Two Chances Aren’t Always Better than One

October 17th, 2011  ~  Bob Mackinnon  ~  No Comments 

Eddy Kantar, a favorite author, has been awarded a prize for his 2009 book, Take All Your Chances in Bridge. A recurring theme is that in declarer play two chances are better than one, if one can take the first chance for success without losing the advantage of a second chance should the first one fail. Commonly, one is advised to play for the drop of an honor in one suit before finessing for an honor in a second suit. To finesse first is to risk immediate defeat.

Kantar’s book is basically a workbook on the theme presented in various settings. He takes the sensible approach of leading the student repetitiously to the correct approach through a natural logical process without piling on abstract mathematical arguments. However, being a contrarian, and a mathematician to boot, I love to pile it on to see if it is in fact true that 2 chances are always better than 1. If not, why not?  How come?

Tim Bourke, a man who has cast a critical eye on many a declarer play, brought to my attention to the following hand presented by Kantar in a 1981 book entitled Test Your Declarer Play Volume 2. Tim asks whether Kantar’s suggested line is always the correct one.

The spade lead is not surprising. West puts up the ♠Q losing the ♠K. Kantar’s suggestion is to play off the AK in the longer minor, clubs, to see if the ♣Q falls. If so, declarer has 9 tricks to cash. If the ♣Q doesn’t fall, declarer is in the dummy to take the finesse in the shorter minor, diamonds, and may still come to 9 tricks that way.

Mathematically we can express this idea in the following equation:

P1   + (1-P1 ) x P2 > P3,

where P1 is the probability the drop play will succeed, (1-P1) is the probability it will not succeed, P2 is the probability the subsequent finesse will produce 6 tricks, and P3 is the probability that a double finesse in clubs will succeed.

The A Priori Odds

The probabilities depend on what one assumes about the distribution of the sides. Let’s calculate the odds for the case of maximum uncertainty which is represented by the a priori odds.

The A Priori Odds of the NS Club Splits

The A Priori Odds of the NS Diamond Splits

Under these conditions:   P1 + (1-P1) x P2   =  52%, and P3 = 48%.

Clearly it is better to take the 2 chances as described rather than stake everything on the double finesse in clubs.  We conclude that Kantar’s line is better by 4%, but only if the a priori odds can be applied with sufficient accuracy. An essential characteristic of the priori odds is that the numbers of vacant places are equally divided. What happens if there are more vacant places in the North, which will tend to favor the club finesse and be detrimental to the diamond finesse?

When South Preempts

Let’s go through the mathematics when South enters the auction with a 2♠ preempt. West still plays in 3NT for the lack of a better alternative. The play to the first trick is the same, but now declarer must take into account that the spades are split 3-6. The a priori odds no longer apply, instead the club splits have the following probabilities.

The A Posterior Odds of the NS Club Splits*

*from J.P.Roudinesco’s The Dictionary of Suit Combinations

The odds of the success of the double finesse in clubs has improved to over 50% as the ♣Q is more likely to be in the North hand in the ratio of 10 to 7. The same is true of the ♦Q, so we expect as lesser probability for the success of the diamond finesse.

The A Posteriori Odds of the NS Diamond Splits*

* from J.P.Roudinesco’s The Dictionary of Suit Combinations

Based on these odds, the chance of success of a second round finesse for the ♣Q is 55%. The chance of the alternative procedure is 47%, so the odds now favour the double finesse by a substantial margin. The one chance in the club suit is significantly better than the combination of 2 chances, the drop in clubs and the subsequent finesse in diamonds.

The Effect of the Opening Lead

If the only information declarer has concerning the distribution of the defenders’ sides comes from the opening lead, the situation is uncertain. As there are 9 spades in the opponents’ hands, the suit cannot split evenly. In Kantar’s text the lead was the ♠5 from a 5-card suit, so the imbalance in the spade suit made the double finesse in clubs an even worse proposition than the a priori odds indicate. The normal lead is in the unbid suit, so it is possible that North led from a 4-card suit, in which case the probability of success of the double club finesse is 50.8% and that of the 2 chances, 51.4%. Thus, whether the imbalance of 1 vacant place is in the North or the South, it is better to play for the drop in clubs.

Some would argue that playing to drop the ♣Q is a safety play of sorts which does not risk immediate defeat on this particular hand. If the difference in the probabilities of success is a few percentage points, consistently choosing the lower percentage play may not entail a significant cost over the short term. However, in the case of a 3-6 spade split, the margin of superiority of the double finesse is substantial, so declarer should believe the bidding. He won’t be far wrong even if the spades are split 4-5.

For some the lesson is ‘don’t put all your eggs in one basket.’ For others, ‘always pursue the line that offers the greatest chance of success, given what one knows at the time of decision.’

Algebra, Bayes’ Theorem, and Vacant Places

October 13th, 2011  ~  Bob Mackinnon  ~  1 Comment 

What would life be without arithmetic but a scene of horrors?

–Reverend Sidney Smith (1771-1845)

This blog is for bridge players who love algebra. There are a few of us. Recently I have gained some sympathy for the Reverend’s unchristian view while recovering from broken leg. Incapacitated at home I have been kept away from the topsy-turvy turmoil of the bridge table and have found quiet comfort in returning to some theoretical work on the effect of card play on probability of the location of a missing queen. As demonstrated in a previous blog the transition of the criteria from the initial probability to the current probability is governed by Bayes’ Theorem. This entails the number of plausible plays that were available for each candidate split. When the numbers of options are equal across the board, vacant place ratios give exact probabilities.

First we shall give a general treatment to the problem of finding the queen when there are 4 cards missing in the suit, namely Quxy where low cards are denoted by u,w, and y. For sake of clarity suppose the suit to be played is hearts. Further suppose that it is known that another suit is split with N card on the left and M cards on the right. If N and M are zero, then nothing is known (or assumed) about the location of vacant places outside the heart suit (the a priori condition).

Here are the situations remaining under the circumstances of the play so far.

Because the numbers of plausible plays are the same across the board, we suspect that the ratio of probability of the queen on the left (QL) to the queen on the right (QR) equal the ratio of the current vacant places, (12-N) divided by (12-M). To prove this we need consider the relative numbers of combinations available in the outside suits (clubs and diamonds).

Summing the weights for Q appearing on the left and Q appearing on the right, one finds:

_____QL = (12-N)x(23-N-M),   QR = (12-M)x(23-N-M), so that the ratio of QL to QR is (12-N) / (12 – M), the ratio of the current vacant places.

Vacant Places and Combinational Weights

One sees that the relative strengths of combinational weights are expressible in terms of products of current vacant places.

We may form a matrix of inclusion (designated by a √ mark) of vacant places in the weighting factors defined by their products.

The pattern is apparent and reveals the connection between the splits and the vacant place inclusion. The elements that are common to all splits (the top line) do not appear in the relative weighting. This makes the calculation of weights easy.

A Case of 5 Cards Missing

We repeat the exercise for the case where the missing hearts are QJuxy, where J denotes the jack which will not be played voluntarily. On the first round of hearts card u appears on the left, card y appears on the right, and on the second round card x on the left.

Summing the eights for Q appearing on the left and Q appearing on the right, one finds:

_____ QL = (11-N) x (22 – N – M)        and QR =  (12 – M) x (22 – N – M).

The ratio of QL to QR equals (11 – N) / (12 – M), the ratio of current vacant places after 2 cards have been played on the left and 1 card on the right.

Hopefully this little exercise gives the reader some insight into how probability and vacant places are tied together by Bayes’ Theorem. Central to the treatment is the assumption that the plausible plays are equally likely to have occurred for all splits.

Probability and Defenders’ Card Play

October 11th, 2011  ~  Bob Mackinnon  ~  No Comments 

Probability and Defenders’ Card Play

Probabilities play a central role in decision making during the play of a bridge hand. Declarers benefit in the long run from choosing the path that is most likely to lead to a good result. There are two kinds of probability to consider: the probability of the random deal, and the probability of the play. The first kind involves the a priori odds, and the second involve everything that happens once the first call is made. Players are familiar with the a priori odds, but are less clear on how those odds are altered by subsequent actions. The use of vacant places to decide the most likely location of a missing queen is well understood, but the transition of the criteria from the initial conditions to the current conditions is not. This process is governed by Bayes’ Theorem. As a demonstration of the application we shall work through a simple problem in declarer play. From this the reader will hopefully add to his theoretical understanding of a process that has largely remained hidden to the average player.

Use of Weights Probabilities of the deal are related to the number of card combinations available under the various conditions. Suppose the conditions are designated A, B, C, and the associated combinations are NA, NB, and NC.

_____NA + NB + NC   =  M, the total number of card combinations currently available.

The critical characteristics are the proportions between NA, NB, and NC .

_____(NA/M) + (NB/M) + (NC/M)    = 1

_____PA   +  PB   +  PC   = 1

We associate the probabilities PA., PB, and PC with the corresponding ratios.

In this way we needn’t calculate the numbers of combinations absolutely, but only in relative terms among the all-encompassing conditions. In general when dealing with probabilities we are dealing with relative strengths and proportions, which simplifies calculations. When it comes to expressing the results in probability terms, one must keep in mind the quantities must add to 1 and must cover all the possibilities without overlap between conditions.

A Simple Problem

A common situation is the finesse for the trump queen, missing Qxxxx, or more exactly, Quwxy, where u,w,x, and y represent  cards of equal rank that may be chosen in any order. It is important to make a distinction between the insignificant cards, as when the cards are played, the players observe particular cards, not just ‘low cards’.

