The Great Two-over-One Debate

May 17th, 2013  ~  Bob Mackinnon  ~  12 Comments 

In the May ACBL Bulletin readers were given arguments for and against the concept of 2/1 forcing to game. Larry Cohen approved of 2/1, Fred Stewart didn’t, suggesting Standard American is better. Comparing the two is not like comparing apples and oranges, it is like comparing pizzas. Do you like pepperoni or salami? extra cheese or bacon? Nutritionally the two may be equally harmful. Cohen went so far as suggesting that all beginners be taught 2/1 methods, currently the current standard approach. Apart from the societal benefits of going with the crowd, is there any justification for doing so?

With regard to the education of the naive let’s consider high school home economics. Recently I saw on television the author of a cookbook making the claim that 70% of the North American diet consists of processed foods. Every sensible person agrees that this is an unhealthy trend as processed foods contain far too much salt, sugar, and fat, but what we know is wrong and what we do in practice are often in conflict. Now, in home economics classes, should the students be taught how to prepare a hot lunch consisting of a can of tomato soup, a ham and cheese sandwich made with sliced bread from the supermarket, finished off with a dessert of vanilla ice cream topped with chocolate sauce? I’ve enjoyed lunches like that, so wouldn’t it be mean-spirited to argue that teaching kids to partake of mainstream American fare is wrong? Not at all. Students should be taught to think clearly and to make informed decisions. Bad habits they can learn at home.

‘So,’ a critic may comment,’ you’re one of those dinosaurs from the dark ages who think women should stay at home every Sunday afternoon slaving over a hot stove while their husbands go off to play golf with the boys.’
‘Sounds great to me,’ I would concede, ‘but during my nearly 50 years of marriage I have never been given the option.’ But I digress.

To get down to basics, should beginners be shielded from conventions and led to believe that ‘natural is best’? Cohen goes rhapsodic on the topic, but we all know that the requirement to be natural is technically disadvantageous. Naturalness should not be an aim in itself. Consider the following combination in which to respond with a natural 2♣ bid is not only wrong, it is downright perverse.

A bright beginner is entitled to ask, ‘why must I bid 2♣ when I know I want to play in hearts? He or she may wonder, ‘isn’t it better to bid 2♦ where most of my points lie?’ Or, ‘why must I risk a Semi-Forcing 1NT when I want to be game?’ Is it the time for the instructor to backtrack and talk about ‘support points’? Rather it is a good opportunity for the teacher to introduce the idea that 2♣, like Stayman, is totally artificial and asks for more information from the opening bidder. It is not a radical new idea; for good reason the Drury convention, named after an esteemed member of the ACBL Board of Governors, has played its part in American bridge for over 50 years. Today his convention is needed even with an unpassed hand. Accepting the idea that 2♣ doesn’t say anything about clubs makes sense, rendering the slam much easier to bid. In fact, this combination was bid to 6♥ using a system within which 2♣ was defined as a totally artificial invitational bid without reference to either clubs or hearts. I think young players love conventions, especially the ones that are useful, crystal clear, and part of a pattern.

It’s been a while since I have seen a reference to a ‘biddable suit’. Most of the time long suits are biddable, but freely bidding a topless suit gives the wrong impression entirely. When responder freely introduces a suit, a minor suit especially, partner is entitled to expect values in that suit. The absence of honors could be advantageous in a competitive auction if the opposition is deceived, but in a constructive mode it may turn against the pair looking for slam. On the above sequence the responder will be reluctant to invite slam when he has a minimum for his 2-level response and knows his club suit has doubtful value, when, in fact, the lack of wasted values in clubs is a prime attribute.

1NT Forcing
The difference between 2/1 and Standard boils down simply to the use of 1NT Forcing. The wider the range, the less information the bid contains. In 2/1 the normal range is 6 to 12 HCP; within that range there is a wide assortment of hands allowed. If the bid is ‘semi-forcing’ as Cohen advocates, opener is allowed to pass with a flat minimum. In a contract of 1NT there is value in the uncertainty which works in favour of the declarer. This can be said of any contract: the more the uncertainty in the bidding the greater the chances of making it once arrived. Because a vulnerable game needs in theory only a 38% chance of making to justify bidding it in a team game, it behooves a partnership to blast away without delicacy to such games. Keep it simple, bid what you think you can make, and worry about it later.

Fred Stewart likes to think of bridge as exercise in logic, so he prizes accuracy and exploration. He states, ‘one problem with 2/1 is that responder can’t locate his side strength with a game invitational hand.’ Well, as Cohen suggests, delicacy in the game zone is not needed, so one should just go ahead and bid games hoping for a good fit or a bad defence. He mentions the success of Meckwell in this regard, but fails to mention they play Precision which allows for an opening bid on 10 HCP whereas 2/1 doesn’t.

After a 2-level response in Standard a partnership may decide to play in a suit contract at the 3-level. With 2/1, 3-level suit contracts have been removed from consideration, the purpose of 3-level suit bids being to exchange information in order to determine the chances in a slam contract. Paradoxically, bidding at the 3-level which reveals strengths and weaknesses may result in a reduction of one’s chances of making close games or slams. Consequently, players are reluctant to employ descriptive 3-level bids just on the off-chance that a slam may make. So, although the bidding space has been freed up for this use, players don’t like to use it. Thus, minor suit slams are very rarely pursued, 3NT being the contract of choice. In addition, bids between 4♣ and 5NT are seldom utilized in a natural sense. Cuebidding controls has become a neglected art. ‘Last Train’ is a control bid without a control! Precipitous ace asking bids have taken over the territory, and for good reason: if someone has to come clean eventually and cough up real information, it is better if only one partner does it, rather than both.

A Better Way
There is a significant difference between 2/1 and Standard on the one hand, and Precision on the other, in that many Precision opening bids are limited to at most 15 HCP. This is critical even when bidding slams. Here are 2 examples from recent games at my club involving Precision with a nebulous 1♦ opening bid where the length of the diamond suit may be a little as 2 cards. This is unnatural, nonetheless, the opening bid is the same 1♦ in all methods.  What follows is quite different.

The opening bidder had substantial values, a maximum Precision 1♦ opening bid under the definition. It was more or less incumbent upon me to show a maximum by a splinter in support of my partner’s spades. Two trump honors with 6 controls are worth an equivalent of 20 HCP. John upgraded his hand with its singleton in diamonds opposite the advertised singleton in clubs, but what natural, descriptive bid could he make? None. His solution was to cue bid 4♦ presumably to show a control, but really it was more of a mark-time bid awaiting developments. With an unlimited hand responder was in charge of the auction at this point, a situation made possible by the original upper limit on my HCPs, so he didn’t need to share the decision-making responsibilities, so didn’t need to make a descriptive bid to put me in the picture. His aim was to extract information, not give it. So, a unilateral RKCB easily led to a good slam on 24 HCP.

Let’s consider these results from the point-of-view of all those who didn’t reach the slam. Their failure cost them a mere half-a-matchpoint. This is hardly something one worries about, but more than that, why risk a very bad score when one can stay with the crowd in comparative safety? This approach represents mediocrity for its own sake. Fine, but let’s not pretend that 2/1 is a good system for getting to slams. In the same vein, here is a grand slam from the next week’s action missed by all.

The bidding is simple if the opening bidder is allowed to make a descriptive splinter bid on his 6-loser collection. The number of HCP is non-factor. When a fit comes to light the holder of a 6-loser hand should take some encouraging action. In the 2/1 system where 1♦ is unlimited, a splinter to 4♣ seems rather to overstate the condition. In so doing my Precision partner showed courage, yes, but also judgement as the ♦J and the ♠ T can be seen to be assets more valuable than their HCP assignments indicate. The good trump fit, the potential for ruffs, the long suit that might be developed, the control in hearts all point towards an exceptionally good mesh. It is critical that opener was marked as having less than 16 HCP – he wasn’t claiming slam potential for his own hand. After the announcement of shortage in clubs, responder went through the motions of RKCB to determine ‘how high?’  Finding partner without the ♣K was a revelation that made it especially easy to bid the grand slam.

Conclusion
Bridge is a game of probabilities, not certainties. Slams are rare and competitive auctions are becoming more and more frequent. If one is to consider the practical advantages of a system it is necessary to include not only what the bids tell you, but also what they hide. Double dummy accuracy and full disclosure are not the only virtues. A system should be adaptable, logical, and easy to use. Sticking to a requirement of naturalness complicates matters immensely; it is much easy to be able to ask a direct question and receive a direct answer, than it is to fish around in murky waters.

One last point: 2/1 is not a single system, it is 3 different systems that vary with the seat position. It doesn’t apply after interference. A great number of unrelated artificial bids are needed to patch over the flaws. This is a recipe for confusion.

Restricted Choice: What Lies Behind It

February 25th, 2013  ~  Bob Mackinnon  ~  3 Comments 

This blog is in response to Linda Lee’s post Do you “believe” in Restricted Choice?

Bayes’ Theorem always applies where play probabilities are involved. Restricted Choice as generally understood is an application of Bayes’ Theorem where there is an equal chance of selecting 1 of 2 equal honor cards when following suit. The probability of having chosen that one particular card over the other is ½. There are cases where a player chooses 1 of 3 equal cards, in which the probability of choosing that one card is 1/3. These can be small cards, but we don’t think of that process as a ‘restricted’ choice, although Bayes’ Theorem applies equally to that situation.

