love of the game and the challenges it presents. They promote bridge and teach by example. This is not in any way an apology. I think they represent non-professional North American bridge at its best.

So onto the match against the Lavazza stars. BBO commentators tend to be either (1) dark and gloomy, or (2) bright and cheerful. Maybe it has to do with their time zones, the former being largely confined to GMT. Initially our heroes were not favorably accepted, but as the match progressed and it became evident that Jim and Mike were really putting it to the favorites, the realization dawned that this was not to be Italy’s day. At the end it was recognized the Canadians fully deserved their huge margin of victory, 71-19 IMPs. Now let’s look at some hands to see what they tell us about improving our own game.

Board 4: Both Vulnerable

Result: down 1, -100

Early in the match Noberto Bocchi took what is considered normal action these days, a hyperactive vulnerable overcall. Where this might lead was a mystery at the time he overcalled, but it no longer remains so: it led nowhere. It is hard to fight the majors with the minors, so Bocchi was probably hoping for more action, but unluckily his partner had the majors and 7 HCP, just enough to silence our pair. The division of sides was 6=6=7=7, so it was a deal where the winners are those who don’t declare the hand.

The Victorians operate in a more conservative mode. They have a philosophy reminiscent of the best French teams of the recent past. They are not so keen on competing for the part scores on minimal values, preferring instead to maintain partnership trust by ‘always having their bid’. So initially Hargreaves took no action over 1♠ and later also passed the correction to 2♠ , for which he was soundly criticized by all BBO commentators. The bidding had gone: 1♠ – 1NT; 2♦ – 2♠ ; Pass. I think it is pretty obvious that on the auction the deal is a misfit, and that there is not a great deal of merit in competing to 3♣ opposite a partner who hasn’t much to contribute offensively. He knows he is not missing a game. Let’s not conclude that Hargreaves is chicken-hearted. It takes courage to pass when those around you are bidding. Result: Italians down 100 at both tables.

The next deal demonstrates that Art is making the difficult appear simple, not in making the easy appear hard.

Board 3

Dealer: South Vul: EW	Hargreaves ♠ A Q 8 6 4 ♥ A K Q J 8 3 ♦ 7 ♣ 6
Duboin ♠ K J 3 ♥ 9 4 ♦ J 10 8 4 3 2 ♣ Q 4		Sementa ♠ 10 7 5 2 ♥ 5 ♦ Q 6 ♣ K 10 9 8 7 2
	McAvoy ♠ 9 ♥ 10 7 6 2 ♦ A K 9 5 ♣ A J 5 3

The commentators began with a criticism of McAvoy’s opening bid, which appears quite normal to me – 7 losers and 5 controls are enough. What to bid if partner bids 1♠ may be a problem, but that is resolved routinely by any serious partnership. When Hargreaves reverses, McAvoy signs off in game with a minimum. 4♠ is RKC asking and Jim shows his 2 aces. They have reached the same point as Bocchi and Ferraro at the other table and the commentators note that, although 13 tricks are available, there seems to be no way to bid it. Then Mike bids 7♥ . Why did he do that when the Italians stopped in 6♥ ?

As we discussed in a previous blog, bidding a grand slam when the opponents are sure to be in six, at least, is not a big gamble. There is a lot of uncertainty; sometimes something good happens, sometimes something bad. As Alan Truscott advised, bid the grand if at worst it depends on a finesse. Mike follows this advice. The finesse would have worked, but was not needed, as 13 tricks were obtained on a cross-ruff. Part of the reason he could bid the grand was that he could trust his partner not to have opened on a load of garbage, as is so often the case these days. This promotes an optimistic atmosphere.

Once Hargreaves has bid 7♥ and routinely wrapped it up, the commentators now shifted tack and began to wonder how many would not reach 7♥ . Surely world champions would not miss this opportunity. But the observers were wrong, as most pairs stopped short. Could it be they were following a false doctrine with regard to grand slams?

It is often said that system doesn’t matter, but this is wrong. One flaw in the Italian methods is that they use an opening bid of 2♦ to show a strong, balanced hand not good enough to bid 2NT, something like this: ♠ AQ84 ♥ KQ63 ♦ 92 ♣ AK9. It is a rare bid that fills a gap in their other constructive sequences. How would you like it if partner passes your 2♦ bid? Well, how do you like losing 9 IMPs for no particularly good reason? Bidding Gap Fillers is bad when they make a hand, especially a strong hand, harder to bid than otherwise it would be. A second flaw in the Italian system is that it favors self-preemption. Their 1♣ bid is nebulous and potentially strong, so it is doubly bad for responder to jump because his hand is weak with a long suit. Ferraro made such a weak jump that cost 11 IMPs. (They repeated the error on the next day, so this was no accident.) I think that if one is going to preempt, one should take care that it is not partner who is being preempted. Avoiding self-generated disasters is becoming a lost Art. Let’s concentrate on the positive aspect of the following deal where the Victorians got it right.