Let’s consider the case where against a contract of 4 hearts spades are led and are known to split 3-5. Declarer ruffs the third round before a minor suit is played and proceeds to draw trumps, planning to finesse against the LHO who holds only 3 spades. Declarer holds ♥ KT86 and dummy has ♥ AJ95, so he plays the ♥ K and leads towards the ♥ AJ9. Here is the vacant place situation the defenders following with low cards throughout, in particular, card u followed by card y followed by card w.

We still expect the ♥ Q to be finessible, but how have the odds changed? Here are the situations remaining under the circumstances of the trump play so far.

The probability of choice is where Bayes’ Theorem comes into play. With a 4-1 split, there are 6 ways for defenders to choose their low cards without giving up the ♥ Q. If the cards are chosen at random, each sequence is equally likely, so the probability of their having chosen specifically u-y-w is 1/6. With a 3-2 split with the queen onside, there are 4 choices, so the probability of u-y-w having been chosen is 1 in 4. This is more likely than in the case of 4-1, so that weighs in favour of the 4-1 split in a ratio of 3 against 2. This can be expressed as a weighting factor to be applied to each initial split.

This is the essence of Bayes’ Theorem: the probability of a given combination having been dealt is affected in proportion to the probability that the observed sequence would arise from that combination. The greater the probability of the emergence of the observed sequence, the greater the probability of its source.

The weighting that accounts for differences outside the suit being played depends on the number of combinations available in the untouched suits, diamonds and clubs, of which nothing has been disclosed. The probabilities with regard to these suits are the probabilities of the deal, so directly related to the number of combinations available.

Now incorporating the weighting due to the play in the heart suit itself, we find

The weights total 37. The Q is on the left for 20 out of 37 of total weights. So, the probability of the ♥ Q on the left is now 54%. Initially, before a heart was played, it was according to the vacant place ratio, 56% (10 out of 18).

One may use the ratio of the current vacant places to calculate probabilities exactly if the card play weighting factors are equal, that is, the observed sequence of play is equally probable to have arisen from the various remaining candidates. In the above situation equality would be achieved if declarer didn’t finesse on the second round, but rather went up with the ♥ A in dummy. When the RHO follows on the second round with card x, the remaining conditions are Q – 0 and 0 – Q, with corresponding weights 4 and 3, respectively. These weights represent the ratio of the current vacant places, 8 and 6.

When the weighting factors are not equal, the probability of Q on the left will not generally be equal to a ratio of real (integer) vacant places, however, one may define a fractional vacant place to achieve exact correspondence. We call this the virtual vacant place (VVP). In the above example, we would define VVP according to the requirement that 8 / (VVP + 8)  equals 20/37. In this case VVP is 6.8, which lies between 7 and 6.

A Second Demonstration

The use of current vacant places in this manner when the observed sequence is equally likely to have arisen from each remaining split remains valid when 4 hearts are missing.

Here are the situations remaining under the circumstances of the play so far.

The probability of the ♥ Q being on the left is proportional to 96 + 84 = 180.

The probability of the ♥ Q being on the right is proportional to 84 + 56 = 140.

The ratio of these numbers is 9:7, exactly the ratio of the current vacant places after 1 round of hearts has been played. Magic. Note that there is a difference in the number of plays required before the equality rule takes effect depending on whether the number of missing cards in hearts is odd (5) or even (4), as reflected also in the familiar rule of thumb regarding ‘Eight-Ever, Nine-Never.’

Controlling Uncertainty

September 6th, 2011  ~  Bob Mackinnon  ~  No Comments 

Beginners are taught to bid according to a set of rules that constitute a system in which the various bids fit together like pieces in a jigsaw puzzle. One thinks of bids as the means of telling partner about the hand one holds, so that together, following the rules, one’s partnership will usually arrive at a good final contract. Failing to do so implies one has made a mistake. However, one soon discovers that it is not just what one knows, but also what the opponents don’t know that affects the outcome. Often there is value in disclosing less. The uncertainty that is inherent in a system may work in one’s favor. To remind ourselves let’s look at a simple example of how it works.

Playing standard 5-card major methods, Bob1 opens 1♣ and Bob2 responds in his 5-card suit, and accepts the invitation to bid 3NT. The ♠6 is led to the ♠A, declarer dropping the ♠8, and a spade returned. Ten tricks are taken where a club switch from ♣AT43 would have led to down 1. Some critics would claim the good result is undeserved as the defender should have found the club switch, however, built-in uncertainty played a part and the defender, unable to penetrate the smoke screen set up by the ‘natural’ 1♣ opening bid, followed his partner’s chosen path.

In every session we come across part-score deals where uncertainty can prove advantageous. In such cases it is not the aim to provide a complete and accurate description from which the opposition may benefit. It may important to compete in hearts, say, without the necessity of disclosing a supporting minor, potentially revealing to the opponents the condition of a double fit in both directions. However, when one holds the preponderance of power, more information is better, because one wishes to bid to the full capacity of the hands, and possibly to catch the opponents if they overstep their bounds.

Accuracy comes to the fore when one contemplates bidding a slam. Players devoted to bidding according to probable outcome will often miss slams that a more informative style may reach. In some cases the bidding system they employ fosters that approach when the emphasis is entirely upon the total number of high card points held rather than on the specific location of suit controls. Let’s give Bob2 a much better hand.

After counting his points twice, Bob2 decides not to proceed to slam on just 3 controls and less than 33 HCP. Declarer makes 12 tricks on a heart lead.  More accurate bidding might lead to a 4 NT contract, held to 10 tricks on a marked club lead after a revealing auction that pinpointed the weakness in clubs. Bob2 bid so as to avoid such a result.

Playing standard methods it is hard to judge early in the auction whether or not the hands in combination have slam potential. Barry Crane is often quoted as telling a partner, ‘don’t play me for the perfect fit’. He may have thought that partner should play him for normal expectations instead. Most often one is not in the slam zone. In the above case, responder makes a judgement based on HCP content without exact knowledge of where those HCP are located. In fact, slam makes because of the unusual circumstance of the side holding two 7-card suits each containing AKQJ, which is very much against the odds. Unexpectedly, it is the club suit that represents the weakest holding.

Some players like this style. If everyone bids in the same way, shrewd guesses come to the fore. There is a rush in making 3NT holding ªT in the dummy and ♠Q6 in hand, as I did last week. Others prefer to attempt to bid as accurately as possible using many conventions that allow for the disclosure of otherwise hidden assets. They may stop in 2NT on the first hand (below average) and reach slam on the second (above average), in the end achieving little for their mighty efforts apart from satisfaction of a task well done. The ideal situation is to bid 3NT on the first hand and make it as a result of non-disclosure and to bid and make a cold slam on the second as a result of full disclosure.

Economical Bidding after the Start 1♣ – 1♦

In his book ‘Building a Bidding System’ Roy Hughes makes interesting general comments on the structure of bidding systems as means of exchanging information. In particular, he notes that the lower the bidding is kept, the more bidding sequences remain from which to describe the partnership holdings. To preserve bidding space maximally, each higher bid should be half as frequent as the bid below it. Thus, a 1♣ opening bid should be twice as frequent as a 1♦ opening bid, which should be twice as frequent as a 1♥ bid, and so on up the line. It is important to note that according to Shannon’s Law of Information, the amount of information in a bid is minus the logarithm of the probability of the bid being chosen, thus the most frequently chosen bid is automatically the least informative.

Hughes notes the consequence of this type of allocation is, ‘the higher the call, the more specific and less frequent it should be.’ Because flat shapes are the most probable, the corollary to this conclusion is that in general, ‘the lower the call, the flatter the hand.’

If a jump response of 2♦ to 1♣ is less frequent than a simple response of 1♦, of necessity the more informative it must contain. With regard to saving space, jumps as wasteful, but compensation is derived if the information provided is of a particularly useful kind. If the 2♦ response shows weak hand with a 6-card diamond suit with 2 top honours, that is indeed informative, but is it better to use the jump in a constructive sense to show a good hand with such a diamond suit? If as a consequence of their definitions the strong response and the weak response are equally likely, the amounts of information in the bids are the same.

The Consequence a Forcing Rebid

Let’s consider the following sequence:

1♣ (least well-defined opening bid)     —   1♦ (least well-defined response)

1 ♥ (least well defined forcing rebid)   — 1♠ (now what ?)

Three bids have been exchanged, and the least possible amount of information has been disclosed. It is possible to design a system along these lines, the Polish Club, for example, having a structure where the 1♥ rebid may include a hand with 3 or 4 hearts that qualifies for a weak NT. Responder will not pass with 5+HCP. The bidding seems to be going nowhere fast, but significant information can be deduced from the bids that were not chosen, which makes it hard for the opponents to judge what is going on here.

In a constructive auction sooner or later someone has to make a bid that gives precise information unless they simply decide the final contract on the basis of probable outcome. Does the fourth bid represent the time when responder must come clean? Not necessarily. In a 2/1 structure 1♠ is usually defined as being 4th suit forcing, a vague bid that requires the opener to make a descriptive bid with game in mind. Responses of 1NT, 2♣, 2♦, 2 ♥ , 2NT are nonforcing, limited, and descriptive, and opener is left to continue as he sees fit.

The second hand discussed above must be bid more descriptively if slam is to be reached. Let’s consider how it might be done.