By saying there was an equal chance of choosing 1 of 2 cards is equivalent to saying the choice was made randomly without bias. This is a theoretical assumption. Maybe some players will prefer playing the queen instead of the jack because they feel it is more likely to influence declarer’s play adversely. The choice is not completely random. Declarer must judge on the basis of experience whether he believes the choice is random. If not he must assign his own best estimate of the chances of the queen versus the jack, say, 2:1. He still applies Bayes’ Theorem on the basis of that bias.

There is sometimes a case for assuming a player must split his honors in front of a tenace in order to give declarer a guess on the next round. Does one always assume the defender will make the correct play and split? That is an interesting situation. If one believes a defender will always play one card rather than the other, or at the very least have a preference, then there is information to be got from the play other than a simple reduction based on random selection.

Dropping the Jack from Queen-Jack
Suppose declarer holding AT65  opposite K987 plays the ace and the jack drops from the RHO. What are the probabilities the jack was a singleton rather than from QJ? Let’s look at a particular situation and put aside for now consideration of the a priori odds. Declarer reaches 4♥ and a spade is led. They prove to be split 4-4. Declarer plays the ♥ A, LHO plays the ♥ 2 and the RHO drops the ♥ J. What are the odds the ♥ J was a singleton?

There are 2 cases to consider: Quwx opposite J  (a 4-1 split) and uwx opposite QJ. Here u,w,x represent the missing low cards that can be freely played without loss.

Case 1

Case 2

The distribution of the minors is entirely unknown and assumed to be the result of a random deal. The number of combinations on a 6-7 split outnumber those on a 5-8 split in the ratio of 4 against 3, giving Case II an edge in that respect.

The play of the ♥ 2 was a choice of 1 of 3 equals so the probability of the ♥ 2 being chosen at random was 1 in 3. For Case I the play of the ♥ J was forced, probability of 1. The one remaining 3-2 combination is Case II with uwx opposite  QJ. Again, the play of the ♥ 2 was a 1 in 3 chance, the same as with the 4-1 split. The play of the ♥ J was a 1 in 2 chance, as the ♥ Q could have been chosen equally on a random basis. Overall the chance of the appearance of ♥ 2 – ♥ J is 1 out of 3 for the 4-1 split and 1 out of 6 for the 3-2 split. The ratio of the probabilities on the play is 2:1 in favour of the 4-1 split.

We now combine this with the number of combinations of the minor suits yet to be played. The result is 3:2 odds in favor of the 4-1 split. As Reese may have put it, the odds are better that the jack was played of necessity rather than it resulted from a particular choice among alternatives. So on the next round of hearts declarer should finesse for the ♥ Q with a great degree of confidence.  The rule of ‘eight ever’ applies.

The a priori Odds
These give slightly different numbers but the resulting decision is the same because the vacant places are evenly distributed between LHO and RHO. Here we don’t assume any cards have been played outside the heart suit, and that there is no clue as to how the other 3 suits are split.  Outside hearts there are 21 cards in the defenders’ hands.

Case 1

Case 2

Based on the (unrealistic) a priori conditions the odds in favor of the particular 4-1 split after the drop of the ♥ J is 5:3. The assumptions are unrealistic as we always know more than the ‘know-nothing’ odds assume. However, the method is the same and the conclusion is the same, the ♥ Q is more likely to be with LHO by a wide margin, 5:3 against the previous 4:3 where the spade suit was counted out.

The Specious Argument
Now let’s examine the argument based on a table of a priori probabilities that begins with,  ‘the 3-2 split is twice as likely as the 4-1 split.’ The table of odds states these probabilities: 4-1: 28.26%;   3-2:  67.83%. The figures include the number of possible combinations: 10 for 4-1 and 20 for 3-2. That is a 2:1 ratio in favor of 3-2. If we consider the probability of one particular 4-1 split and one particular 3-2 split we find the percentages to be 4-1: 2.826%, 3-2 3.3915%. The ratio is 6:5 in favor of 3-2, as reflected in the Others Weights given above. So comparing one 4-1 split against one 3-2 split is quite different from comparing all 4-1 splits against all 3-2 splits. The 2:1 odds that David G. quotes are largely, but not entirely due to double the number of combinations available for the 3-2 split. His argument is false when one is comparing just one combination against another.

One can say with greater accuracy, ‘3-2 splits are more likely than 4-1 splits largely, but not entirely, because there are twice as many of them.’ The play of the cards eliminates some combinations that were included in the a priori tables, and that basically is why the a priori odds aren’t an infallible guide, and certainly aren’t accurate mathematically after cards have been played.

Probability of Distribution Patterns
The same is true of the comparison of 4-3-3-3 shapes and 4-4-3-2 shapes. Table I in the Official Encyclopedia of Bridge (1984) shows both the total percentages and the specific percentages. We all know that 4-4-3-2 is more probable than 4-3-3-3 at the beginning (or rather before the beginning), however, one particular 4-3-3-3 is more likely than one particular 4-4-3-2. That is, 4=3=3=3 is more likely that 4=4=3=2. If one is down to a choice between the 2, the a priori odds favor the 4=3=3=3 (2.634% versus 1.796%).  So one can say with accuracy, ‘4-4-3-2 shapes are more likely a priori than 4-3-3-3 shapes solely because there are one-and-a-half times more of them.’

Similarly one sees from the table that 5=4=2=2 is more likely than 5=4=3=1, even though there are overall more 5-4-3-1 shapes than 5-4-2-2. This is the basis for the argument that as play progresses, if one has to choose one particular shape over another, always choose the flattest shape regardless of the a priori odds. (Bob’s Blind Rule). There are more 2=2 combinations than 3=1 combinations, and 3=3 combinations than 4=2 combinations.

Matchpoints and Democracy

February 20th, 2013  ~  Bob Mackinnon  ~  3 Comments 

The matchpoint game is the most democratic form of bridge. Like it or not one finds oneself thrust into a mix of humanity of various abilities and mistaken beliefs. It is reminiscent of the week I spent in a hospital bed with a broken leg (my leg not the bed’s). There was ample time to observe a part of the world with which I had previously not been in close contact. We in Canada are very lucky to have a universal health care system, at the core of which are a group of hard-working professionals who have recently immigrated from all over the world to help us through difficult times and share in our democratic way of life.  I remember especially the Philippina who cleaned toilets 8 hours a day so that her 3 little daughters would have the chance of a better life in a colder climate. Like the surgeon, she is a necessary part of the system, a fact established by Florence Nightingale during the Crimean War.

On my last night in the hospital the bed next to mine became occupied by a young roofer who had had a 3-hour operation to restore knee ligaments torn during a foolish prank. Of course, it was the other guy’s fault. Who am I to scoff – wasn’t my predicament the result of a moment of careless inattention at the top of a step ladder? The next day I couldn’t help overhearing the conversations with his visitors: a comical brother, his bossy mother, his wayward father, and 2 dazed girl friends with whom he was been sleeping, their visits well timed so as not to overlap, his brother keeping an eye on the parking lot below just to make sure there wasn’t a further accident. These people live in a world quite different from mine. During one visit I was amazed to learn a woman can get a birth control rod with a 5-year warranty stuck in her arm. Was it 5 or was it 3? I sure hope she got it right.

Bill Clinton, twice elected president of the United States, once said that the American electorate always makes the right decision. Well, he would, wouldn’t he? (What does Al Gore think?) The theory is that the great mass of ignorant voters will split the vote evenly between Democrat and Republican, leaving the discerning few to decide the election after due consideration, presumably after having paid close attention to the boring TV debates. With regard to the numbskulls at the next bed, if the 3 males voted Republican, and the 3 females voted Democrat, that would leave my vote the all-important deciding one. It’s not a theory in which I find comfort – what if they all voted Republican?

The reader can see where I am headed: matchpoint scoring is like a democratic election. Just as the Wall Street banker living his golden pavilion penthouse has the same one vote as his doorman, a frightening concept to some, a false hope for others,  so too a humble +50 may carry the same weight as a stupendous +2220, and there are more of the former than of the latter. On every board each individual by his actions ‘votes’ for the best score. Some make a bad choice, some make a good choice – usually those whose actions closest conform to reality. Your score is determined by where you sit in reference to those diverse outcomes. It is normal to lie above the majority of the players who are worse players than you are, and below the majority of those who are consistently luckier. In other words, most of us belong to the middle class. The process is subject to random fluctuations, but over several boards an averaging process takes effect, and one will normally arrive at the appropriate standing in the end. If one makes consistently sound decisions one can expect to do well. Sometimes the worst pair wins the session, but seldom does the best pair come in last. There is a distinct bias towards excellence.

In the previous blog I described how my partner played in 2 slam contracts and scored tops. In the end we achieved a mere 45% result overall. Terence Reese once warned against being overly concerned with pairs who outscore the field on isolated boards – these are not the most dangerous rivals, he noted. The best pairs work hard for their average plus scores and let the tops take care of themselves. The so-called swinging pairs give away as much as they steal. That being said, it can be annoying if a pair does the right thing against you when most of the field gets it wrong. Here is an example.