Board 12

Dealer: North Vul: NS	Hargreaves ♠ A K J 7 5 ♥ A ♦ K J 6 5 3 2 ♣ 6
Duboin ♠ 9 8 ♥ K ♦ A 10 8 4 ♣ Q J 8 7 5 3		Sementa ♠ 10 4 ♥ 10 9 7 6 ♦ Q 7 ♣ A K 10 9 2
	McAvoy ♠ Q 6 3 2 ♥ Q J 8 5 4 3 2 ♦ 9 ♣ 4

In the other room Bocchi opened his nebulous 1♣ . Ferraro preempted to 3♥ and played there for +140, accurate bidding as far as the hearts were concerned. The cards didn’t cooperate as partner held the unbid suits. As noted, Mike prefers the correct bid, so he opened in his longer suit, a minor, which had the effect of allowing McAvoy to show his heart suit at the 1-level without instant and irrevocable commitment to that strain. Duboin started a campaign against a possible vulnerable game in spades with a tentative 2-level overcall and Sementa pitched in enthusiastically to force a decision at the 5-level.

Under the circumstances most would find the 5♠ bid automatic. There is no problem because NS took care not to create problems for themselves. Because of their solid approach, McAvoy can assume that Hargreaves has full values for his reverse, so, once more, what might have been difficult now appears routine. Sementa leads the ♣ A, looks at the dummy, thinks, and leads the ♣ K, giving an immediate ruff and sluff. That doesn’t strike me as the best alternative. Mike ruffs in hand, ruffs some diamonds, in the end giving up a trick to the ♦ A and claiming the rest. Well done, guys.

Post Script: Well, it didn’t last as our heroes were dropped out by Swedes in the round of 32. Lest the reader thinks I have been converted away from Precision, I admit I wavered overnight. Then I witnessed this unprovoked instability by US experts against Lavazza.

Bridge and the Empire of Illusion

October 4th, 2010  ~  Bob Mackinnon  ~  8 Comments 

In his bestseller, Empire of Illusion, curmudgeon Chris Hedges bemoans the dumbing down of America, putting the blame largely on television and its corporate sponsors. He considers credit cards to be membership cards to the Cult of the Self the aim of which is to derive mindless pleasure through emancipation from reason and societal restraints. Think of millions of wannabee Caligulas and Messalinas sitting down to nights of vacuous TV viewing. In such an atmosphere it is hard to imagine the game of bridge returning to a prominent place among the past-times of the masses. Bridge is a partnership game that features perseverance and concentrated effort, not quick self gratification. It puts constraints upon the individual and requires due regard be given to reality. The great majority who can’t make change at the grocery counter need never try it.

Illusion is eternal insofar as it feeds upon uncertainty, so it has a prominent role to play in the game of bridge. To be disillusioned is to learn the truth. One of the skills of a player is to create an illusion that may lead an opponent astray, but one must be careful that partner doesn’t get caught up in it as well. I have story to tell in this regard on a hand that arose in a recent Sectional. Like all good bridge stories mine has a beginning, a middle, and a happy ending for the teller – I’ll skip the history to keep it short.

An Illusionary Elimination Play

In the middle phase of a good matchpoints game, we come to a table where I fear we are outgunned in the brains department. The player on my left is a man of logic who has devised a complicated system with 100 rules and 200 exceptions. It is the exceptions that get you. His wife, despite all the restrictions, manages to get her own way most of the time. They have a kibitzer, a former partner, so I am determined to do well.

In third seat, none vulnerable, I have to choose an opening bid with this holding: ♠ AK ♥ 832 ♦ AJ98 ♣ AK104, 8 controls and 19 HCP. In first or second seat I would open a Big Club as the hand is too rich in controls for the slam-killing 2NT. In third seat I prefer when possible to open with a limited bid, so 2NT it is.

Bridge is a partnership game, meaning there is always a partner around to help out. Partner holds: ♠ 1043 ♥ J654 ♦ 87542 ♣ 8, and decides he would rather play in 3♠ , if it comes to that, than in the optimum contract of 2NT. As with most human activity, whether it be drilling in the Gulf of Mexico, or building cities on a fault line, the prevailing attitude is, ‘well, if the worst happens, we’ll deal with it when we come to it.’ He bids 3♣ . Even with a single solitary point in their hand, some players can’t be shut out. This is why I like limited bids: they give partners the freedom to act on distribution alone.