1♣ (least well-defined opening bid)    —   1♦ (least well-defined response)

1♥ (least well defined forcing rebid)    — 1♠ (tell me more, game forcing)

2♠ (4 spades, forcing)    — 3♦ (forcing)

3♥ (strength showing)    — 4♣  (control slam try)

4♦ (control)    — 4NT  (sign off)

6♦ — Pass

Thanks to the use of an artificial 1♠ bid, the players have ample bidding space available for a sequence of forcing bids that allowed them an exchange precise information that could be interpreted in the context of a slam exploration. Both players were able to avoid the removal of bidding space through the necessity to jump to 2NT to show strength. A certain momentum was established that prompted the opener to go to slam on the basis that his diamonds represent excellent support within the established context. In a cooperative mode both players can contribute to the evaluation of slam potential taking into account secondary honors that can’t be shown explicitly with the methods available. This is an especially desirable feature when both hands are balanced.

Next we consider the information in opener’s rebid in the sequence:  1♣ – 1♦; 1NT. In standard American practice, 1NT shows a balanced 12-14 HCP that may include a 4-card major. With Polish Club 1NT has the range of 18-20 HCP, which is ¼ as likely to have been dealt. The Polish 1NT rebid is much more descriptive. It is bad practice to use up space to describe a common occurrence. Here is a nightmare scenario for standard.

The spade fit wasn’t established until the 3-level, and responder has to make a decision on whether to bid 3NT or 4♠ without much evidence one way or the other. To avoid this nightmare, a responder may choose to bid an anti-systemic 1♠, postponing problems until the next round. Upon getting a raise to 2♠ he might bid 2NT, which he doesn’t expect to be passed, suggesting 3NT as an alternative contract, while hiding his diamond suit. That would work, when opener has the type of hand that would make 3NT attractive.

Flexibility is a desirable feature when it allows for the exercise of judgement within the context of a meaningful exchange of information. Bids that show shortage should not be defined in terms of HCP, but in terms of losers and controls. The perfect fit, although rare, does sometimes exist. Wouldn’t one like to bid the following slam on just 25 HCP?

This is not the most efficient auction possible, and the splinter bid is not ideal, but it gets the job done. The opener holds an exceptional club suit in a 5-loser hand, and responder’s controls are well placed. The minor suit fits are unusual with opener’s 3-card diamond support containing the ♦AK and responder’s doubleton club being ♣Kx. It is possible to define 2♠ as a splinter bid only if a rebid of 1♠ by opener is forcing, a splinter being defined as a jump one level above a forcing bid in the same strain.

A Different Criterion in Competition

If one takes into account that the opponents will often enter the auction and take away bidding space, the criterion for bid definition is changed – now one wants to choose an opening bid according to the amount of information it contains on its own. The average amount of information in an opening bid at the 1-level is greatest when those bids are equally likely to be chosen. The message sent is, ‘this is my best suit.’ An overcall (presumably) sends the same message. Once the opponents enter the auction, there are 2 bids that take up no bidding space, pass and double. Pass is the most common competitive bid of all, therefore, the least informative, and therein lies the weakness of a wait-and-see pass. From information-theoretic considerations, it would be ideal if the 2 calls were equally likely, hence contained the same amount of information. The modern trend has been to abandon penalty doubles, which are rare, but informative. Now we double often with flat hands and hope it works out later. In theory this is a sound informative strategy, so the trend to flexible doubling should not be at all surprising.

Asking Bids

August 12th, 2011  ~  Bob Mackinnon  ~  8 Comments 

Slam Investigation

Sadly, some strongly held beliefs are wrongly held beliefs. With regard to bridge, many believe that for the ordinary player, and especially for beginners, the fewer conventions the better. The conclusion is that players should be taught to bid naturally, calling a spade a spade, leaving the fancy stuff to the experts. At the beginning teachers set down bidding rules based on HCP evaluation, so bidding sequences are designed to name suits while fitting within preset high-card limits, which then become the determining factors in the choice of bids. This is the wrong approach, as the players should be taught first how to play the cards competently. Why? Because it is the number of tricks taken that determines the success or failure of the contract one reaches, not the number of points held. Thinking should revolve around winners and losers, and how to get in an efficient manner the information needed to reach good contracts at the end of the process.

Obviously frustrations will arise when following a rigid set of bidding rules results in less than optimum results. Beginners gradually find that it pays to lie, that is, break the rules when they deem it appropriate. Good thinking under the circumstances, but a bad attitude to have foisted upon young minds. Better to allow freedom of information exchange through artificial asking bids. Even beginners can comprehend easily the use of an asking bid. Deception is not involved. Asking bids are fun, because they provide information easily, accurately, and without feelings of guilt or justifiable resentment.

If we want to keep beginners happy, we should provide them with the means to bid slams accurately. Let’s go back to fundamentals and ask ourselves what are the elements we find in a well-bid slam. One needn’t discover everything about partner’s hand, even if that were possible with the limited space available, but there are certain elements that take us beyond simple guesswork into the realm of probable success. In a suit slam sequence we expect to find 4 basic steps: 1) finding a fit, 2) establishing critical suit solidarity, 3) determining total high card controls, and 4) placing controls, with regard to both high cards and shortness. The order of their occurrence may vary, but this order is the easiest to manage. If RKCB is the only asking bid available, steps 2 to 4 are often combined, albeit inadequately and belatedly. Natural bidding covers only step 1, where transfers can serve as well, or better. Although suit length correlates to high card content, bidding naturally will not provide accurate control information, and, indeed, may be misleading when a topless suit is bid of necessity solely because of length considerations.

Let’s look at a sophisticated 2/1 auction that didn’t get the job done in the 2011 Grand National Teams Final. A Grand Slam in spades depends on a 3-2 split trump split or, baring that, luck in the diamond suit.

* 4♥ was a balanced slam try

Here is a case of two balanced hands with a combined 33 HCP, just the situation for which beginners are taught to reach 6NT. It is obvious that the experts’ methods were not up to the task of reaching this fine contract which could withstand horrific splits. Their bidding simply didn’t provide the necessary information. It is particularly inefficient to have to use a self-preemptive jump to 4♥ as a slam try, but there is no natural bid that adequately describes the opener’s holding, so he must bid artificially, or lie. Having wasted their own bidding space, the pair resorted to the all-too-familiar RKCB asking bid. One of the advantages of RKCB is that the responses are non-specific with regard to the placement of controls, the uncertainty sometimes against a small slam making the defenders’ task more difficult. The disadvantage is that even after 1-over-1 start the bidders may jump about and reach the wrong contract, as they do here.

At the other table sat Rodwell and Meckstroth armed with one of the most sophisticated systems in the universe. Would they do better with these balanced hands? No.

Their auction is replete with artificial bids, yet the same bad contract was reached, which argues for keeping it simple. 1♣ showed 16+HCP, 2♥ showed a balanced hand with 14+HCP, 3♣ asked for a 4-card suit with transfer responses, 3♥ showed spades, and 4♦ was RKCB in spades. This would be considered a nightmare auction by some, but note that Meckwell were more efficient in their use of space than were Robinson-Boyd. In the end RKCB was again invoked, the wrong questions were asked, as the exact placement of responder’s kings was not established, nor was his shape. So we see generally that at some point a decision must be made on the basis of probability given the current state of partial information. If responder held 4=3=3=3 shape (more probable than 4=2=3=4), then 6♠ would have been quite high enough, and maybe even too high.

One aspect of Meckwell’s bidding was that they always had a well-defined bid available with which to continue the auction and explore for slam below game level. There was no fudging required. The transfer response of 3♥ ®3♠ was particularly useful in saving space. Might we do better without RKCB? Here enters my suggestion for using a cooperative 5NT (D.I.) to pin point controls. I use a similar structure to that exhibited by Meckwell, but shun RKCB, opting rather for a bid that asks responder for the total number of controls held (Step 3). The exact placement of those controls is left to further investigation if a slam is the target. In a Precision slam auction the opening 1♣ bidder is expected to hold at least 6 and often 7 controls. He is the partner who will do the asking. If responder holds 3+ controls, their placement may be known to the opener without the need to inform the defenders. This is a huge advantage over RKCB.

In my version 2♠ shows a balanced hand with 14+HCP, 2NT asks for 4-card suits up-the-line, 3♥ shows spades while denying diamonds and hearts, 3♠ asks the honor composition of the spade suit (Step 2, to establish suit solidarity.)  4♥ asks for total controls (Step 3).  It is discovered that responder holds 5 controls, which must consist of the ♠K, the ♣A, and 2 kings as yet unspecified. At this point bidding space has become highly restricted. 5NT asking for kings up-the-line wouldn’t really solve the problems related to shape. Asking bids tend to take responder out of the loop, which may be a disadvantage when responder has something to contribute not covered by the asking bid response structure. It is better if opener is able to get responder back into the loop.

The solution is rather nice. It is obvious that 6♠ is the minimum level to be reached, so opener may elicit partner’s cooperation with a bid of 5NT which says, in effect, ‘tell me more than I already know, as we may be able to get to 7♠.’  Responder bids 6♣ to show a concentration of values, then signs off in 6♠, thus denying the ♥ K. The minor suit kings have been identified. This gives opener the courage to bid the Grand Slam. Thus, an auction that begins artificially ends up as a judgement call by responder, but one based on a great deal of accumulated information. What about shape?