As he put down the dummy, Roy commented, ‘I know we have a 4-4 fit, but with 29 points you will usually score the same number of tricks in no trumps’. How true, as on a normal diamond lead Ewa had no trouble scoring 11 tricks to share a top with one other pair. All others were in 4♠ scoring the same 11 tricks. To add insult to injury, the spades split badly. Well, one might think that it was unlucky for us to play this particular hand on this particular round, but that would be wrongheaded. We should accept there is a great deal of randomness in the game, and not only in the lie of the cards. It is a game of probabilities in which good and bad things happen at random beyond our control.

As Nietzsche noted, winners don’t believe in luck. Some losers bemoan the effect of chance. We hear statements like, ‘if I could exchange the ♦7 in dummy with the ♦2 in my hand, I would have made it,’ or, ‘you were lucky dummy came down with such good trumps.’ Such statements border of self-pity. Why should we expect justice on every hand? The fact is that randomness is an essential feature of environment in which we operate. The player who acts against the field may gain on any particular hand, much to our annoyance, but by acting in this manner he gives us a chance at an undeserved bonus.

Defensive Signal
The killing opening lead has been made the subject of 2 books by David Bird and Taf Anthias which provide a survey of results from computer generated hands. Which lead is best when playing the hands double dummy? Of course, there are cases where the standard opening lead will not prove best. The idea is that by studying these exceptions a player may gather a feel for when on opening lead to depart from the norm. As one of our club members remarked, ‘how can you tell when partner has made an unusual lead?’ This gets to the heart of the matter of informing partner.

The common approach is to plug away unimaginatively on defence doing nothing unusual. Most likely there will be others doing the same. By falling in with the majority of players with your cards, you ensure a score somewhere in the middle.  Ayn Rand worshippers might consider this a major flaw in the matchpoint approach because it bears the taint of socialism. One doesn’t deserve a reward just because one has plodded along within the guidelines of mediocrity. Those who deserve reward are those who separate themselves from the masses. That’s the elitist creed as practiced by the Masterminds.

The Mastermind prefers an active approach where pressure is placed on the apparent weak spots, which Bird and Anthias attempt to reveal. Most players realize that if their partners must carry the bulk of the defensive load, it behooves them to try to cater to partner’s best assets on the opening lead. It may be the last time they will be on lead, so they try to make the best of it. Players generally realize that if they have most of the missing HCPs, they should be alert to the possibility of an unusual lead. On the following deal just in case partner had nodded off I left nothing to chance.

After 2 passes North opened 1♣, so it was probable that she and I held the majority of the points between us. I estimated that our partners most probably held 6 HCPs each. As you see this guess was accurate. I bid 1♦ as lead directing. Holding the vast majority of points I could direct the defence from an advantageous position. Of course, if partner had a major to show he could still bid it. The ♦9 was dutifully led, taken by the ♦K. Do you see any hope of beating 1NT?

At the table I switched to the ♥J. Declarer ducked, a mistake, so continuing with the ♦A and a low diamond was all that was needed to sever his communications and achieve the excellent 75% score for +100. What do you think went wrong?

Like Hamlet with dagger poised above the back of Claudius knelling in prayer I began to have second thoughts. Partner had signaled encouragement, so could it be he had excellent hearts? I wavered, then continued foolishly with ♥A and the ♥2. This had the opposite effect to the one intended, as South, thus helped, scored up 8 tricks, a top for him, a bottom for us.

Signals generated by selective carding are the way defenders exchange information. In the absence of a clear signal a defender plans according to what is most probable given the information contained in the bids, what he sees in his hand, and what has emerged in the dummy. It is my contention that partner should not have signaled encouragement with ♥Q75, no matter what he thought I held (he envisioned AJTx). One should indicate what one has, not what one hopes partner has. When the ♥J held the trick, it was obvious West held a high honor in hearts, but there was no need to rush to cash it. So, unless the message is urgent, a signal shouldn’t tell partner something he knows already.

A redundant signal contains very little information. It is like coming home dripping wet and telling one’s wife, ‘I forgot my umbrella.’ Maybe she’ll say, ‘oh, is it raining?’ but an understanding wife will say, ‘Stay there and I’ll bring down some dry clothes before you catch your death of cold.’ A good partner is like that. They can skip the hot soup bit.

One further thought on this hand: it shows I am not a true Mastermind. The 1♣ bid is the most suspect of opening bids.  Rather than thinking defensively from the start, I should have bid 1NT without a club stopper and let the opponents worry about the defence. Scoring 120 our way would have tied for top. Truly, it’s a bidder’s game, besides which it is easier, and sometimes merciful, if one player takes on the heavy burden of worry for both. One head is better than two, as the errors are reduced at least by half.

Too Scientific?

February 19th, 2013  ~  Bob Mackinnon  ~  1 Comment 

Bidding to a contract is a process. At each step more information is made available. At each turn one may ask, ‘do I have enough information to place the contract with confidence?’ If the answer is ‘yes’, then one goes ahead and bids what one thinks is best. Of course, that is a judgment call based on present conditions. Extending the bidding process will get you more information, but will that information increase the chance of your arriving at a better contract, and, having done so, will the additional information exchange decrease your chances of achieving a high score?

The ACBL Player of the Year for 2012 is Zia Mahmood, the fifth time he has earned the award. In an interview published in the ACBL Bulletin he criticizes himself for being ‘too scientific’ on this hand from the Blue Ribbon Pairs: ♠ AKQ982 ♥ K8 ♦ — ♣ AKQJ2. As a scientist I resent it when players use the term ‘too scientific’ when they mean ‘too chicken’. His LHO opened the bidding 1♦ and his RHO bid 1♥. In retrospect Zia thinks that with his cards he should have done what Frederic Wrang did, overcall 1♠ , then bid 6♣. Zia, no hand hog he, is willing to let his partner make the final decision if the situation warrants it. Partner holds ♠ T73 ♥ T74 ♦ J964 ♣ T98, and will correct to 6♠ . There is an entry to dummy in clubs for a heart play towards the King.

Wrang practiced good science when he provided the relevant information and his partner made the choice. The opposition’s bidding increases the probability of finding a useful black card in the dummy, so it is against the odds that partner has a totally worthless hand; even if he has, a heart might be led solving that problem. All in all, given the information he had at the start, Wrang would have been unlucky to go down in 6♠ .

Taking Everything into Account
Very often we read analysis based on a discussion of what can go wrong. A better question is:  what is the probability that something will go right? Here is a hand that came up on the last board of my last matchpoint session.

Looking at both hands, one sees that 6♥ is hopeless on a diamond lead, but how probable is it that a diamond will be led? I maintain a diamond is unlikely to be led unless the opening leader holds both the ace and the king. Otherwise, in the miasma of uncertainty a passive lead is probable. Let’s say the odds of a diamond lead are less than 1 in 3.

If I could have seen partner’s cards I might have bid 6NT to decrease the odds of a diamond lead to the theoretic limit of 1 in 4, but that would constitute negative thinking, more appropriate to IMP scoring where the overtrick is not important. Making 510 in 4♥ was worth a undeservedly high matchpoint score of 5 out of 12 as some were playing in 3NT taking just 12 tricks. Making 1010 in 6♥ was worth 10 out of 12.

A further observation on the bidding: 4NT was a bad bid in theory, the 5♦ response giving my RHO the opportunity to double for a diamond lead. We would be held to 11 tricks, a  bottom on the board. The potential disadvantage bypassing 4NT and blasting to 6♥ is that it increases the chances of the lead of the unsupported ♦A. The opening leader may feel the need to take his trick before it goes away. So, although there is a risk attached, 4NT as a false indicator of balanced power may act as an inhibitor.

If the reader feels that one shouldn’t risk a score of 5 in order to achieve a score of 10 when, in theory, there is an obvious risk of scoring zero on a diamond lead, he should consider a posteriori odds based on what actually happened. The chance of getting a diamond lead was 1 in 13. Yes, of the 12 other pairs in the field, only one was held to 11 tricks -  all others made 13 tricks. If one were in 4♥ and got an inspired diamond lead, one’s score for 450 would have been 1/2 . So, in effect, bidding slam risks half a matchpoint to make 10, because a diamond lead would be disastrous in either case.

The Mastermind
As soon as he gets a good feeling about the hand, the average player is ready to launch into some form of Blackwood – ‘decide not describe’ being the prevailing attitude. Why? The reasons are partly psychological, and partly practical. Players learn that bad bidding pays off due to the uncertainty it creates in the opponents’ minds, especially for those who tend to be passive in their approach through fear of giving something away. The Mastermind is the type who takes things into his own hands early in the auction and places the contract after a minimal exchange of information. He takes his partner out of the loop, because he feels his educated guess will prove better than a partner’s reasoned conclusion.

Where do we draw the line? How much information is enough information? If one considers the Zia hand described above, a successful approach may have been to overcall 6♠ immediately. One might even get doubled. That would rule out getting to 6♣ when that is right, so we can’t say we condone that approach, successful as it may turn out. On a lesser hand where slam is unlikely, players who concentrate on spades and neglect the minors are following the expert’s path, they think, because a spade game both scores more and needs less to make. Slam is different, as merely getting to a makeable slam usually scores well. An inferior game may be reached when it turns out slam in a minor was there for the bidding, but the cost of missing it is minimal at the club level. The players assume that the normal conditions apply and lazily follow the well-beaten path in the game zone leading to 3NT or 4 of a major without looking for the special circumstances that may turn out to be slam-favorable.