I respond 3♦ , which is passed all around. When the dummy comes down, the opponents are enthusiastic in their praise and I wonder why. Are we in trouble? Maybe 3♦ is the second best contract. Will I screw it up? Probably, so it is merely a matter of how to go about it. I notice there are 4 diamonds missing, the ♦ KQ104. These are more likely to be split 3-1 than 2-2, so playing ace and another potentially leaves 2 losing diamonds outstanding. But I am getting ahead of myself, as usual. Here is the full (rotated) deal.

Board 24

Dealer: North Vul: None	North ♠ 10 4 3 ♥ J 6 5 4 ♦ 8 7 5 4 2 ♣ 8
West ♠ Q J 6 ♥ K 10 ♦ K Q ♣ Q J 9 6 3 2		East ♠ 9 8 7 5 2 ♥ A Q 9 7 ♦ 10 3 ♣ 7 5
	South ♠ A K ♥ 8 3 2 ♦ A J 9 6 ♣ A K 10 4

The ♣ Q is led, and one can see that nothing could be simpler than making 9 tricks in diamonds: win the ♣ A play 2 rounds of trumps, claim, and go for coffee. However, a little knowledge is a dangerous thing, and, like Hamlet, I began to have my doubts. Imagine West’s being dealt ♦ QT3. He takes the second diamond, leads hearts, and ruffs the 4th heart with the promoted ♦ 10. Ouch! So I devise a devious plan. Luckily my opponents are experts, so can be fooled if one goes about it in the right way.

Winning the ♣ A, I cash the ♣ K and lead the ♣ T towards dummy. West fails to cover, so instead of ruffing I pitch a spade from dummy, a totally illogical play that gives the false impression I hold 3 spades. After East wins a cheap trick she exits safely with a spade, not a heart, won by the ♠ K – no point in false carding against a pair would keeps track of the HCPs. When attempting to deceive it is best to appear as normal as possible in the minor details. Now in quick succession the ♦ A, a club ruff, the ♠ A and a diamond exit puts West on lead. My plan is about to come to full fruition. The ♥ K is followed by the ♥ T, ducked in dummy and overtaken by the ♥ Q. If you have followed the plot to this point you will realize that cashing the ♥ A will set up the ♥ J in dummy. If declarer has started with only 2 hearts, he can ruff the ♥ A return and get to the dummy with a ruff to get a pitch on the ♥ J, but if he started with 3 hearts, the ♥ A should be cashed now.

Can we condemn East for playing a spade, giving a ruff-and-sluff with the hidden losing heart going away? Not really. She was yet another victim of razzle-dazzle. It is difficult to defend against an illogical play without signals from partner. The pointless pitch of a spade from dummy was a persistent early impression. So it is that I once again arrive at the best result possible via the worst possible route. The +110 score was worth 66%.

Giving the Wrong Impression

One of the worst (or best) ways to convey a false impression is the off-shape double. I feel strongly if one has a suit one should bid it, not double and hope to correct the first impression of a flat hand capable of supporting several strains. OK, sometimes one is dealt a hand so strong that one cannot avoid having partner pass a simple overcall, but these are rare, and one must be able after doubling to keep control of the subsequent auction. Here is an example from the Sectional of a ‘power’ double going horribly wrong.

In first seat I opened a wimpy weak 2♦ on ♠ 863 ♥ 764 ♦ AQ98763 ♣ –. My LHO doubled. Partner passed. How would you advance on: ♠ KJ976 ♥ Q ♦ KJT4 ♣ 763? My RHO teaches bridge, but I cannot confirm that her choice of 4♠ , fast arrival, is of the textbook variety. Perhaps her hand is not strong enough for 3♠ , (never preempt over a preempt), and too strong for a simple 2♠ . The full auction went as follows:

My double was a Lightner Double, often the subject of a classroom demonstration, but seldom seen in practice. It calls for an unusual lead. Partner began to think, but I was not unduly worried because the longer he thinks the more likely it is that he will do something ‘creative’, and not do what others might be led to do in haste, namely, lead dummy’s first bid suit. It was with some degree of admiration that I saw his opening lead was the ♣ 5. We took the ♦ A and 5 tricks on crossruffs, to score 1400. Hopefully that will teach them not to double on a strong 2-suiter, at least until next time. I have reached the stage where I feel sadness when old acquaintances demonstrate they have not learned from experience. I had the same sad feeling recently when in a team game our opponents, a long-term partnership, failed to reach a cold 7♥ because one of them was void in clubs and couldn’t use RKCB. Apparently they are resistant to change and not interested in hearing about Exclusion Blackwood. Oh well, it was a tie board.