With 4=3=3=3 shape, responder does best to bid 6♠ over 5NT, or even 6NT when holding the ♥ Q. He is expressing an opinion. It is possible to devise a system in which shape can be revealed at an earlier stage through a revised 2NT asking bid. This might overburden most partnerships, and it might not help in the end. Let’s suppose that a 3♦ response shows 4 spades and 4 of a minor, an added complication that rules out 4=3=3=3. The auction might proceed as above, but over 5NT, the 6♣ bid doesn’t suggest a 4-card suit, as it is not clear that responder doesn’t have 4 low diamonds and ♣AK3, not a good holding. This example shows that a certain degree of flexibility (uncertainty) can be a good thing when both partners are focused on a single problem. Slam bidding is best pursued after a good trump fit is established and the objective is clear in the minds of both partners. Two heads can be better than one. Information exchanged subsequently is pertinent to the specific problem at hand. Mature judgement can be exercised in which several considerations are taken into account involving undisclosed assets.

I suggest it is more fun to be able to bid 7♠ on the controlled Precision auction above than it is to stumble around in a mist and reach the Grand on the basis of a good dinner and a rush of adrenaline. Here is a possible faulty but successful sequence:

1♦ – 1♠;  2NT  – 6NT;  7♠ – Pass.

In a constructive auction there is little merit in the idea that one should call a spade a spade. Not wanting to stifle his partner with a jump raise to 4♠, opener chooses to ‘lie’ by showing a flat distribution with stoppers in the unbid suits. He hopes to show his spade support later. As the late Al Roth might have commented, if he can get through this round he should be OK. Responder bids 6NT on the basis of the total number of HCPs held, and opener follows through optimistically. Even if he passes 6NT, he has outbid the experts on this combination. The fact that such a badly defined auction could succeed where sensible auctions fail points to the need for a forcing rebid by opener at the 2-level that includes the possibility of a hand of the type dealt to opener in this example. I suggest that the meaning of a reverse to 2♥ could be expanded. (2♥ relays to 2♠, and opener rebids 2NT, say. With hearts and  diamonds opener rebids 3♣ or 3♦ over 2♠.)

A Modest Proposal to the ACBL

It is my strongly held belief that Precision is the easiest system to learn and play, and may even be the best system available at this time. Yes, I may be wrong, but let’s look at the evidence. The greatest American partnership of all time is Jeff Meckstroth and Eric Rodwell, who have played Precision over 4 decades. In Japan they would be considered Masters of the Way of Bridge, worthy of emulation, but Americans have difficulty in honoring living geniuses in their midst, whom they consider primarily as misfits. Am I too harsh? Well, why aren’t Meckwell in the ACBL Hall of Fame ahead of a multitude of players of lesser accomplishment? Is the Hall of Fame legitimate without them?

Rather than build upon Meckwell successes, the ACBL largely ignores their advanced methodology and continues to push an inferior system that is both harder to master and worse to employ. In fact, the ACBL impedes advancement. If one builds upon an inferior base, more repairs are needed to bolster weaknesses, which is the main reason why there has been an unending parade of odd, basically inadequate conventions needed as patches.

My proposal is that the ACBL commission Rodwell and Meckstroth to produce a simple version of Meckwell Precision that represents a basic framework on which to build more complex systems to follow… Meckwell II, and Meckwell III. The framework should include from the very first useful conventional elements such as transfers, asking bids, splinters, etc, whereas the details in the follow-up bids may be kept ‘light’. The idea is that a player who begins by learning Basic Meckwell can progress easily to Meckwell III by adding detailed agreements without changing his approach or violating basic principles. It is up to individuals how great a memory load they are prepared to shoulder.

Such a progression may seem to be easy enough to accomplish, but it is actually a task that only a master can assume. Too often lesser lights lose sight of the whole picture in their pursuit of minor details that add very little to overall efficiency. Eric Rodwell, in particular, has gone through a process of system evolution in his own partnership, so should be well prepared to pick out the essential elements without being distracted by pet agreements that come and go, but don’t add much to overall efficiency. He has reached the right age for this task. For the sake of bridge, let’s hope his experience and knowledge do not go wasted.

Adventures in the Minor Suits

August 4th, 2011  ~  Bob Mackinnon  ~  No Comments 

Statisticians realize that random events occur in bunches, but to most others coincidences smack of the supernatural. In a previous blog I expounded on the failure of an expert male pair to reach 6♦ on a 2/1 auction that began 1♠ – 2♦; 3♥, the last bid being a splinter in support of diamonds. Soon after in the recent USWBC USA1 Final a pair of ladies showed us all how to do it even if you are in a hurry.

It is considered dangerous to cuebid in partner’s spade suit, as he (or she) will only be encouraged to play the contract on spades, even though the splinter ostensibly agrees to diamonds as trumps. In fact, a bid of 3♠ doesn’t even promise a control in the suit. So responder must take charge, and as the partnership can never stop in 4♦, one might as well utilize that bid as RKCB. Of course, if opener has splintered with the ♥A, as happened in the USBC Open Trials, confusion will reign. If responder goes slowly and bids 3♠ on the prior agreement that this is a cuebid showing the ♠A or ♠K, then the auction can proceed informatively: 4♣ – 4♦; 4♠ – 5♣; 5♠ – 6♦.

It is always gratifying when a partner trusts you implicitly, and I was touched last week when my partner bid a slam on trust, although he was not happy after the fact.

As we know, current standard practice is to allow considerable scope for individual tastes in the choice of bids. I considered what might happen if I opened a stogy 1♦ and someone introduced a major into the auction. I couldn’t see rebidding diamonds, even though there were 6 of them, with my points concentrated in the black suits. So, to avoid future problems, like an up-to-date expert, I upgraded to 1NT, adding a point for the long minor in which tricks might be developed. I was quite pleased when partner transferred to clubs, and I showed that I liked clubs by bidding 2NT. Partner liked clubs even more that I did, so we quickly and efficiently reached the optimum matchpoint contract. A spade was led and 6♣ sailed home. For different reasons neither of us was happy with the result which scored 11 out of 12 matchpoints.

Pard: What went on there?

Bob: You made 6♣.

Pard: But you opened 1NT on 13 HCPs.

Bob: Well, 14 actually. Did you count the ♦J?

My ungrateful partner was displeased because I departed from ‘standard’ practice, and I was unhappy because he could have finessed the ♥Q and tied for top. Some people can’t stand success and I suppose he would have preferred me to have something like: ♠ AQ3 ♥ T84 ♦ KJ87 ♣ KQ8, with slam failing on passive defence. The fact that we scored so well points to the inadequacy of standard bidding on minor suit auctions – 2 pairs played in a minor partial, which in part justified my fears about opening 1♦. Several were in 3NT, some unduly rewarded for making 6 when the opponents failed to take their 3 diamond tricks off the top. I was headed there myself.

Be that as it may, we can see that the acceptance bid of 2NT established the good fit in clubs, and the point had reached where exploration could have moved the basis of decision from general expectation to specific exploration. In general terms responder can count 6 losers and may expect 5 cover cards, so normally he should expect to make 12 tricks in clubs. However, this should be confirmed with specifics, as the ♦K may not provide cover in this case. With nothing wasted in diamonds, he might even opt for a grand slam. It is too early to rush to judgement, but the problem is how to proceed. Some might use 4NT as RKCB, but I think 4NT after a NT bid should be used as a safe resting place that enables slam exploration above 3NT. The simplest solution is to bid 3♥ and see where that takes one. Having agreed to clubs, opener can see this is now a slam auction.

Here is more table talk that should tell you something about our club.

Nice Old Lady: Here comes Bob – we actually had a sort of conversation on the way to the club.

Bob: Well, we had a conversation of sorts – I complimented you on your sunglasses, and you told me about your great-grandchildren’s pre-school experiences.

NOL: Oh, dear, I guess I hadn’t turned on my hearing aid.

We all had a good laugh and then she took us to the cleaners in 3NT. Her bidding is as disjoint as her conversations: she bid Stayman with 9 HCP and 0=3=5=5 shape. Innocently against 3NT I led a diamond from JTxx setting up 5 tricks in the suit. By the time I left her table she had vaulted temporarily into first place.

Back to higher things at the USWBC Finals where a grand slam was missed at one table, bid at the other. It was another of those minor suit hands that give so much trouble.

Here we see a combination of a splinter bid and a key card asking bid, together with an expression of slam interest (the 2♠ bid). Opener showed her strength and the weaker hand took charge. They gained 13 IMPs when at the other table the final contract was 6♣. Nevertheless, the optimum contract is 7♣. The key to the hand is that there is nothing wasteful in hearts opposite the undisclosed void. With the ♣T looming large I prefer opening 1♣ on the actual hand, being prepared to bid clubs, diamonds and hearts up the line, because partner will more readily to try for slam with the ♣A than with the ♦QJxx. On the above combination the bidding is easy after 1♣ – 2♣. However, Campanile-Stansby play the latest bit of razzle-dazzle, 1♣ – 1♦ as showing hearts and 0+ HCP, so a 1♦ opening bid is systematically preferable, to say the very least.