Mastermind or Scientist?
Because of the scoring rules bidding systems are eschew from the start tilting the auctions in preferred directions. Information provided is biased towards reaching a preferred goal. Players may add their own bias, as I did on the following deal.

After partner opened 1♦ I felt the primary feature of my hand was the fine club suit. The hearts didn’t appeal, and the hand was worth just the one bid, which served to limit the HCP and described the shape if not the components thereof. Partner did the right thing given what I had told him, but much to my chagrin 3NT was doubled by my RHO. My philosophy is, ‘if you have made the bed, you get to lie in it,’ so I passed and faced the lead of the ♦T, which held the trick. There followed a long pause during which my hopes rose immeasurably. Could it be? Yes! The opening leader switched to a spade, ducked to the ♠ J. When the smoke had cleared, I made 9 tricks, scoring +750, for a miracle top.

 That’s not the whole story or even the most interesting part. Most played in 4♥ from my direction. With the ♣K offside that contract can be defeated easily enough on a diamond lead, however, 3 declarers did escape that defence. What about that opening bid? The control-rich hand is worth more than 19 HCP, more like 23 HCP, so the proper opening bid is 2NT.  This solves a potential play problem by placing declarer on the proper side after 3♣ Stayman from partner. I suppose some who went down in 4♥ felt they didn’t deserve their bad score because they had done nothing wrong, but I think they were unjustly rewarded for joining the herd who rigidly followed the rules by opening 1♦. On the other hand, those who opened 2NT and made 4♥ declared from the right side deserve a reward for their initiative.

A Mastermind thinks his judgment is better than a set of system rules that poorly fit his current situation. It’s not like choosing on which side of the road one prefers to drive today. The late Marshall Miles was famous for suggesting bids that others would miss, and he always had a good argument for doing so. In many aspects of partnership agreement it may pay to be flexible. This reduces the information content involved but that may not be important if the final decision is to left to the player best suited to making it, himself. That approach doesn’t work so well if both players are striving to be masterminds; someone has to be reliable and tolerant.

I saw recently a documentary on the Lindbergh kidnapping in which an ‘expert’ speculated that Charles Lindbergh himself masterminded the crime. Unbelievable! But it turns out that he was a perfectionist, a pro-Nazi racist, and a non-believer in the democratic process, who after the age of 54 fathered 7 children in Germany with 3 mistresses. The secret families weren’t revealed until 2003. One is reminded of another genuine hero, Thomas Jefferson, who also had an emotionally starved relationship with his numerous illegitimate offspring. I mention this as a reminder that although we may pride ourselves on our reasoned, technically sound, and largely successful approach to the external world, our actions are sometimes ruled by undercurrents of emotion that defy logic. Bridge is a pursuit during which we can demonstrate our rationality, but that is only a part of the game. Most of the time we are sane, but there is always a finite probability that even the best players will occasionally fall off their perch for no apparent reason. Luckily, it’s only a game.

Partnership Matters
It is in the nature of things that many of the best partnerships consist of a combination of 2 types, the Mastermind and his Servant. As Terence Reese once commented, don’t underestimate the value of reliability. The flamboyant adventurer need a reliable partner on whom he can count to provide that little bit of undisclosed extra that makes his gambles pay off, a partner who won’t push too hard for fear of getting too high. On the other hand the cautious underbidder needs an active partner to push things along. This is true especially of pairs who play a ‘natural’ system where both players are allowed to made judgmental decisions as the auction progresses.

What happens when 2 highly aggressive players who are fond of making unusual pressure bids, i.e. masterminds, get together? Will it be chaos or can they learn to get out of each other’s way and function as a smoothly operating unit? The latest experiment to watch will be the new pairing of Brad Moss and Joe Grue. Brad Moss became ACBL Player of the Year when playing with the careful Fred Gitelman, and Joe Grue became a feared opponent when playing Precision with Curtis Cheek, a system that imposes a certain degree of discipline. Their maiden voyage in the 2012 Buffet Cup was not a great success when they were outplayed by Nicola Smith and Sally Brock on this deal from the BAM 7-board segment won by Europe 3-1.

Here we have the evidence of a moment of madness. Like Hitler’s invasion of Russia, Grue’s 6♦ bid was far too ambitious. Moss failed to come up with ♣A, along with all the other good stuff. I suppose Brad got to feel something of what Field Marshal Paulus felt at Stalingrad about the paucity of the resources being provided. Sally and Nicola did much better, sedately stopping in 4♠ , making 10 tricks. I imagine they were surprised to win a board that appears routine. Can we attribute the loss to Trendafilo’s innocent 2♣ overcall on ♣ AK8753 which had the effect of a red flag waved in the face of a bull? Just joking. We shall follow the Moss-Grue development with interest to see how they handle the problem of sharing the captaincy.

Mixing It Up

February 11th, 2013  ~  Bob Mackinnon  ~  5 Comments 

Getting into the bidding with a weak hand can cause confusion, and if you can get partner involved, so much the better, confusion-wise. Some believe that distribution is everything, so they will enter the auction on topless suits. ‘I have never seen a 6-card suit I didn’t like’ is their motto. Bidding in this manner reduces the information content of their bids, but that is a small price to pay in their way of thinking. If the opponents are misled, so much the better, as there are 2 of them and only one partner.

The aim of undisciplined preemptive bidding is to have the opposition play in the wrong contract, or to misplay the hand if they reach the right contract. There is an art to this. You mustn’t bid too high, and you mustn’t bid too low. Your aim is to give the opponents a losing option. If you don’t accomplish that, then not only is your effort wasted, it may also aid the opponents in their quest for a good score against you.

One of my rules is: don’t preempt if you have more points outside your long suit than you have within it. So it was with grim satisfaction that I witnessed an undisciplined preempt from my partner that got us the shared bottom it deserved. His second seat bid of a weak 2♦ was based on ♠ AK ♥ 85 ♦ Q96532 ♣ 842. His RHO balanced with 4-4 in the majors and the opponents reached 2♥, their best contract. I raised to 3♦ on ♠ T752 ♥ 643 ♦ A7 ♣ AKT6, a good sacrifice at -50, but a shared bottom, as the deal had been passed out at most tables. Missing the AK in both black suit, the opponents were not about to be pushed to the 3-level.

In a recent issue of Bridge Magazine, World Champion Sally Horton commented that her late husband, the British expert Raymond Brock, felt that the most effective preempts were made in 3 of a major or 4 of a minor, and that her experience has borne this out. Such proved to be the case when later in the session, both vulnerable, my partner preempted to 4♣ over 1♠ on this collection : ♠ Q94 ♥ 5 ♦ J ♣ K9876542. This caused enough confusion to get away with, a rare occasion where -200 represented a good matchpoint score. If the opposition had bid to 4♥ they were in trouble on the 5-1 split, and the LHO was reluctant to raise spades on ♠862, so the ♠Q played its part.

Consider what to bid on this hand, ♠ 3 ♥ 4 ♦ T86542 ♣ JT874, after partner opens 1♣ and your RHO doubles. It seems to me there are 2 options, ‘pass’ because you have nothing, or 2♦, for the same reason. Our opponent chose a middle path, not the best choice as so often the case. Look at the deal from our point of view.

 Before the opening bid on my right I was pondering the best way to approach this 3-loser hand. I had decided to open 2♣ to find out first how many controls partner held. 6♥ was my primary target. I was somewhat surprised to see my RHO open 1♣. Much as I hate takeout doubles dominated by a long suit, this hand did provide an alternative to hearts in the form of a good 4-card spade suit. Over 3♣ Jack bid 3♠, guaranteeing a 5-card suit. After RKCB revealed the ♦A, it was easy enough for me to bid the Grand Slam with confidence. I expected an average result, as it was possible we could make 7NT if partner held the ♥Q. It came as a surprise that only one other pair managed to get as high as 7♠. Definitely North had his 1♣ bid (14 HCP and 3=4=3=3 shape), so what happened?

My feeling is that the 3♣ preempt helped us immensely, as it gave Jack the opportunity to show his 5-card length. If my LHO had passed, a jump to 2♠ would not have guaranteed a 5-card suit. The temptation to bid an informative 3♥ was there, placing the auction in a cooperative mode when really we do best if the doubler can take charge and extract information from his partner. I conclude that the best action by South was to pass. As is often the case, bidding on nothing does very little to hinder determined opponents, and may help them. Doubt must be genuine to be effective.

An interesting point in the play of the hand arises. The ♦K is led to the ♦A in dummy. What is the best way to go about making 13 tricks? Should you start with hearts or with spades? It seems safe enough to start with the ♥A and a low heart to ruff. On the second heart the preemptor ruffs with the ♠T. You must overuff, so what now? Do you play for spades having been dealt 2-2, so play for the drop in spades? Well, the preempt has been informative. It is most likely that the cards are divided 3=4=3=3 in opener’s hand and, therefore, 1=1=6=5 in the preemptor’s. It follows that declarer must immediately finesse the ♠9 through the opening bidder in order to bring in his contract. A second finesse will be needed. Note that if the spades were split 2-2 it is most likely that the honors are split (in accordance with the law of restricted choice), so the same finesse is indicated, although it is not as urgent.

In the old days it was claimed that bad bidding demands good play, and such was the case on the next hand, although bad defence was required as well. I suspect this was always so.