Back to the Local Club

After a day of rest from bridge, many Victoria seniors were eager to be back at the local club for New Moon Week which encloses my birthday. The spirited action fitted the occasion. An interesting bidding problem arose late in the session. My creative partner opened 1♦ in first seat, overcalled with 1♥ by my RHO, our best card player. I prefer my doubles and 1NT bids to be descriptive shape-wise, so I was rather restricted in my choices holding: ♠ 93 ♥ K8763 ♦ AK94 ♣ A9. Nothing seemed right. With +1400 fresh in my memory, I didn’t want to double and encourage a spade bid from partner. True to my general approach when in doubt, I supported partner with a bid of 2♦ , admittedly nonforcing, but, realistically, is everyone going to pass that? Here is the full auction:

*bid with the comment, ‘well, it is matchpoints, after all.’

Uncharacteristically partner had not self-preempted with ♠ KQJT  ♥ — ♦ Qxxxxx ♣ Jxx. Normally this partner goes against my admonishment never to preempt with more stuff outside the suit than in it, so it’s nice to know where he draws the line. Are his wide-ranging preempts a part of a well-reasoned strategy, or merely an indication of the onset of the male menopause? I’m not sure. Recently he had jumped to 5♦ with a void in hearts, so I went with that. Right! When the overcaller failed to find the killing club lead, my losing club went away on a spade, so 6♦ was made, not doubled, but still a top.

Attitude Doubles

We are all familiar with defensive carding by which one conveys an attitude. To what the attitude applies depends on the situation in which the signal occurs. The same applies to an ‘attitude’ double, which may be for takeout, or for penalty, or both, depending on the context in which it occurs. So an attitude double, even though it may be an agreement, cannot be defined before the hand is played, as it may change as the hand is being played.

With everyone bidding like crazy, the double has become an essential tool in the fight against illusionary bids. At present players have not adapted their methods fully to the increase in uncertainty brought on by unsound practices, but it is obvious that the proper use of doubles is going to be part of the strategy of the future, if for no other reason than the double saves the bidding space the opposition is keen to destroy. The same property is characteristic of transfer responses whose popularity is on the rise. The penalty pass must remain a viable option, otherwise one is liable to get pushed around without recourse, the normal state of affairs as they currently exist. Here is an example from the Sectional.

Board 18

Dealer: East Vul: N/S	North ♠ 9 7 4 ♥ A 8 6 ♦ 10 3 ♣ A Q 10 8 5
West ♠ J 10 2 ♥ — ♦ K J 7 6 5 ♣ K 9 7 6 3		East ♠ A K 8 3 ♥ K Q 3 ♦ A 8 4 2 ♣ 4 2
	South ♠ Q 6 5 ♥ J 10 9 7 5 4 2 ♦ Q 9 ♣ J

As one can see 4♥ * is down 3, for a top for EW. 3NT makes, so EW must protect that score. Normally bidding on to the 5-level in a minor is not the best way to protect a score at 3NT, especially if there is the option of doubling for penalty. My suggestion is that West should balance with an attitude double, even with a void, leaving it up to East to decide. Clearly, with 4 spades and doubling values West would have doubled 3♥ earlier for takeout, therefore East has a good idea that West’s values lie primarily in the minor suits. Bidding to 5♦ remains an option, so, really, the attitude double is a free shot at a top score. The balancing double is defined in the context of what went before, what may follow, and what exists at present, which would be defending against 4♥ without a double. Against accurate bidding East may do best to take out the double, but if errant opponents have given you the opportunity for a top score, why not take advantage of the opportunity? Here East should take a plus and be pleasantly surprised to score 800.

Vulnerable Grand Slams and Games

September 10th, 2010  ~  Bob Mackinnon  ~  7 Comments 

The two situations in which the expected action of the opponents plays a major part in constructive bidding have to do with vulnerable games and grand slams, the first being common and the second being rare. The game situation engenders reckless abandon, the grand slam situation, extreme caution. One would think that holding hands that have the combined assets to make 13 tricks would be a pleasurable and momentous occasion for any pair, but many nervously anticipate the event more with apprehension than joy. Some come ill-prepared. Alan Truscott in his book, Grand Slams, suggested that grand slams that at worst depend on a finesse should be bid, yet it is common enough to hear veteran players advice novices not to bid a grand slam unless they can count 14 tricks. Larry Cohen has commented on BBO to the effect that grand slams are overvalued in IMPs, as a single board can produce a disproportionate swing that may determine the match winners. In effect, there is wide-spread feeling that bridge would be better if grand slams didn’t exist, and many bid as if they don’t. That shortcoming influences one’s strategy.