Precision Big Club Auction

In Precision after an artificial 1♣ it is the opener who is in charge of the auction, and he needn’t describe his awkward shape. That makes the bidding easy. After the start 1♣ – 2♣ it is pretty much a matter of whether to bid 6♣ or 7♣. The first 2 steps have been taken: 1) finding the fit, and 2) establishing trump suit solidarity The rest is straightforward when the opener has a simple asking bid structure at hand. First he establishes the fact there is no 4-4 heart fit, but there is a double fit in the minors. (If a 4-4 heart fit existed, the final contract might still be 6♣, but hearts would need to be very well stocked to prevent a loser in the suit.) He asks in diamonds rather than clubs so as to uncover the critical ♦Q. He finds 4 controls that may be ♣A, ♠K and ♥K, but the void in hearts discloses that the 2 black aces are held. He bids 7♣ because the clubs will be longer than the diamonds on this sequence and a losing diamond might be discarded on the ♥A if necessary. He has determined the total controls, and 4) the exact placement of the controls, in shape and high cards. Responder has passed information passively.

A well-bid slam sequence contains the aforementioned 4 elements, which may occur in differing orders. Some players don’t like opening 2♣ with 2-suiters, but if one uses control responses the task becomes much easier. Last week I opened 2♣ on ♠ A ♥ A7 ♦ AKQ65 ♣ KQ853 and partner responded 2♠, showing 3 controls, obviously the ♣A and a major suit king. I bid 3♣, he bid 3♦, I jumped confidently to 7♦. What is remarkable is that this scored 10 out of 12 matchpoints. No need to worry unduly about missing 7NT.

Let’s look at another USWBC slam that was misbid by a pair of champions. Responder lazily neglected finding the 4-4 club fit.

It might be said by way of apology that 6NT was unlucky to go down on a spade lead, ducked to the ♠Q, but apologies don’t carry much weight when a cold 6♣ and was bid at the other table. The major-suit orientated bidding system failed to satisfy the primary requirements of finding a 4-4 fit and determining the solidarity of the suit.

The hand on the left whispers ‘No Trump’ in my ear, but I resist temptation, in part because of the minor suit aces. I would open 1♣ on the reasonable hope that partner will declare in 4♥ or 3NT with spades protected, but once in a blue moon there will be a situation in which the ♣T plays an important role. The hand on the right screams ‘Slam!’ and in practice there was available an asking bid, but the answer didn’t provide the information that was needed to find the excellent club slam. The auction stands as an example of pseudo-science at work. It is inappropriate to extend this attitude of ‘majors or no trump’ into the slam zone. The greatest irony is that despite all the emphasis placed on the heart fit, the pair didn’t declare in 6♥ which makes even with the ♥K offside.

Of course, it is all too easy to criticize on the basis of one 13 IMP loss. That’s fast food for hungry bloggers. To look at a different configuration, let’s see what happens when the opener bids 1♣ and responder is short in clubs. With slam in mind she responds with 1♦.

The bidding is entirely natural, hence co-operative. When the opening bidder can’t bid 2NT to show a spade stopper, and can’t bid 3♥ to show a heart control, responder jumps to what she thinks she can make. The auction is efficient because the 1♦ response takes up so little room. If current systems are so much geared towards major suit games and 3NT, it is of little consequence if one opens 1♣ or 1♦ when holding 4-4 in the minors. If 3NT is the final destination, the length in diamonds may have had little bearing on the decision. In fact, keeping the relative lengths hidden could be beneficial to declarer.

In the slam zone the relative lengths in the minors can be critical and the nebulous Precision 1♦ structure may give cause for complaint. Standard bidders should have the edge, so why not make use of it and distinguish the suits on the basis of strength as well as length? The saving in space represented by opening a natural 1♣ is worthwhile when bidding towards slam without interference. Diamonds needn’t get lost. As always, playing for the normal expectation is neither good nor bad; it is, by definition, mediocre.

As Time Goes By

July 21st, 2011  ~  Bob Mackinnon  ~  1 Comment 

My year is marked with two ritualistic viewings of black-and-white movies from my youth in which cynical hard cases are transformed overnight into idealistic good guys: Scrooge at Christmas and Casablanca on the fourth of July. It is one of those strokes of accidental genius for which Hollywood is famous that Dooley Wilson’s quintessential version of As Time Goes By got into the film and stayed there despite the fact that the actor could neither sing nor play the piano. I remained infused with an appropriately melancholic spirit of resignation after belatedly reading Eric Kokish’s comments on Board 5 of this year’s World Wide Bridge Contest. Once more we were faced by the dilemma of how to make the best out of a balanced hand that contained 17-19 HCP after being forced by the system to open a natural 1♣ . Truly, Sam was right when he sang that the fundamental things apply as time goes by. A year ago I had blogged about this problem suggesting a wide-ranging reverse of 2♦ that included the NT possibility, and recently in the USWBC we came across a pair, JoAnna Stansby and Migry Zur Campanile using a system in which 1♦ is used as a relay to 1♥ to cover a 1♣ opening bid that may be a balanced 17-19 HCP. So the problem has not gone away and it’s still the same old story. Let’s see what Kokish recommends in an uncontested natural auction.

Koach, as he is known, comments ruefully that there is no ideal solution. He notes his approach may miss a 4-4 spade fit, but he prefers it to the more revealing auction that proceeds with total honesty: 1♣ – 1♥; 1♠- 2♣ ; 2NT – 3NT, or more surprisingly to his fans, 1♣ – 1♥; 1♠- 2♣ ; 2♦ * an artificial forcing bid seeking more information. He doesn’t comment on what might follow a jump to 2NT – would 3♦ be a transfer back to hearts? It seems as if the professor has resigned himself to the fact that in the real world perfection, like a rainbow, is both elusive and transitory. Bidding problems only coincidentally have ideal solutions – most of the time a compromise is required.

It is best to think of constructive bidding as an exercise in constrained optimization – optimizing the gain got by increasing the information content of the auction weighed against the loss engendered through guiding the opponents to their best defence. If we examine the above hands we see a division of sides of 6=7=5=8 with a total of 26 HCP. On that basis we may conclude the optimum contract is 3NT played by South, and that the sequence that gets NS to that destination is optimum if it increases the chances of a spade lead and decreases the chance of a diamond lead. The Kokish sequence does that. A more revealing auction in which South bids his 4-card spade suit will decrease the chances of a favorable spade lead, thus it is not optimal.

Of course, initially the players have only a partial picture, so they fill in the details as they proceed. As a passed hand North might decide to respond 1NT to 1♣ to limit his high-card content and show the balanced nature of his hand. This leaves a blank space, but it would be a reasonable approach if 1♣ were artificial and strong, and 8 HCP constituted a game forcing holding. Better still if under those circumstances North were to able bid an artificial 2♦ to show exactly that type of hand, leaving it to South to decide how to proceed. Rather than explore a major suit fit, South might just bid 3NT straight up, judging on the basis of probability that this might well maximize his gain at minimal cost.

This illustrates that it is the nature of the information as well as its gross amount that must be considered in the optimization process. It is not full disclosure, but useful information that we seek, information that guides us to the solution that has the greatest probability of success. There is risk involved by being selective and keeping partner in the dark, but full disclosure also involves risk, especially, as here, one is likely to end up in 3NT regardless. South, holding the strong hand, is in the better position to judge.

Next, we look at the results obtained when the deal was played at 4730 tables world-wide. From these we can see what would have been the result of various bidding sequences, for example, what would been the cost of stopping in a part score when holding a combined 26 HCP? Surprisingly, missing game might not be as costly as one expects.

From this table we gather that the most frequent contract was 3NT, reached about 60% of the time. (The score 600 is ambiguous as it could have resulted from a contract of 5♣ .) If declarer made 630, not difficult after a spade lead, he would score 87% of the matchpoints, whereas if he went down 1, he would score around 18%. The contract was defeated on more than 50% of the cases, so on aggregate it would appear not worthwhile to bid the game as the cards lay. At IMPs the aggregate when vulnerable is more favorable. However, as we have indicated above, making or going down is not merely a matter of a flipping a coin, it more a matter of loading the dice – making 630 means declarer did not get a diamond lead, and that happy situation depends greatly on the bidding sequence chosen. To paraphrase Shakespeare, if ‘tis to be done, ‘tis best done quickly – without mentioning spades.

Let’s consider the effect of a broken sequence where in an uncontested auction the partnership does not come to grips with the fact that they should normally reach 3NT on a combined 26 HCP. Suppose the bidding proceeded as in the following 2 sequences

In the first sequence an overly subtle South was disappointed when North passed as he felt his 2♥ was an encouraging move when, if minimum, he could have passed 2♣ in a known fit. North made 170 and was rewarded with a score of 53%. In the second sequence North perceived a weakness in diamonds, so chose the safest part score, making 150 for a matchpoint score of 48%. Despite the weak efforts both contracts scored close to average.

Some NS pairs might congratulate themselves on avoiding a 3NT contract that ‘should be defeated’. Their thinking is directed towards minimizing the loss if they happen to make the wrong decision by overbidding. Certainly, neither 4♥ on a 4-3 fit nor 5♣ on an 8-card fit appeals to many players, so it becomes largely a matter of 3NT or a part score.

The Contested Auction

The art of competitive bidding lies in withholding information from the opponents while welcoming information coming from their direction. Very often the opposition’s contributions, if accurately evaluated, given some credence if not afforded full credibility, help greatly in determining the optimum contract. Light actions are especially useful. Here is the full deal with a hypothetical construction of EW actions.

East is happy for a change to be able to open the bidding in a minor suit in which he holds full values. South doubles planning to bid NT later – with better diamonds he might bid 1NT immediately, but with good spades he can afford to await developments. West makes a silly bid on the belief that he who holds the spades rules the world. South shows extra strength by bidding 2NT and North has full values under the circumstances. When South belatedly shows tolerance for hearts, North is able to raise himself to game on the decent quality of his trump suit and his lack of values in the suits advertised by the opposition. With secondary values in diamonds he would be more cautious. He is prepared to believe East has an opening bid in which case West is exposed as a fraud.