At matchpoints 3NT is the obvious spot, but Jack has been playing a lot of team games recently in preparation for the Regional Knockouts coming up. When he went bypassed 3NT with a bid of 4♣ there was nothing to do other than blast to slam. With only bad bidding to go by, the opening leader chose to lead her fourth highest from a suit headed by a queen.  Hurdle #1 was cleared with flying coattails when the ♠J won in dummy. A plan was formed. Jack played off 4 rounds of clubs. He eliminated the majors and led from ♦ 765 towards the ♦AQ4. North played the ♦8, dummy, the ♦4 and South, the ♦T, thereby forcing herself to lead back into the ♦AQ tenace. South had misdefended earlier when she discarded the ♦3 from ♦KJT3, guaranteeing the endplay.

The perils of the cooperative approach to slam bidding when one player should be the captain were demonstrated a week previous when, using Precision techniques, I was able to score a clear top by reaching a slam missed at every other table. Perhaps 2/1 players might like to try their hand at this combination.

The auction features a myriad of asterisks, but is not difficult to grasp. Basically the stronger hand asks questions about controls and the weaker answers as best he can. 2♦ is a limited NT bid, 8-10 HCP. 2♠ shows a spade suit and asks for support. 3♥ shows 3-card support the transfer allowing opener to ask how good the spades are. 4♣ shows a control honor. 4♦ asks for a diamond control; 4♠ shows the ♦K. 5♣ asks, how good are your clubs? 5♠ reveals the ♣A.  It was at the very end that I made the mistake of bidding 6♠ – the Matchpoint Devil made me do it. The safest contract is 6♦, and there was no need to risk a slam contract that no one else will reach. A bid of 6♦ would have given responder the option of bidding 6♠, but here he would pass as I had bid his best suit.

The main weakness of the asking bids employed is that distribution is left somewhat a mystery until the very end when responder has a chance to get his 2 cents in. With a distribution of 3=3=4=3 two losers could be disposed of on the 4th and 5th spades.

Let’s now speculate on how the hand might be bid using 2/1 methods. Presumably, even today, no one outside China will open 1NT. So we start 1♠ – 2♠. OK, I give up. I can’t see how to reach 6♦.

Highland Village Verses

Fair Mary MacNaughton
Will do what she oughtn’t.
Her head there sits on it
A tam not a bonnet.

She is my blossom,
I am her bee.
She is my apple;
I am her tree.

Ten toes point towards Heaven;
Ten toes point towards Hell.
Which way we are headin’
Nae-body can tell.

Stillman Andy MacVey
Lets a quart go astray,
As the Good Lord intended
When Scotch He invented.

Hooray for Matchpoints

December 18th, 2012  ~  Bob Mackinnon  ~  15 Comments 

In the Dec issue of the ACBL Bulletin a letter writer, Bob Chambers, took exception to the statement by Joel Wooldridge that ‘matchpoint scoring is not real bridge.’ Bob pointed out the many technical challenges that a matchpoint game presents, in particular the need to play to the hilt in order to maximize the score on each and every hand. Conceptually this is true enough, but matchpoint players do very well by bidding towards the middle of the field and taking their tops where they come, either through clever play or gifts from the opponents. It’s the scoring that Wooldridge refers to, and I think he is wrong on that point as well. At matchpoints it is up to the individual whether or not he wishes to follow the field and bid like a dozo.

At IMPs one can get lazy and toss away overtricks without much concern. Recently I misdefended against 3NT, making 520, which was a tie board. My partner and I bid to 6♣, making 940, losing 1 IMP to the pair in 6♥. The punishment for declaring in clubs and missing this cold Grand Slam was a pittance. It would have scored a deserved zero at matchpoints. There are rewards for bad bidding. Over 28 boards my partner and I bid 3NT on 5 occasions, going down 3 times, but gaining 9 IMPs overall, because one of the games lucked through. At matchpoints these terrible bids would receive scant reward.

Recently my Precision partner and I achieved a score of 70%, which clearly represents a miracle by Enrico Fermi’s statistical standard. As we were the only Precision players in the field, one can claim that we were bidding against the field on many hands, even though we never opened with our strong 1♣ bid. We played in 3NT 3 times, achieving a score of 34 out of 36 without the benefit of an overtrick. I put this down largely to superior bidding methods, not to wild gambling such as we encounter in Teams. Of course the advantages of 3NT are ever present. We defended 3NT 6 times and achieved a 55% average on those boards, thanks largely to one occasion when the contract was set 7 tricks for the rare score of 700 when declarer tried frantically to make 9 tricks.

The strategy in a matchpoint game is like the strategy of a major league baseball team trying to make the playoffs – tie on the road (when defending), win big at home (when declaring). One won’t score many tops against the good pairs, so we have to make up ground against the others. Against the 4 best pairs in the field, we scored a miserable 44% over 8 boards, but against the lesser lights we did exceedingly well. One may talk disparagingly about ‘gifts’, but errors are a part of the game. One must be in a position to score well against the errors that inevitably occur, which means one must push to the limit on every hand possible, especially against the weaker pairs against whom an average result is tantamount to falling behind the field.

Many players think they are playing at IMPs where a penalty double of a partial is all but unheard of.  We scored 45 out of 48 matchpoints by doubling part scores: 1♥, 3♣, 3♥ and 4♣. At Teams we wouldn’t double any of these, and the results would have been insignificant on the Victory Point scale. Of course there were risks, but when we push to the limit and beyond we have put ourselves in the position of maximizing the gain when we are right. This is one of the weaknesses of IMP scoring – there is little punishment for overbidding outrageously. The most interesting matchpoint double came on the following combination and it didn’t depend on an overbid for its success.

My reasoning may have been faulty but it worked. My book bid is 2NT, going down 1. Even an underbid 1NT doesn’t look profitable as it won’t score well on the marked heart lead. As partner might have balanced with 1♠or 1NT, we can assume declarer’s points lie largely in the heart suit, leaving partner with stuff in the minors. Playing to put declarer down 1 is especially risky, but as the opponents are vulnerable +200 would be a great score for us. So it transpired: declarer had 6 tricks off the top and we had 7. It would have been a bottom for us if declarer’s shape had been a more suitable 3=5=3=2 instead of 3=5=2=3. However, one zero is tolerable, and we would still have scored 70% out of our 4 doubles of part scores. Partner was understandably perturbed by my pass, but we can only hope this doesn’t deter him from balancing doubles in the future.

It is worth noting that the division of sides was 8-7-6-5 with a Total Trump count of 16, a exact predictor of the Total Tricks available. If partner had had 1 more club and 1 less  diamond the division of sided would be 7=7=7=5, a Total Trump count of 15, but declarer would make 7 tricks unless we were smart enough to cash 2 top clubs before attempting a trump promotion on the 4th spade – not an easy defence – impossible after my trump lead. I think this illustrates the excitement one may create in a matchpoint game. The requirement is there for accurate play and defence that would not be a factor at Teams, where I would be obliged to grope for a game just in case one of them was making. (In fact, a Moyesian 4♠could come home, but no pair achieved that result.)

The Adventure of the Four Nines
There is no great merit in playing to avoid disaster. It is akin to converting your paper money to gold coins and burying them in the backyard, as Samuel Pepys did during The Great Fire of 1666. Very often at Teams one declares a hand in a plodding fashion which appears to represent the safest route to making a contract. Here is an example of a hand that was turned into an exciting adventure, not always the best approach.

After partner’s 1♦ overcall, which promises good value, I explored alternative contracts with a cue bid of 2♣, not guaranteeing a fit with diamonds. The jump to 3♦ was unwelcome, and I was endplayed into bidding the ubiquitous 3NT. When the dummy appeared I noted the absence of the ♦9, the curse of Scotland. Not being superstitious and keeping in mind that at matchpoints one should play for as many tricks as may be made on a good day,  I planned to set up the diamonds. I had the entries.

At Teams I should ignore the scant possibility of setting up diamond tricks and play to make 3 tricks in spades – win the ♣A and overtake the ♠9 and plug away expecting to have an entry both in clubs and hearts. Boring!  At Matchpoints I put in the ♣9 hoping that would provide an additional entry to dummy from which to play a low diamond towards the hidden hand. No such luck as the ♣9 was covered by the ♣T and my ♣Q. Maybe the ♣7 would provide some protection.

The next step was the lead a diamond towards dummy hoping to drop the ♦9 in 2 rounds. The quick appearance of the ♦K gave me pause. I ducked and a club put me back in dummy. I played the ♦A pitching a spade, but the ♥9, not the ♦9, made its unexpected appearance on my left. Interesting card. The bad news was that the RHO had diamonds to cash, but hopefully with no entry. So now we had to revert to overtaking the ♠9 and hoping for some help from the LHO who seemed to have all the opposition’s points outside diamonds. Here is the full deal.

Here was the position when South took the first spade.

South, who scored 50% on the session, went for the quick kill by cashing the ♣K hoping to drop the ♣J from either hidden hand. The uninformative cuebid added to the confusion as I might have been dealt a 5=4=1=3 hand. When that failed she found she had endplayed herself. If she had exited a heart I would have played 3 rounds ending in my hand before playing another spade. The play of the hand had turned into an adventure akin to Around the World in Eighty Days full of misadventures and suspense but with a happy ending albeit one lacking the bracing presence of Shirley Maclaine.