Standard bidding methods are poorly suited to exploring grand slam possibilities. If one starts the bidding at 2-level, worst at 2NT, one has eaten up valuable bidding space, so it becomes difficult to obtain sufficient information on which to base a critical decision, especially with regard to the minor suits. It so happens that this week we received further evidence on this point. In the Bridge Canada Magazine Michael Yuen reported this success in the 2010 Canadian Seniors Team Championship where he and partner, Maurice De La Salle, reached a contract of 7♣ when their opponents bid to 6NT and stayed there.

The sequence has some odd features in that the one who holds the stronger hand and makes the asking bids does not get to decide the final contract and does not get to play it. Some players like this approach as it allows the responder to make the final decision on the basis of undisclosed features. It is like the old burlesque fan dance, where the performer flutters about seductively promising much while revealing little that can’t be guessed. Over the limited 2NT, Yuen begins by describing a powerful hand with the minor suits. Opener can ask concerning the quality of the club suit, and would be very surprised if partner couldn’t show the ♣K. 5♥ is another asking bid, but like Blackwood 5NT it is also descriptive, here showing all the key cards in clubs are held. Yuen decides enough is enough and executes a grand leap to what he thinks he can make, as the lights go out. The strong hand is left in the dark, unable to bid a confident 7NT. Nonetheless, the effort was worthy of applause and 9 IMPs.

2NT is an especially badly designed part of popular systems. It’s easy to imagine the bidding going: 2NT – 6NT. Responder with just 14 HCP might very well doubt that a grand slam will be bid or that it can make without that a hoped-for favorable lead. Thus players are condemned by their own reluctance to disclose specific features, so remain unsure as to how good a grand slam might turn out to be on the lie of the cards.

Playing a Big Club system I could open 2NT based on the high-card content, but my preference when holding 8 controls is to open with 1♣ . Responder bids 2♥ to show minor suit orientation with at least 5 clubs and 4 diamonds with honors distributed in the minors. One sees that the 2♥ response is fully 9 steps below 4♣ , the point where Yuen can impart a similar description. This saving in space is a great advantage to the Big Clubber.

This example demonstrates why grand slam decisions are based partly on the perceived capabilities of the opposition. This is expressed mathematically by PB, the probability the grand slam will be bid. If I held a hand like De La Salle’s I would be aware that against standard bidders I have a great advantage. As the bidding progressed I would be encouraged to move towards a grand slam as my superior methods can land me in a good contract others are unlikely to pursue. On the other hand, against expert Big Clubbers I would bid the grand slam in a close decision expecting to tie the board. The theoretical point of neutrality is where it is 50-50 that the opposition will bid the grand slam (PB=½), and the probability of making it, PM, equals 17/30 (a 57% chance.)

Vulnerable Game Strategy

Grand slams are the nectar of the bridge gods, whereas vulnerable games are the ham sandwiches of the masses. Sometimes they survive on baloney alone. The neutral point is at PM=3/8, PB=½, a point far removed from the point of maximum uncertainty, PB=½ and PM=½. The dice are heavily loaded in favor of bidding the game. One doesn’t need much hope when bidding on, especially when many will be bidding the game as well, poor as it is. The gain if successful is 10 IMPs, the loss if not is 6 IMPs. The optimal rule is to bid the game if PM>3/8 (37.5%). Above that threshold on aggregate the expected score is greater for bidding the game. Plainly put, one should bid game on any excuse, the quicker the better. That is not the whole story, as there is a downside. The risk is minimized under the prevailing rule of not doubling mutually agreed contracts at IMPs. So one can hope to enjoy the benefit of making the contract without fearing unduly about the consequences of arriving in a hopeless one. This leads to loose action which provides thrills, suspense, anguish, and rapture – exactly what wise mothers warn against.

The Full Picture

Below is shown the full map of the critical decision zone over a range of PB and PM. The numbers given are the expected scores in IMPs for the game on the left and the partial on the right. The aggregate for each contract is given below the line. This is the pattern:

The comfort zone, wherein the criteria to maximize the gain and minimize the loss both require that the higher contract be bid, consists of the boxes below the critical boundary line at PM=3/8. Two exceptions are highlighted in blue. On the left one minimizes the loss by staying in the part score, but the gain is 0.41 IMPs against a potential loss of 1.53 IMPs, so even if the opposition is not bidding this game, the odds favor doing so at IMP scoring. On the right one maximizes the gain by staying in a part score when most will be bidding the game. One gains 0.22 IMPs, gambling a potential loss of 1.33 IMPs. Clearly one should go with the opposition on this one in order to minimize the potential loss. This is entirely consistent with the optimal rule.