In competition a player should believe his partner and suspect the opposition. It is very helpful if partner has a bid that promises values in a balanced hand. The takeout double serves nicely in that capacity. In the uncontested auction South had a problem separating the tasks of showing a strong balanced hand and showing a hand that could play in spades. A double is more flexible than a bid of 1♠in the uncontested auction. West’s silly bid simplifies the NS auction by eliminating the spade suit from consideration, but if North is put off by this nonsense NS may stop short of game, nevertheless, if NS play even in a partial heart contract they will score above average thanks to this dubious action.

If East’s opening 1♦ bid is of the nebulous variety and South ends up declaring in 3NT, West may lead a spade in the mistaken belief that it is safe. With little hope of developing tricks in the spade suit and no entry to cash them if they were to be happily supported, the most likely result is that East will eventually find himself endplayed after an asute declarer has obtained a full count of the hand and exits with a diamond. That may account for some of the 600 scores. As Kokish points out, the ♦ T is a valuable entry to the West hand which could enable East to avoid an endplay in the heart suit, so leading the ♦ T at the start, as some would, could prove disastrous. The ♦3 is best.

One further point: if West boldly jumps to 2♠ , can NS possibly extract a penalty? An examination of the results indicates few pairs were able to extract penalties, but when they did, they scored very well. Even +300 scores above 62%. All that is needed is for North to double 2♠competitively, showing a balanced hand, and for South to leave it in. Easy to see after, but at the table most players bid on in the hope of making game, so West goes unpunished and can continue to act with impunity. In this ‘let’s pretend it didn’t happen’ mode, NS are merely attempting to return to the normal contract of 3NT. South can see the danger in 3NT as the diamond situation is fragile, so should be inclined to pass for penalty in hopes of a good score no matter how many undertricks are realized.

That argument may not convince some who may ask, ‘what is North to bid if he has an unbalanced hand with hearts and clubs?’ The answer is 2NT, for takeout. This is logical, for with a balanced hand and the values to bid a natural 2NT, it is better to double and give partner the option of converting to penalty. For distributional hands with game ambitions, North has a choice of 2 cuebids, otherwise, with no defence, he just bids his best suit. That’s a fine collection of bidding tools based on a balanced double.

We conclude this one deal encompasses many of the features of tournament bridge. Fate was kind to some bold ones who took their chances as well as to some undistinguished others who were awarded an average plus for merely muddling through. It rewarded skill in declarers who devised a clever endplay when the opportunity presented itself. A few lucky ones get on the night plane to Lisbon, while most are left behind in Casablanca. Prominent among the innocent victims were the Wests whose partners wouldn’t open in a minor suit on less than 12 HCPs, and the Easts whose partners had a tin ear and led the ♠ Q, regardless. Yes, it’s still the same old story – so shuffle, deal, and play ‘em again, Sam.

More USBC Slams

July 4th, 2011  ~  Bob Mackinnon  ~  5 Comments 

Thanks to BBO reportage the 120-board matches played in the USBC Trials give us a good sample of deals played at a high level of competence with which we can test our ideas and distinguish between faulty assumptions and brilliant insights. Recently commentators have got away from the idea that the team that gets the slams right wins the match. It seems competitive tactics have gained prominence, because there are more part score deals than slams. That affects how one goes about bidding a hand. However, as there are several competitive deals bid under uncertain circumstances, the law of averages tells us that in the long run gains and losses may balance out on the hands which can be played randomly by either side. This was the case in the 2011 USBC Final where 2 ‘young’ teams with similar tactics duked it out.

There was a contrast of styles in evidence in the semi-final in which the veteran, value-driven Welland team (Welland – Bramley, Schermer– Chambers) faced an active Diamond team that featured 2 Precision partnerships. The swings on 6 hands on which a slam was bid accounted for 48 of the 50 IMP winning margin, Welland gaining on just one hand. This strikes me as odd, as one would expect solid citizens who always have their bids to have the advantage over those who by design open on garbage. What happened?

In the previous blog we introduced the idea of an information filter. Bidding in a natural setting is a ‘broad band’ filter that is designed to express general values within the context of the individual’s hand. Bids are selected in a setting in which the general nature of the hand is taken into account. Usually good minor suits take a back seat in the bidding schemes geared to finding major suit fits. This makes sense on the basis of the probable outcome, but minor suits slams, being improbable a priori and may be missed on the rare occasions when they do arise. Bidding according to the Law of Total Tricks, a statistical rule that reflects normal conditions, may prove faulty when unusual distributions are in play. A slam exploration should provide specific information that separates exceptionally fortunate conditions from what is most probable.

Normally accurate slam bidding in a suit requires an approach in which the hands being bid are considered in a narrow sense with regard to a mutually agreed trump suit. The bidders must consider how their values fit into a particular requirement for 12 tricks for which tricks can be generated through judicious cross-ruffing. Asking bids and cuebids act as ‘narrow-band’ filters that pass exact information that is not subject to speculation based on probability. That’s the theory – let’s see how the results support this view.

When More is not Enough

Here we see 2 balanced hands with wasted values in the heart suit. How much nicer it would be if the ♥K were the ♠Q, for then 6NT would largely depend on the clubs coming home. Bramley and Welland got it wrong when Welland bid 3♠ rather than signing off in 4♠, and Bramley, not ruling out a Grand Slam with 10 controls and stuffing in his long suit, launched an inquiry with RKCB. The double of 5♦ directed the killing lead. Welland did altogether too much holding a weak, balanced hand with weak support – yet another case of the tail wagging the dog. I think they are wrong those who argue that Bramley should have jumped to 6♠ over 3♠. Over a weak 4♠ raise, yes!

The Precision auction at the other table illustrates that a HCP evaluation worked better when there was no ruffing potential to add to the number of available tricks. The bidding was restrained, and the club suit was entirely lost – a potential disaster one might think.

Basically all Platnick knew was that the partnership didn’t hold more than 30 HCP, less than the usual requirement for 12 tricks without ruffs. There is not much to recommend in the jump to 3NT other than it was to the point, but the final pass was good as declarer made just 10 tricks while gaining 12 IMPs.

Fortune Favors the Shapely

Next we look at a deal where vague description common in a natural auction, but made here by a Precision pair, worked in their favor by getting them to a slam missing 2 cashable losers. Less information resulted in more IMPs. In contrast to the previous deal, the 2 hands were balanced in HCP values (13 opposite 14 HCP) but one hand contained a known singleton in a side suit. The ‘blind’ opening lead proved critical.

The bidding makes a lot of sense until you look at Greco’s hand which he described as a maximum when he responded 3♠ instead of 3♣, the response that shows a minimum. His concept of a maximum greatly differs from mine. One important feature is trump solidarity, another, controls, especially aces. Bidding should be geared towards those features. With distributional hands there is less need to transmit a complete description of the partnership’s holding to guide an opponent to a killing lead. Given a tempo, inevitable losers may disappear. The opponents may not attack a side suit for which one has shown length, and with the AK missing the chances of the opening leader holding both top honors is low. That doesn’t mean one should count on split honors, but it does mean one shouldn’t be too concerned when the killing lead is found with little guidance.

In the previous blog we noted that in the final Greco-Hampson had a similar auction based on a Precision 2♦ opening bid in which Greco again promised a maximum he didn’t have. Hampson didn’t bid the making slam on that occasion and lost 12 IMPs. If he had remained consistent he would have gone on. Nonetheless, the evidence indicates this concept of ‘maximum or minimum’ is not working well. If one is asked to describe one’s hand as being ‘above average or below average’ the expectation is that half the time one would categorize one’s hand as being ‘above average’. Such a process doesn’t provide much in the way of distinction as it merely conforms to expectations. A better response structure would distinguish between ‘slam suitable and not.’ Such a distinction should include information concerning the number of controls held.

Welland – Bramley suffered a lack of resolve in a similar situation where one hand was known to be shapely, but information on the total number of controls was lacking.

Welland was able to give a complete description of his shape, but to him 5 controls represented a minimum. Recall that Greco with 3 controls thought he possessed a maximum under similar conditions. The answer to a question one asks should provide the information one needs. If Welland were able in response to 4♣ to disclose that he held 5 controls, a subjective description would be transformed into hard facts and Bramley could easily have bid 6♣ and tied the board. One sees that a vague, general description relating to the expected HCP total for an opening bid is not suitable when both hands feature shortage. Even if Bramley were 2-2 in the reds, slam would have been biddable if he knew the necessary controls were in place. I think with 5 controls one should encourage slam, whereas with 3 controls one should let it go.

Splintering with an Ace

Shortage in a side suit adds tricks when ruffs can turn losers into winners. That can be taken into account easily enough, but the bidding becomes more difficult when the shortage is a singleton ace or even a singleton king. Partner shouldn’t discount his high honors in that suit as the shortage is no longer a liability opposite a strong holding. That may be obvious, but look at what happened on a hand where at both tables a player in a 2/1 auction, according the BBO commentator, splintered with a singleton ace.

Looking at the 2 hands one feels it should be easy to reach a contract of 6♦ once responder bids 2♦, whether that constitutes a game force or not. If the opening bidder could discover that responder held 5 controls, the ♣A, ♦A, and ♥K, he would surely be prepared to take his chances in 6♦. How can he go about obtaining the information without getting too high if conditions aren’t ideal?