There are 2 points to make.  If I had played safely from the start I would have achieved the same top score that required a defensive error and a double thrown-in. With half the field in 3NT it had appeared initially that overtricks were important. Not so. This was a difficult hand to play, so being competently careful would have been enough. Secondly, resting in 3♦ making 130 would have scored 80%, so there was no need for heroics. One needn’t imitate the field in its errant ways. It’s like the stock market: by getting it right one profits when the market is going down as well as when it is going up. Proper hand evaluation is the key, and bidding solely according to HCP is not it, but when all’s said and done the contract was fun to play, which is what counts most.

When compared to Matchpoints Team equals Tame. One must be careful if for no other reason than consideration for one’s teammates. Bidding with abandon without fear of punishment, never doubling contracts on the off-chance they might make, playing as safely as possible in anticipation of bad breaks, avoiding good slams, all these practices make for a boring game. A long match against experts can be a good test in which psychology plays a part, but a matchpoint game against variable opponents requires a finer judgement that varies with the circumstances. Hooray for Matchpoints.

What Happens When We Increase the Retirement Age
Announcement: Passengers are reminded for their own comfort and safety to speak loudly and clearly when addressing the cabin crew.
Passenger: Steward, please bring me a bottle of plain, distilled water.
Steward: Another? You must be part camel! Say, aren’t you Doris Day?
Passenger: Ma’am, I’d like a tuna salad sandwich on half-rye, no pickle.
Stewardess: Fine, but go and wash your hands first, young man.
Stewart: Nancy, how about you and me getting together after we land?
Stewardess: Thanks, Larry, but I got to baby-sit my granddaughter’s kids.
Pilot to Co-Pilot: Remind me again, what’s our destination?
Co-Pilot: Hold on, I wrote it down someplace.

Highly Defective Bids and Plays

December 10th, 2012  ~  Bob Mackinnon  ~  No Comments 

Frank Stewart is a respected bridge columnist whose work appears regularly in the ACBL Bulletin. In the Dec 2012 issue Frank turns angrily upon a fellow contributor who had the audacity to describe as highly effective a weak 2♥ on the following collection: ♠ 8642 ♥ KJT865 ♦ QJ4 ♣ —. He writes, ‘it distresses me that some players would embrace….flights of fancy that disrespect the partnership nature of the game’, and ‘I question the tendency to bid when no bid is descriptive.’ At least he recognizes that there is method in this madness where an advantage is being sought through chaotic actions that leave everyone in the dark, including one’s partner. He simply doesn’t like it. It’s against the law of political correctitude to question any strongly held belief however misguided, and I hope he sets us an example by getting away with it.

We sympathize with Stewart’s oft expressed view that bridge is a game of logic and discipline which acknowledges that one has a partner who is entitled to use his judgment based on the accurate information provided him. That is an approach that is becoming rare in today’s bridge environment. Increasingly players adopt an individualistic approach. My impression is that whenever I make a highly unusual bid very often I generate a good matchpoint score, and the worse the action the better the result, on average. Of course the tendency is to forget the bad boards. Be that as it may, there are circumstances in which partner for good reason needn’t be told everything.

The chaotic approach is scientific – behind it stands the science of statistics which deals with accumulated random events. One may play with the field patiently waiting out the process by playing for averages and accepting the tops when they are presented. If yours is an average pair in a field of 13 pairs you may have to wait a long time for your turn to win, which requires more patience (and time) than many possess. Alternatively one can strike out against cruel fate and throw the dice playing for tops and bottoms thereby increasing the variability of your end results. You’ll win more often and look bad more often, being on average just your average selves. It’s easier than thinking long and hard. As for long-suffering partners, they have to learn to bear with an errant co-conspirator who is merely doing his best (or worst) to secure a top.

To reasonable folk the strategy of misinformation detracts from the game which doesn’t need more randomness than it legitimately possesses. To such players I present the following case of payment come due. How do you play the following hand on the lead of the ♦T with the bidding as shown?

Playing 2/1 I shudder when I pick up a beautiful 18 HCP hand rich in controls. The bidding promises to be a nightmare. West bids 2NT without a club stopper and East has no accurate way to describe the nature of his powerful support. EW have reached a sub-optimum contract when 12 tricks are available in either major, but, not to worry, at matchpoints overtricks count for a lot in a mixed field. Suppose declarer ruffs the opening lead and finesses the ♥J losing to the ♥K. The ♦9 is ruffed in dummy, South dropping the ♦K. The ♠J is finessed, losing to the ♠Q. The ♦8 is returned, ruffed by South. A heart is ruffed by North.  Somehow declarer has managed to go down 1, but as the saying goes, he has company, 6♠ being bid by some zealots. The passive defenders as usual take only what they are given, but here that was plenty. At our table a crazy preempt got in the way and I found myself as East playing in 4♥.

It looks as if the preempt has done its work, and confusion reigns. Why didn’t Pard bid 3♠?  Anyway, the ♦K is led. Doesn’t that ring alarm bells? North’s penchant for undisciplined preempts is burned in my memory and this looks like one of those as he has a long suit headed by the Queen at best. I play low and ruff in hand to lead towards the ♥AJ6 in dummy, putting up the ♥A dropping the ♥K. Outside honour #1 has just made its appearance. I lead a club to the ♣A and lead a second heart to the ♥9 and ♥J, winning when North shows out. Hmmm. This is looking extremely fishy. So there follows the ♠A and the ♠K dropping the ♠Q, outside honour #2. I had been planning to discard a spade on the ♦A, playing for the clubs to be 3-3. Instead I discard the ♣6 on the ♦A and lead a club from dummy. The ♣Q appears, outside honor #3. A heart exit to the ♥Q and a spade back means I lose 2 trump tricks. Not optimum play to be sure, but a tie for top with the wimps who played 4♠ for maximum safety. Here is the full deal.

It certainly appears the contract would be better played by West in 4♠ (or 6♠), so the preempt seemed to have served its purpose, but a little knowledge goes a long way when facing a player whose errant tendencies are familiar. Prior knowledge is part of the information package we bring to the table, but what if we are facing unfamiliar opponents? Now we must rely on partner’s bidding to reveal the nature of the overcall. Standard methods tend to show overall strength without specific reference to the overcaller’s suit, with the result that 3NT can be missed when each player holds honours there. The natural assumption is that the overcaller has values in his suit. This is no longer guaranteed. It helps to known just how bad the overcaller’s suit is.

Suit Combinations
The Friends of the Forest Handbook contains this advice on the very first page: ‘if the occasion for taking a finesse presents itself, take it.’ Later on it states, ‘losing a trick unnecessarily to rectify the count is just what it says, unnecessary.’ Here is a suit combination discussed under the category of easy decisions: ♥A94 opposite ♥KJ6. ‘The best way to make 3 tricks in the suit is to cash the ace and finesse the jack’. Alright!

Contrarian that I am, I want to prove the book wrong, so playing in 2NT  on a club lead, I win and duck a spade with ♠AKT94 in dummy. Later a heart discard from ♥ KJ6 sets up a triple squeeze in spades, hearts, and diamonds. Being clever may not to be smart – most made more tricks by finessing the ♥J on a heart lead from the Queen and playing the spades off the top. The point is that the best play in a suit often depends on the external circumstances: not everyone is going to make the same lead.

Here is an example where I can show the full deal. How do you play this spade suit for the maximum number of tricks in 3NT: ♠A7 opposite ♠QT654? Suit Play advises playing the ♠A and finessing the ♠T. Love those finesses. Duncan Smith, our local expert on suit combinations, played the ♠A and the ♠Q making 4 tricks in the suit. When questioned by his brother Matt, the internationally respected director, he claimed this was the textbook play. The result was another total top for the Smith brothers.

Personally, at the table I never question a winning play, preferring to think there had to be a good reason behind it. Why dim the warm glow of success? Back home I question everything. The Dictionary of Suit Combinations makes a distinction on which opponent is more likely to hold the ♠K. If the LHO, play the Queen; if the RHO, play the ♠T. There must have been something in the play that suggested to our expert the right course of action, something he was not eager to reveal. Here is the full deal.

The opening lead was the ♣7 to the ♣9-♣T-♣Q. There was the clue. A lead of declarer’s bid suit when there is no sequence behind it, even when that suit is clubs, indicates a tough choice had to be made. Of course, a spade would never be led, but why not a red suit? The tea leaves indicate poor holdings in the red suits, and a possible entry in spades in case the club lead proves successful.

Well, one can see that I missed my chance when the ♠A was led at trick 2. Do you see it? I should have dropped the ♠J. Now Roudinesco recommends declarer duck a spade all ‘round, so I would make my ♠9 and Pard his ♠K. But that depends on declarer buying my having a doubleton ♠KJ. That doesn’t quite fit, although it’s worth a try.

What is the best lead? Recently there has been discussion on short suit leads against 3NT inspired in part by the computer studies of Tad Anthias presented in the book Winning Notrump Leads co-authored with David Bird. It is one of those deceptions that can fool declarers and partners alike, but if one hits a good suit in partner’s hand the deception applies to declarer only. Low from a doubleton is the current practice, so with this hand the ♦2 might do the trick. Now when declarer plays the ♠A and the ♠J drops under it, there is more reason to think it could indicate ♠KJ doubleton with the opening leader holding ♠9832. It might work against a clever declarer who knows what he is doing, but readers of the F-o-t-F Handbook will not be deterred from finessing the ♠T next. The instinct for self-preservation is a wonderful thing. The result can be no worse than the zero we received. I find that I am saying that a lot.