What if in their enthusiasm the opposition has bid a filthy game, represented by the line PM=1/3? If the probability of their doing so lies between PB =4/9 and PB=5/9, there is less than one-tenth of an IMP to be lost on average by bidding on. This reduces the penalty for being foolish. The effect is to degrade the game of bridge in such a way that good judgment based on hand evaluation is not well rewarded – boldness is.

Defensive Action versus a Vulnerable Game

If the opponents are vulnerable and you are not, there is good reason to expect them to strive to bid game. On the assumption they will bid game most of the time, the task at hand is to prevent them from making it. Every decision should taken with that in mind.

ANY ACTION (OR INACTION) THAT HELPS THE OPPONENTS MAKE THEIR VULNERABLE GAME IS BAD.

One sure way to help the opposition is to make a lazy overcall on a bad heart suit in a mediocre hand. Lately this was demonstrated to me yet again when I opened a standard 1♦ on: ♠ A87 ♥ Q6 ♦ AKJ86 ♣ A83. LHO overcalled 1♥ and partner bid 1NT which I unhesitatingly raised to 3NT. RHO led a heart and partner easily racked up game after losing the finesse in diamonds. Game would have been in danger if the RHO had made his natural lead of a spade from KJxxx, and LHO had switched to a club upon winning the ♠ Q. Automatic nonvulnerable overcalls have become for some a bad habit.

On the other hand I love overcalling 1♠ even on a bad suit. In the same session I overcalled 1♠ /1♥ on: ♠K8763 ♥A3 ♦AK ♣9874, not an especially brave action. The LHO raised to 2♥ , partner raised me to 2♠ , and the RHO went directly to 4♥ . Obviously, I had a plan. I led an unusual ♦ K, and found ♠ QJT4 in dummy. The ♠ K was wasted paper, but my holding it made it more likely partner held the ♠ A. The ♦ A, a low spade to the ♠ A and a diamond ruff ensured a 2-trick set. My overcall and partner’s raise actually set up the defence for us before I made the opening lead. If my LHO had bid 1NT instead of raising hearts on 3-small, our prospects would not have been so bright. Support with support, yes, but trump support on 3-small should mean there is hope of a ruff to be had in the short-trump hand, especially when raising an opening bid.

The lead-directing aspect is a very important when partner will be on lead against a vulnerable game. That increases the attractiveness of overcalls of a minor on a good 4-card major, preferably spades. Such overcalls may prevent the opponents bidding a thin 3NT and making it on a favorable lead. The less you hold in HCPs, the tougher will be partner’s decision if you don’t bid, as he may hold scattered values in 2 other unbid suits.

The Victory Point Distortion

The worst form of team play is the 4-round Victory Point Swiss. It is not duplicate bridge as around the room teams are playing different boards. One needs must maximize the gains against teams in the early rounds, as a pair of small margin victories puts one’s team well behind the leaders. The need to maximize the gains distorts priorities so that one is inclined to gamble on risky vulnerable games and slams that require a misdefence.

Last month going into the last 7-board match our team was behind the leading team by 4 VP’s as a result of a well deserved loss to them. In order to overtake our rivals and win the event we had to outscore our final opponents by a large margin, that is, we had to maximize our gains on the big hands if such opportunities arose. We bid a vulnerable game the opponents missed, a gain of 11 IMPs, and partner boldly proceeded to a slam making 12 tricks when the opposition stayed in game making just 11 tricks. As a result of these swinging actions, we emerged with 20 VPs and won the event by the slimmest of margins, as the leaders could manage only a highly respectable 15 VPs on their last round. I consider this unjust, as we were playing a different set of boards. Playing good, steady bridge and scoring honorably flat boards against a good team in the last match leaves one at the mercy of the deals being played by the third place team. Often at Swiss Teams there is a psychological advantage to be had for coming up from behind, and at Victory Points this advantage can be amplified by a swinging set of boards. This offers hope to the lowly trailers, which may account for the immense popularity of the event.

Expectations at IMPs and Matchpoints

August 31st, 2010  ~  Bob Mackinnon  ~  No Comments 

Most players prefer to play in team matches against their peers, bad players because it’s easier to win, good players because it’s harder. An important difference from the matchpoint game is that the opponents one has to beat are not the diverse crowd situated throughout the room, but are the 2 pairs one’s team is facing directly. You must play well to win against a team of 4 good players. A large field makes for a fair game at matchpoints as the distribution of the scores on any given hand tends to reflect normal conditions. In a small field unusual results have more of an effect and there is more need to swing for top scores against the poorer pairs in order to win.