Mashall Miles in his book ‘It’s Your Call’ reasoned through examples that one’s choice of bids should be directed towards reaching the most probable good result as one sees it at the time. This constitutes filtering information so as to steer towards a suitable conclusion. Those without shortage assume the world is flat, whereas those with shortage know it isn’t. Let’s speculate in this light after the start 1♠ – 2♦.

Chambers: This has become a slam exploration in diamonds.

Schermer: This is a 3-card game forcing raise in spades, and not a great one at that.

The major task at hand for Chambers was to convince partner that he liked diamonds a lot, and he used a splinter to 3♥ conveys that message. Schermer continued to think that a contract in spades was where the bidding was headed,

so he bid accordingly. With a flat hand he thought probabilistically in terms of the a priori odds, and a splinter on a singleton ace is extremely rare (therefore ill-advised).

So what is the solution? Opener should raise diamonds directly. If 2♦ is a game force, so much the better, as 3♦ can be the start of an informative sequence. Responder must resign himself to these facts of life: 1) if you can’t describe your hand with one bid, it may require several, 2) in a natural sequence ambiguities will arise, and 3) the more information exchanged, the better the position when making a final decision.

So, over a raise to 3♦, responder should bid a descriptive 3♥. Some might suggest 3♥ is a ‘torture bid’ as it leaves open too many options, but isn’t flexibility good? It is especially good when one holds a balanced hand with 5 controls and the bid coincidently saves space. Let’s see what Bob2 has in mind.

Bob2: I am not sure where we are headed. For the time being I’ll accept partner’s suggestion of diamonds as trumps and bid accordingly. Partner knows as well as I do that any game is preferable to a diamond game, so spades can wait while I describe my features. As my best suit is hearts, I’ll bid them next. I won’t be surprised to hear 3NT.

Bob1 bids 3♠ to indicate club weakness, therefore, strength elsewhere. The bid of 4♣ indicates interest in slam without being fully committed to it. With a stronger hand for spades responder could have launched into RKCB over 3♠, so a bid of 4♠

shows a willingness to stop in game. Bob1 has to look back over the entire sequence and resolve whatever ambiguities exist. Looking back and guessing with more information is better than looking forward and guessing with less. Responder’s

Goldilock’s approach was just right: too weak for slam, too strong for merely signing off in game. Bob1 bids what he thinks can be made, preferring the sure 9-card fit to the probable 8-card fit. 6♠ would have made as well as 6♦, but getting to the safer slam is always commendable at IMPs.

I don’t intend to suggest that natural bidding is the best approach, rather that it is the exchange of information that is the key. It is pseudo-scientific to use bids that have the appearance of science without actually providing the necessary information. Numbers are the basis of science, so scientific bidding is quantitative in nature rather than qualitative.

Let’s consider the Ogust 2NT asking bid. The primary objective is to determine whether the preemptor’s hand is game-suitable, so simple good-bad distinctions are sufficient for that task, but not for slam exploration. Compare this to the Precision 2♦ auction where opener responds 3♠ to a 2NT ask. As the partnership is already committed to game, it is now a question of whether the hand is suitable for slam. So a further 4♣ ask must be geared to slam, and the responses must be designed with that objective in mind. Similarly with the Welland-Bramley hand where 4♣ was the asking bid, so game was not in question. The response to 4♣ must be specific to the question at hand: slam or no slam?

On the last hand, after 1♠ – 2♦, the partnership is forced to game, so any questions must be related to slam-suitability. Who is going to be doing the asking? If a 3♥ bid is a normal splinter, a ‘telling’ bid, then responder should take the initiative. With the actual deal it would be better if 3♣ could be used as a slam-try relay to diamonds, asking responder to bid 3♦ so that opener can cuebid his aces up-the line. This allows for some flexibility on the part of an apologetic responder who could bid 3♠ or 3NT as a negative response to a slam try. A simple raise to 3♦ by opener would show a lesser, balanced hand without slam ambitions. It seems that we need some improvements over the present state in which good players feel they are obliged to make splinter bids on singleton aces.

So what if the bidding starts: 1♠ – 2♣? Please, one problem at a time.

Grand Slams in the USBC Finals

May 31st, 2011  ~  Bob Mackinnon  ~  2 Comments 

The 2011 USBC was won in impressive fashion by the Bathurst team, six young men in their 20’s and 30’s. For years the ACBL has decried the lack of popularity of our game among American youth, so is this the advent of the renewal that they have been hoping for? I somehow doubt that, because bridge as we know it is contrary to the post-Woodstock culture of ego-based superficiality within the context of an extremely short attention span. One must be careful of what one prays for in case one’s prayers are answered. To the ACBL, which runs its operations as a welfare state where masterpoints serve as entitlements, an influx of youthful enthusiasts would be like unto an invasion of rowdy collegians into an old folks’ home. If Youth were to prevail, rules and playing conditions would change drastically, much to the annoyance of Old Age.

This is not all hypothetical as there is a history to guide us. Some thirty years ago Marty Bergen introduced a style that so greatly upset the Establishment that border fences were created to guard against creativity and vigor. The USBF was one fallout, ACBL senior events, another. Bergen has left the table, but most of his innovative ideas have prevailed, as evidenced by the actions of the younger players in this year’s premier events where his ‘Points-Schmoints’ philosophy is prominently invoked.

Be that as it may, we want to look at the results of the 2011 Finals to see what we can learn something about the way bridge is being played today at the highest levels. Youthfulness is a side issue; cards are cards no matter what. We start with the easiest situation to analyze – slam bidding. In their small slams the Bathurst team gained hugely (61 IMPs) over the Diamond team which had 2 pairs playing Precision. When a grand slam was bid, the advantage swung greatly (52 IMPs) in the other direction. This contrast between small slams and grand slams is the subject of our first investigation.

The Need for Information Accurate slam bidding requires information that is both reliable and relevant. This is in contrast to what is desirable in competitive auctions where bashing works as uncertainty can be played upon advantageously. In slam bidding one’s fate often depends on what partner reveals. His input must be gauged on its usefulness, and sometimes one wishes to gain information on a particular aspect of his holding. Here is a very simple, but instructive, example, that illustrates that ‘Bridge is an Easy Game’ when you follow basic principles and get it right.

First, consider the 2 hands if Lall, playing Precision, were allowed to open 1♣. Grue would respond 1♦ (0-7 HCP), and Lall would have to make a second forcing bid in order to elicit more information. Possibly 1♠ would be forcing and they would be able to proceed slowly towards slam. Let’s see how Greco’s light opening bid changes that. In fact, it helps, because Lall is able to make a forcing bid that identifies an area of particular interest to which information is to be directed, which an opening bid of 1♣ does not do. Grue’s 2NT shows ‘values’ in the context of a minor suit contract. This was enough encouragement for Lall who simply jumped to 6♣, a fine demonstration of the Bash Brothers’ style. We will not criticize him for missing a Grand Slam when 13 tricks materialized on a cross ruff which set up a long spade trick on a 4-3 split.

At the other table 1♥ was opened and Gitelman, the oldest participant at 46 years of age, overcalled 1♠. If he had been able to open 1♠, his partner would have made a response on even less than he held, and there would have been no story to tell, however, the fact that a 1♠ overcall is nonforcing and often of the garbage variety meant that Moss was no longer obliged to protect a partner who held unlimited power. He passed, and away went 15 IMPs on Board 4. The problem was that in terms of spades alone, his hand was not that promising. This shows how a simple, light opening bid can destroy the ability to communicate meaningfully. The old solution of doubling with a good hand and making it up later doesn’t work that well; partner is confused and the information he transmits may not be directed towards the most important area. Perhaps we need to define 1NT as ‘semi-forcing’ in response to a vulnerable major suit overcall, or is that too restrictive on those who would overcall on garbage?

Here is a hand where the concept of ‘values’ was not well enough defined for Greco and Hampson to reach a slam bid and made at the other table. Even though Hampson had detailed information on the distribution, his knowledge of strength was vague.

2♦ was a Precision 3-suiter, 2NT asked for shape and size, and 3NT revealed 4=4=0=5 shape with a ‘maximum’, which usually requires 14-15 HCP. A relay to 4♦ followed by 4♥ indicated general slam ambitions without the resources needed to take action through RKCB. This sequence shifted the captaincy to Greco who made the final decision.

One may say that Greco was right to pass as he had less than might be expected for a ‘maximum’ reply. Instead of 3NT he could have responded 3♣ to 2NT to indicate a non-maximum, which in my opinion, apart from the distribution, is what he held. To qualify as a maximum, he should be rich in controls with good secondaries in the majors and 2 of the top 3 honors in clubs: ♠ AJT6 ♥ QJ93 ♦ — ♣ AQT86, just 14 HCP with 4 controls, so not a total maximum, but flexible enough to withstand game tries with only 12 HCP opposite. So when Greco was asked for his opinion concerning 6♥, understandably he decided, ‘no’, although 13 tricks were readily available. Lose12 IMPs on this one.

The problem was that there was no working definition of what constitutes a maximum. If Hampson could rely on the characterization to resemble what I think is appropriate, he could have bid 6♥ over 3NT without further consultation. After all, he made 13 tricks opposite a hand that wasn’t really a maximum. So in his approach he definitely showed a lack of resolve. It is often a mistake to give partner too much leeway. In the previous hand Lall assumed that 2NT showing non-specific ‘values’ meant something good was going to happen. On this hand the designation of ‘maximum’ should have engendered the same, if not more, enthusiasm. With little space remaining for exploration below game, one should act with optimism in the face of uncertainty: partner may have his bid.