What America is Coming To
Tonight’s sports break is brought to you by  Squeeky Sneakers:
Chicago Bulls 119, San Antonio Spurs 109
……late in the third quarter
I am Barak Obama and I approve this message.

Pass or Bid?

November 27th, 2012  ~  Bob Mackinnon  ~  3 Comments 

It is generally acknowledged that the side that opens the bidding gains an advantage. That attitude has spread to the side that faces a light opening bid – it is better to get into the auction early than it is to see what transpires before making a move. The result is that bids have become less informative as the traditional restrictions have been lifted, with the result that auctions today intentionally involve more guesswork. Inferences are less certain. It follows that competitive bidding is an increasingly important aspect of winning bridge. Before we get into that, let’s have a brief look at some factors affecting the decision as to whether or not one should open the bidding ‘light’. Here is a deal from the recent English Premier League Match 7-7 broadcast over BBO where the commentators expressed mixed feelings as to whether West should not have passed initially.

The hands possess a 8-7-6-5 division of sides with a trick total of 16 in accordance with the Law of Total Tricks. NS can make 110 in 2♥, EW 90 in 2♦. The optimum contract for NS is 120 in 2NT. Both sides should go down in a contract at the 3-level.

The South hand is clearly worth an opening bid on the power of the 14 HCP held. The West hand has just 9 HCP, but if we add 3 points for a void, the resultant sum of 12 points qualifies the hand for an opening bid of 1♦ under the guidelines advocated by Charles Goren. Under the Zar point method the West and South hands are equally qualified. The difference in quality is that composition of points for the South hand is predominantly in ‘transferable’ power points, whereas the composition of points for the West hand is dominated by shape. The West hand may generate many tricks if a fit is found in diamonds and/or spades, which is not guaranteed, but not improbable.

Pass Now, Pass Forever?
At one table the West player seemed to gain an advantage by passing throughout.

In 3rd seat opposite a passing partner Osborne made a protective preempt on an inappropriate hand. Jason Hackett reached the optimum contract for NS, but his brother, Julian, aimed higher. Hinden led the ♦4, won by the ♦J. Unaware of the situation, declarer led a heart to dummy to set up tricks in that suit, won the club return, and unblocked his ♦A before leading a spade from his hand. Hinden won with the ♠K and cleared the diamonds with the entry to cash them later.  This resulted in down 2, an extra undertrick that would be very valuable at matchpoints, but which stood to gain little at IMPs. The major factor in the NS loss was the exuberance of the North player, which is understandable as no one chooses to play in 2NT these days.

At the other table the West player entering the bidding at a later stage, but that led indirectly to a big loss. Psychology played a part.

Once again, in 3rd seat a player felt the need for action, but the lower level gave South the chance to bid under less pressure. Having passed initially, King felt the diamonds were worth a bid within a constructive context. Allerton might have bid an invitational 2NT on values, but went for the game bonus. King felt his hand was worth a great deal on defence opposite a questionable opening bid from partner. Which side would benefit most from the information exchanged?

Jagger won the lead with the ♦J, but unlike Hackett he began by playing a spade towards dummy. Of course, he had been made aware of the danger in the diamond suit. A spade to dummy, a club finesse, followed by a second spade allowed West to win the ♠K, take his 3 tricks in spades, and exit with a diamond. Here was the 6-card ending where declarer was stuck in his hand having to yield the setting trick to East for a tie board, but a strange thing happened.

South led the ♥2 to dummy, but East ducked! This error enabled declarer to cash the ♦K squeezing East in hearts and clubs, so 3NT* made for a gain of 12 IMPs. The reason this lapse on defence holds our interest lies in the question as to what extent it was caused by the unusual bidding of the West player. In theory East should have had all the information needed to come up with a simple conclusion. As with many errors that don’t make sense, we have to look to the surrounding circumstances. This error might have been avoided if West had followed Hinden’s example and passed throughout, or better yet, opened 1♦ and let the auction take its natural course. The double of 3NT punished partner’s initiative with no partner-proof opening lead to back it up. East, not at his best, may have suffered from the pressure.

The Psychology of Multi-Source Messages
If this were an isolated example one might dismiss it as totally random event of the kind that shouldn’t have happened but did. There is more to it than this as it is not uncommon even for experts to err egregiously during and after a competitive auction.

Normally the more sources of information the better, but that doesn’t work out well when the sources are putting out different messages. (The US intelligence community has proved that once again in the Benghazi incident.) When conflicts arise one has to choose how much credence to give to each source. It is easier to evaluate the information given by one player than it is to collate information from 3 participants. The mind may become overloaded with information with all players active, giving their own self-interested interpretation of reality. So, just the fact that all 4 players are bidding can cause unwarranted confusion as the players’ circuits get overloaded. There are computer programs that can extract the message from the noise. One must train the brain to do the same, but it is made much harder by reactions of the mind to a variety of stimuli, a necessary function in times of danger. For example, in broad daylight one happily ignores background noises, but home alone in the dark, one is sensitive to unusual sounds. Later, given time to reflect, one can calmly draw the correct conclusions, but at the time one’s mind was playing tricks by over-reacting to what was harmless ambient noise.

From this one concludes there is always something to be gained from entering the auction if for no other reason that to generate the confusion inherent in multi-source communication. This is quite apart from transmitting a desire to compete for the contract. An example of how this works comes from the 2012 European Champions Cup.

East-West were the Russian pair Mikhail Krasnosselski and Eugenyi Gladysh who proved fair game for the psychological ploys of their famous opponents. Helgemo made an innocent-looking vulnerable overcall on a decent spade suit with a second major suit available in an emergency. It was lacking in other respects. Krasnosselski doubled rather than show where his main hope lay. Helness added to the noise with a featherweight raise that ate up bidding space. The Russian bid their suits without implying extras with the result that they stopped in game. That would be a reasonable conclusion if NS held 12 HCP or so, but their opponents at the other table, Zimmermann and Multon, were able to bid and make 7♥. Obviously the Russians didn’t have the methodology at hand to counter trivial interference; they were unable to turn on the lights, as it were.

Let’s consider what information must be made available for EW to reach slam, then we might find methods for getting there.  West would like to known East’s holding includes: ♠A  ♥ Q ♦ K ♣ AKQxx . East would like to know West’s holding includes: ♥AKxxx ♦ A ♣ xx. It is easier for East (the stronger hand) to get the necessary information. So West has to bid hearts early, show his 5 controls, and deny shortage in clubs. This is actually quite easy to do, as follows.

The essential first step is that Krasnosselski has to show a game forcing hand with a long heart suit, the main feature of his hand.  Gladsyh has a heart fit, so needn’t fool around with clubs directly: he asks for key cards, disclosing the fit. 4NT asks for more information on the way to slam. 5NT agrees to slam without a specific feature to show, the 2 jacks being undisclosed positive attributes. Gladsyh knows enough to bid the grand. He expects to take 1 spade, 5 hearts, 2 diamonds, and 5 clubs. The appearance of the ♣J is a welcome sight, otherwise he might have had to rely on a minor suit squeeze.

Of course, Gladsyn doesn’t know everything, so he cannot guarantee 13 tricks in 7NT. He does know what is probable. It helps that Krasnosselski is given the opportunity to express general encouragement. That could be based on a 6-card heart suit, or perhaps, the ♦Q. Whatever it is appears to be enough. The opponents bidding of spades was helpful in that EW could confine their interest to the quality of the other suits.

General Guidelines for Competitive Bidding
If the opponents are going to hand out extra bids, one should use those extra bids efficiently to transmit trustworthy information that distinguishes between power points and distributional values. The more unreliable the opponents the more accurate must be a partnership’s constructive agreements. Show your good suit(s) early and use doubles to show flexibility. Have a way of asking for key cards cheaply below game. Use 4NT to elicit partner’s opinion. Use cue bids as a general game forcing bid with the implication that 3NT may be a viable alternative. A cue bid may be used to initiate a cooperative effort when the opening bidder hasn’t enough in the way of controls to take charge unilaterally. It is not necessary to limit the bid to being a raise to game in responder’s suit. For example:

Bridge bidding has the charm that there is underlying the exchange of information a reality that will be revealed in its entirety when the last card is played. The lie of the cards is the focus of endeavor, be it to resolve the uncertainty, or to increase it. In the end one cannot speak comfortingly of a compromise between two subjective versions of the truth, yours and mine – there is only one irrefutable truth which eventually becomes apparent for all to see. The partnership whose perception is closest to the truth in the essential details operates with a distinct advantage – simple as that.

Specificity and Probability

November 19th, 2012  ~  Bob Mackinnon  ~  1 Comment 

Normal English conversation tends more towards vagueness than specificity. ‘What exactly do you mean by that?’ is considered an impolite challenge to the speaker. The requirements of mathematics demand exactitude; the primary tasks of a mathematician are to define his terms and to limit his frame of reference. Unlike in political discussions hand waving appeals to general principles that may or may not be applicable to the matters under consideration are to be avoided. Unfortunately, common usage applied to mathematical problems may sometimes mislead the untrained mind along the wrong path. This is especially so with regard to probability, as words like ‘probably’ and ‘likely’ are vaguely understood. When asked for a definition of ‘a miracle’, Enrico Fermi replied, ‘anything with a probability of less than 20%’. Whether of not you can agree with that, it does present a firm basis for discussion.