On many hands at teams the gains for bidding a higher scoring contract and equally balanced by the losses one encounters if the contract fails. On such hands the gain-loss ratio reflects the conditions at matchpoints, the difference being that at teams there is more at stake when bidding games. We shall study this important category in detail, the results being applicable to either matchpoint or team play.

At teams one is facing opponents whose tendencies are well known if not entirely predictable. It makes sense to adapt to some degree to the known quality of the team one is facing. Overall, adopting the tendencies of the opponents is equivalent to playing for a tie. The swing hands are those where there is maximum uncertainty whether or not a contract will make and/or whether or not the opponents will bid it. Traditionally the number of tie boards was considered an indication of a well-played match, but recently one finds players attempting frequently to increase uncertainty, thereby creating swings one way or the other, much to the annoyance of idealists who would prefer matches to won through accurate bidding and double dummy card play.

In our previous blog we considered the effect of the field on matchpoint strategy. Here we pursue the theory for team play where the potential gains and losses are not the same for every hand. There are 4 possible situations: 1) you bid a higher scoring contract and it makes; 2) you bid a higher scoring contract and it fails; 3) you stay in a lower scoring contract and a higher scoring contract makes, and 4) you stay in the lower scoring contract and the higher scoring contract fails. The probability of making the higher score is PM; the probability of the opponent bidding it is PB.

As previously we consider hands with just 2 outcomes. If the opponent is in the same contract, we assume there is a tie, so the score on that board is 0. If the opponent is in the alternate contract, either you gain an amount G or you lose and amount L, where G and L are in general different numbers of IMPs. Under the 4 situations listed above the expected scores, S1 through S4, are as follows:

The advantage to bidding the higher scoring contract that provides gain G is:

S1 + S2 – (S3 + S4) = PM x (G + L) – L

This is the gain factor. The optimum strategy is to bid the higher scoring contract if this quantity is positive and not to bid it if the quantity is negative. Let the potential loss, L, be represented by kG, where k is the ratio of L to G. One bids on if:

PM > k/(k + 1)

Under normal circumstances k lies within the limits 0.5<2. If the gain and the loss are equal, k=1 and the optimal condition becomes PM > ½, as with matchpoint scoring. If the potential loss is twice the potential gain optimally one bids on only if PM> 2/3, as in the case of bidding a grand slam at rubber bridge. At teams, the k associated with a vulnerable game is 0.6, so the game should be bid if PM>3/8.

At IMP scoring the gain factor changes from board to board according to the number of IMPs available for making the correct decision. If one bids the higher contract and the opponents don’t, the expected gain is (1 – PB) times the gain factor. If one bids the lower contract and they bid the higher one, the expected gain is PB times the gain factor. Of course, the gain factor turns into a loss factor if one makes the wrong choice and the opponents the correct one.

Minimizing the Loss, Maximizing the Gain

One may aim to minimize the loss when making the wrong bidding decision on a board, in which case one should avoid bidding the higher scoring contract under the following condition:

| S2 | – | S3 | > 0, such that

(1 – PM) L > PB x [ L – (G – L) x PM ], which can be rewritten as

1 > (PB + PM) – r x PM x PB, where r equals (k-1)/k.

Note the symmetry with regard to PM and PB which act interchangeably. If L equals G, r is zero, in which case one should bid the higher contract if the probability of making it plus the probability of bidding it is greater than 1. This is normal for uncontested auctions.

The gain for bidding the higher scoring contract and making it versus the gain got by bidding the lower scoring contract is given by the following expression:

S1 – S4 = G x PM – L x PB + (L – G) x PM x PB.

To maximize the gain, bid on if PM > k x PB – (k – 1) x PB x PM.

If L equals G, bid on if PM > PB, that is, if the probability of making the higher contract is greater than the probability that the opponents will bid it, even if PM is less than ½, which is contrary to the optimal strategy. To minimize the loss, don’t bid on if the probability of the opponents’ bidding the higher contract is greater than the probability it will fail, that is if PB > 1 – PM. To maximize gain and to minimize loss are not incompatible aims at IMP scoring, and a ‘comfort zone’ achieving both ends is possible.

The Max-Min Diagrams

In a previous blog we introduced text maps as shown below. ‘Yes’ indicates one should bid higher to achieve the aim, ‘No’, that one should not, and the dashes signify a toss up.

Maximize the Gain

Minimizing the Loss

The boxes that contain a ‘Yes’ in both diagrams are representative of the comfort zone.

The ‘maybe’ boxes clearly lie along diagonals that separate the Yeses from the Nos.

The conditions for maximizing and minimizing can be represented graphically by lines in a more detailed PM/PB diagram as sketched below. When G equals L the maximize line runs diagonally from the upper left corner to the lower right corner. The shaded area to the left of this line represents conditions in which the gain is maximized by bidding higher. The minimize line is a diagonal from the upper right corner to the lower left, the area to the right representing conditions in which the loss is minimized by bidding the higher contract. The diagonals cross at PM=PB=½, the point of maximum uncertainty. When the gain is not equal to the loss the point of intersection is elsewhere, where there is less uncertainty, as will be discussed in a later blog.

A decision to bid the higher contract can be associated by a point in the diagram that reflects the de-facto probabilities. If the point lies within the comfort zone, one has acted both to maximize the gain and to minimize the loss. If the point lies within the ‘no-no’ zone, one has chosen poorly on both counts. If the point lies in one of the other 2 zones, one has acted either to maximize the gain (on the left) or to minimize the loss (on the right). Another viewpoint is that any mistakes that are made are due to a miscalculation of PM, due to a lack of information on how the cards lie, or a poor prediction of the probable action of the opponents, PB. In a double dummy analysis PM is entirely dependent of the lie of the cards, but in practice the defence may benefit from any information received during the auction.

The Full Picture

Below is shown a map of the decision zones over a range of probabilities when the potential gain G equals the potential loss L, the situation that occurs most frequently with constructive bidding both at matchpoints and IMPs. The numbers given are the expected scores times 1000 for the higher contract on the left and the lower on the right. The aggregate for each contract is given below the line. So we have this pattern displayed for each pair of PM and PB:

To obtain the expected scores in matchpoints, divide by 2000, add ½, multiply by the number of opponents playing in the same direction. To obtain the expected IMP scores for a nonvulnerable game, divide by 1000 and multiply by 6; for a nonvulnerable slam, divide by 1000 and multiply by 11.

The small area in blue italics is the comfort zone wherein the criteria to maximize the gain and minimize the loss both require that the higher contract be bid. If one is to bid the higher contract outside the area, then one is deciding on the basis of either maximizing or minimizing in isolation. Bidding the higher contract if PM>½ results in a positive aggregate score, sometimes at the expense of a greater potential loss, as in the case of PM=5/9 and PB=2/5, a good contract unlikely to be chosen by the opponents. One gambles a loss of 45 to achieve a gain of 155, a good gamble. This is the situation where a superior system of slam bidding is likely to gain IMPs. Bidding the lower contract at PM=5/9 and PB=3/5, achieves a minimization of the loss by an average amount of 55, but at the average cost of 155, a bad gamble.

The area in the upper right represents a popular contract that is likely to fail. We often see the comment, ‘where there are 8 tricks there will be 9’, so it is very common that one rejects stopping in 2NT and moves on to 3NT even if the contract may prove to be a poor one. In theory one shouldn’t follow the field by bidding a poor contract, but one does so in order to minimize the potential loss. The condition of PM=4/9 is good enough for bidding a vulnerable game, but not a nonvulnerable game. When PB=5/9, PB + PM =1, and the potential losses are balanced between bidding or not bidding 3NT, but there is something to gain by staying in 2NT. This is an opportunity to swing some IMPs. In a recent 7-board Swiss Team match nothing much happened at my table, but I knew we had lost as on 3 of the boards the opponents had scored 120’s, all large losses for our side.

The Maximum Uncertainty Border

Many players live in doubt. The horizontal area representing PM=½ is of particular interest as it represents a border area where everyone is of necessity in doubt. The comfort zone lies below, the no-no zone, above. Along the line the aggregate scores are 0 whether one bids on or not. If one is inclined towards maximizing gain, one does better by staying in the lower contract when the opponents are not. If one is inclined towards minimizing the potential loss, one follows the inclination of the opposition to bid on. The area of maximum uncertainty as to the better decision is centered squarely at PB=½, when it doesn’t matter on average what one decides. A lot of mediocre players live in this neighborhood. They look to general rules to provide guidance in a difficult situation. Of course, on any particular hand decisions do matter, as that determines who come out on top, but on average it’s a toss-up. This is a fine characteristic for a game of chance as the best player does not have an advantage in a situation of maximum uncertainty, so the best player doesn’t always win. Under those circumstances the best policy is to lose gracefully.

In close decisions it is often boils down to a matter of hand evaluation, and there the good players have the advantage. Good players attempt to obtain an accurate estimate of PM and will act accordingly. They look at suit quality and the loser count, whereas mediocre players merely count up their points. Good players recognize texture. Based on the bidding, they anticipate the opening lead, and imagine the play from that point onward. Mediocre players may fear the killing lead and hope to escape it by ‘giving nothing away’ during the bidding, or may avoid the problem by staying low. It becomes a matter of personality. Sometimes, not often, the meek players win.