Here is an example that illustrates how specificity can mysteriously transform probabilities. The key conclusion is that probability in card play depends not only on combinations, but also on permutations in play, or as we put it, ‘plausible plays’. Suppose we have two packs of cards. From each we draw a card at random. The question is: what is the probability that 1 red card (r) and 1 black card (b) have been drawn? Most will know that the probability of that occurring is 50%. Both red and both black draws each have a 25% chance of occurring. Let’s look at the 4 possible permutations in the draw.
b-b b-r r-b r-r
 Checking the r’s and b’s we can see how the expectations are manifest in the possible draws.

Next we ask the question, ‘if one of the cards is red, what are the chances that the other card is black?’ Note we have added information by restricting the results of the draw. Without much thought one might conclude that the other card stands to be red, because the a priori odds of b-b was only 25% whereas the odds of one black and one red was 50%. The ratio of 50 to 25 is 2:1. Let’s look at the remaining permutations:
b-r r-b r-r
Sure enough, there are 2 permutations for mixed colours and only one for the same colour.
One might conclude that the information provided has not changed the probabilities one iota. On this basis many bridge writers wrongly tend to rely on a priori odds in their analysis of card play.

Let’s now be as specific as we would at the card table and say that one of the cards is the ♥ Q. What is the probability that the other card is black?  A false argument is that it doesn’t matter which red card was drawn from the one deck, the draw from the other deck is independent of that, so the odds must not be affected. This is where Galileo got it wrong. To get it right look at the possible permutations:
b-♥ Q ♥ Q-b r-♥ Q ♥ Q-r
The chances that the other card is black is now 50%. What has happened? The r-r permutation has been split into 2 equally probable draws: ♥ Q on the right and ♥ Q on the left. If the ♥ Q has been drawn on the left, it is 50-50 that a black card has been drawn on the right, and similarly if the ♥ Q has been drawn on the left. It is obvious that the probability of a black card being drawn is 50%, provided you think of it in the proper way. The surest way to the correct answer is to consider the possible permutations in the draw. Specify.

Specificity in Card Play
With reference to the previous blog, let’s consider the case of declarer playing a club to his ace when the opponents hold 5 clubs. We shouldn’t think of the cards as ♣QTxxx, we have to be specific: ♣QT842. Next we assume the defenders would not follow with a club honour unless they have no choice, but that the other cards can be played equally at random. Consider the case where the clubs are split 2-3. There are 10 combinations for 6 of which the ♣Q on the right and for 4 of which the ♣Q is on the left, so the odds are 3:2 the ♣Q was dealt to the RHO. Here are those combinations.

Suppose that on the first round of clubs the LHO has followed with the ♣4 and the RHO has followed with the ♣2. The 7 combinations listed on the right are no longer possibilities, leaving us with just 3 possible combinations listed on the left. Before play in the suit they were equally likely. Is it still so? That depends on the probability that the sequence ♣2-♣4 would have been chosen at random. With the first 2 combinations, the RHO could have equally played the ♣8 or the ♣2, so there are 2 equally likely permutations in the play ♣8-♣4 or ♣2-♣4. With the third combinations the RHO was obliged to play the ♣2, but the LHO could have played the ♣8 instead of the ♣4, so again there are 2 equally probable permutations in the play. All 3 combinations have 2 possible variations in play to choose from, so they can be treated as equals in the calculation of the probabilities. The probability of ♣Q on the right is now twice the probability of  ♣Q on the left, because there are 2 equally probable combination of that sort to 1 of the other.

A False Argument
Let’s now put forth a false argument of the kind one might encounter at a casual post mortem in the pub. Let the clubs be designated as ♣Qxxxx, where x represents a low card. On the first round of clubs the RHO and LHO follow with low cards. That leaves us with 3 possibilities remaining: Q opposite xx (1 case) or x opposite Qx (2 cases). So it appears the chance of ♣Q on the right is twice that of ♣Q on the left. This was true when the cards missing included the ♣T and the number of plausible plays is the same for each combination remaining, but it is not true for ♣Qxxxx. Let’s lift the play restriction on the ♣T by converting it to the ♣6. Again there are shown on the left the 3 combinations still in the running after one round of clubs is played.

With the first possible combination the RHO could have equally chosen to play any of 3 low cards, so the chance of seeing ♣2-♣4 is 1 in 3. With the other 2 combinations, the RHO had 2 equal choices and the LHO had 2 equal choices, so all together there are 4 available permutations (plausible plays) to choose from, so the chance of seeing the ♣2-♣4 is only 1 in 4 for each. The fewer the number of choices available the greater the probability that a specific choice has been made. As a consequence, the existence of the first combination is greater than the second or the third in the ratio of 4:3. However, there are 2 combinations with the ♣Q on the right, so the probability that the ♣Q is on the right is 3:2, just as it was before a club was played.

This demonstrates that under the circumstances the play of 2 low cards has not changed the a priori odds that the ♣Q was dealt to the RHO. To achieve this result we had to consider the number of plausible plays for each combination, otherwise we might conclude wrongly that odds have changed to 2:1. On the other hand, if the number of plausible plays is the same for the remaining combinations then a direct comparison of the number of combinations remaining is a valid procedure for obtaining probabilities.

Consequences
The a priori odds are subject to change. If one is to calculate the a posteriori odds on the location a queen, it is not sufficient to compare solely on the number of combinations remaining for the queen on the right and the queen on the left. It is necessary to allow for the number of plausible plays available for each combination. Only if the number of plausible plays is the same for each combination can a direct comparison be made.

A Best Laid Plan

November 8th, 2012  ~  admin  ~  6 Comments 

The following problem was suggested by mystery man Jim Priebe who in a team game defended a slam in which both declarers went down.  The problem involves a fundamental probability calculation after a number of cards have been played. It illustrates the difference between a priori probabilities and a posteriori probabilities.

In order to calculate probabilities in 2 suits after something is known about the other 2 suits from the bidding and play, we assume a random distribution in the unplayed suits. This means that probabilities can be calculated exactly form the numbers of possible card combinations. This relates to the probability of the deal. Sometimes a refinement must be added that complicates matters as on the following example where the distributions of spades and hearts become known, and a decision must be made on best play in clubs and diamonds when there is a wide discrepancy in the number of vacant places.

North leads the ♥J heart, ruffed in dummy. Declarer leads the ♠7 towards his hand and is much surprised to see South show out. He wins in hand finesse in trumps, cashes the ♠A and return to hand with a club to the ♣A in order to draw the last trump. South has discarded hearts throughout. When he draws the last trump he shall have to discard a card from a minor suit in the dummy, so before that he must decide how he will play the minors for 1 loser. There are 2 apparent choices:
play North for at least one of the missing diamond honors, roughly a 75% chance a priori;
play for the clubs to have been split 3-2, a lesser a priori probability .

Let’s see if the bidding and play have changed the preference for the play in diamonds. The discards by South indicate he began with 5 hearts, leaving North with 6 hearts. North had 4 trumps, so the vacant places available for the accommodation of the 11 minor suit cards is 3 in the North and 8 in the South.  These are the possible splits remaining.

Now we must take into account that one round of clubs has been played in which North followed with a low club, but not just any low club, but with the ♣2 specifically. This means that the only possible remaining 1-4 club split is  ♣2 opposite ♣QT84.
Furthermore, suppose South has followed with the ♣4 so the remaining 2-3 club combinations have been reduced to just 3 in number: ♣82  opposite ♣QT4, ♣T2 opposite Q84, ♣ Q2 opposite ♣T84. At this point the combinations remaining are as follows:

To simplify the calculation we assume that South would have played differently if he had been dealt 6 diamonds to go along with the 5 hearts, so this possibility can be neglected, leaving us with 2 cases to consider. The club play will fail for all 15 combinations with a 1-4 club split, but will succeed for all 18 combinations with 2-3 splits.

If South had been dealt 4 diamonds, the best decision would be to play on diamonds hoping for split honours there. The numbers of successful conditions for leading the ♦J from hand planning to run it if North plays low are given below.

The number of combinations for which the diamond play will succeed is 15, so the club play is favoured in the ratio of 6:5. Note that taken in isolation the chance of the diamond finesse succeeding when the diamonds split 2-4 is not 75%, it is only 60% (9 out 15 possible combinations), so it is dangerous to generalize from the a priori expectation.

There is one further refinement to be considered, and that is the number of plausible plays in the club suit. The plausible plays determine the probability that the plays of the ♣4 and the ♣2 would be chosen by the South and North players under the various conditions shown above. It so happens that there are 2 plausible plays for each combination shown, so a direct comparison of the number of club – diamond combinations is justified in the determination of the relative probabilities. This comes about because neither defencer would part with either the ♣Q or the ♣T if there were an alternative play available. Thus we are in a restricted choice situation, and what I have called the Extended Kelsey Rule can be applied. (That is, in the calculation of probabilities it is correct to compare combinations directly when there is equality in the number of plausible plays.)

The Unexpected Ending
It remains to give the solution to the real-life mystery: the winning play at the table was to go for split honours in the diamond suit. Against the odds clubs were dealt ♣QT84 to the South, the only losing combination for the club play. Here are the hands in full.

It might be said that the declarer who played on clubs, not diamonds, like Brutus at Philippi, could feel he’d earned the right to fall honourably upon his sword.