Of course, if one can obtain the relevant information even from a reluctant partner, one should do so. Here is an example of an enthusiastic Precisionist on the Bathurst team who failed to see far enough ahead to ask the right questions.

Justin Lall opened a Big Club with high expectations of playing in a spade slam. Hampson showed a club suit and partner, Joe Grue, admitted to long diamonds within a game forcing context. If at this point Lall had to guess, he might well have bid 6♠, as he needed little in the way of spade support. The key to higher things was the diamond suit. Even though Lall had little thought of playing in a diamond contract, it doesn’t hurt to ask, when one is in a position of being able to force the final decision. So his first move should be to determine the quality of the diamond suit opposite. Let’s say he bids 4NT over 2♠ as RKCB in diamonds and receives the reply of 5♥ . Now he bids 6♠ and Grue should feel obliged to pass. By showing spades and evoking RKCB in spades, Lall doesn’t get the relevant information needed and makes a wrong guess, losing 11 IMPs. To make matters worse in theory, but better in practice, Gitelman and Moss don’t go beyond 4♠ on a 2/1 auction that goes as follows: 1♠ (2♣) 2♠ (Pass); 4♠ all pass. Again, a seemingly harmless action caused great damage to an auction when the player with the strong hand didn’t extract useful information concerning a side suit. Jumping to 4♠ put the emphasis on description rather than on inquiry, leaving it to the holder of the weaker hand to make the final (wrong) decision on the basis of inadequate information.

Youth likes its freedoms and has difficulty adhering to the principle of captaincy. There are 2 primary elements involved: the Captain and the Crew. It is wrong not to assume the captaincy when it is appropriate to do so. We have seen where Gitelman failed in this regard on 2 slam hands, partly because he was disinclined to take charge, a reluctance tempered by past experiences, no doubt. The more common failing lies in the mutiny of the Crew. The Diamond team was in deep water when Wooldridge threw them a rope on Board 74. He held: ♠ Q9765 ♥ AKJ72 ♦ — ♣ A63, and saw partner open 1♠. The ensuing auction allowed him 7 descriptive bids, but when Hurd, after an RKCB enquiry, signed off in 6♠, Wooldridge mutinied and bid 7♠ on the basis of his diamond void. Greco and Hampson held 11 diamonds between them, but had wisely remained silent throughout the auction, otherwise Wooldridge might have recognized clubs as the weakness with ♣ J875 opposite his ♣ A63, not diamonds with ♦A4 opposite his void.

It wasn’t until the players got to Board 118 that a pair was able to bid a Grand Slam in a decent manner. Before that one could conclude on the evidence it would have been best to put Grand Slams out of their minds altogether. Grand Slams allow for little margin of error, a margin often exceeded with a bashing style. This is a sad commentary to make on teams that are near the top in the world, nonetheless, Greco and Hampson in desperation managed too late to put it all together on the following combination.

The largely natural auction shown above is a stripped-down version of their highly artificial sequence. Sometimes artificiality serves only to cloud the issue. A natural approach works here because the controls in opener’s hand are well placed in his long suits. It is a matter of establishing a fit, finding the supportive aces and taking the plunge. Greco was well placed to assume the captaincy and set the final contract. By the way, I understand from my reading that Greco’s hand would not qualify as a forcing club bid under British rules as it contains a mere 15 HCP. Evidence of stultification and decay, this reveals a pathetic reliance on point count to define strength.

The auction at the other table was interesting as it showed the disruptive power of a ‘noisy’ bid. Gitelman opened a weak 2♦, and Wooldridge, holding Greco’s cards, made a Leaping Michaels bid of 4♣. Hurd, holding Hampson’s cards, boldly jumped to 6♣ without attempting to find out more about partner’s holding, which is understandable as 4♣ didn’t promise the world. As noted, Wooldridge’s hand qualifies for a forcing bid that establishes the captaincy, and the aim should be to extract information from partner before making the final decision. Let’s suppose that over a weak 2♦ an overcall of 2♥ were to be considered as forcing. We suggest the following route is a live possibility:

2♥ (F) – 2♠(F); 3♣(F) – 3♦(GF); 4♣ – 4♦; 5♦ – 5♠; 5NT – 7♣.

Over a preempt new suits should be treated as forcing, removing the need to go jumping about in the subsequent exchange. The cue bid of 3♦ sets trumps, and information on suit controls is exchanged in a cooperative mode. 5NT asks for extras, and advancer is able to bid the Grand on the basis that the ♣A must be what partner seeks. However, the bidding would be the same up to 5NT if advancer held the ♠AKT985 and ♣ JT65, and it would not be clear that he should stop in 6♣.

Natural bidding sequences contain ambiguities that are hard to resolve especially when both hands encompass shortage in partner’s long suit. It becomes difficult to gauge the value of secondary honors in the long suits as support cards in a better-fitting, mutually agreed trump suit. Neither side likes to cuebid their shortage lest it be misinterpreted as showing an honor card. Greco was able to use 5♠ as Exclusion Blackwood to obtain a precise description from Hampson, who simply jumped to 7♣ – a very good guess.

Without specificity bidding to a grand slam is hazardous. That argues for specificity, doesn’t it? Natural bids are often chosen in the context of the hand taken as a whole. The information contained is broadly based. For example, one may bid a major before a longer minor or avoid bidding a bad suit in a good hand. We may think of an asking bid as a device that filters out general information while letting through exact information with regard to a small area of interest. Exclusion Blackwood is a filter that focuses on specific controls by excluding a designated suit concerning which any information is largely irrelevant. We show how ‘narrow-band’ filtering works in a Precision auction with asking bids on an infamous deal from the 2011 Vanderbilt Final in which both teams using 2/1 methods reached an impossible 7♦ through a misunderstanding regarding a key card asking bid. The losing team would have won if they had stopped in 3NT!

The asking bid structure here is a crude filter, as at the end there is much about the East hand that West does not know, and vice versa. West initially is the captain and up to a certain point East merely answers questions. When East shows a long diamond suit, West should realize that the conditions within this 9-card fit are of primary importance regardless of the final contract. (Opening a natural and unlimited 1♠ gets the partnership off on the wrong foot.) West checks the quality of the diamond suit. He finds 2 of the 3 top honors, so the suit is not solid. He then asks for the total number of controls held. There is no need to exclude spades from consideration, as West can see that East cannot hold a control in the spade suit. From his holding in clubs and hearts, West can deduce that East’s 4 controls consist of either ♦A – ♥ A, or ♥ A – ♦K – ♣K, or ♦A-♦K and ♣K. In any case one certainly doesn’t want to be in 7♦. He signs off in a general strength 3NT yielding the captaincy to his partner. East has enough undisclosed extras (♣Q and ♥ Q) to bid 6NT opposite a hand holding at least 16 HCP and diamond support, despite the void in spades – another case of don’t ask and don’t tell. East doesn’t know everything, but he certainly knows enough to get to the best contract.

When someone asks me at the table, ‘how could I have bid the slam?’ I often answer, ‘Just go ahead and bid it – you can never guarantee success.’ Contrary to current practice, if you can maintain your composure, exchange exact, useful information, and get the easy ones right, you can go a long way.

Woolsey and Stewart’s Cavendish Win

May 16th, 2011  ~  Bob Mackinnon  ~  2 Comments 

This year the Cavendish Invitational IMP Pairs was won by Fred Stewart and Kit Woolsey, playing Precision, in the classic come-from-behind fashion. There were entered 36 pairs, each playing 4 boards against the other contestants in random order for a total of 140 boards over 5 sessions. The score on each board was an IMP score totaled against all the other scores obtained in the same direction. One could score very well if an opponent made a gross error and let you make a high scoring contract.

The main thrust of the bidding was aggressive, a logical approach that some commentators in the early going found objectionable. To reach a game that might be made on less than optimal defence is a way to score very well on the board without it costing much. This accounts for the tendency to bid speculative games (especially 3NT) without giving away information. On Board 3 Jacek Kalita was criticized for his alpha-male tendencies when, nonvul vs vul he bid 4♠ on this auction:

Kalita held: ♠ KQJT8642 ♥ K76 ♦ — ♣ Q2. The point being made was that Kalita could have bid a safe 3♠, making 140. That is true enough, if the opponents would not bid to 4♥ despite his efforts to divert them. If they had, 4♥ would make, so Kalita would have to bid 4♠ or concede a vulnerable game. If he belated bid 4♠ he could be doubled, and incur a bad score in that way if 4♥ was going down. So Kalita’s ‘aggressive’ bid was actually a largely defensive move – a preempt that might actually end up making 10 tricks. If Kalita were really brave he would do as the commentator suggested, bid 3♠, then bid 4♠ over 4♥ , daring NS to double him. Brave, but foolish. If one makes the opponents guess, it is wrong to think subsequently that they have guessed right. That gives the opponents 2 chances to be right, first, by bidding 4♥ , if that makes, and second, by doubling 4♠ for a good score even if 4♥ makes but is not bid in the other tables. In other words, the opponents can hardly go wrong against that approach.

The field was full of famous names, so the contestants couldn’t sit back and expect gifts due to faulty play. Gifts from the bidding were a different matter, as many of the pairs represented infrequent partnerships, and many of those were ‘rubber bridge’ players whose methods tended to be psychological rather than scientific. They won’t win many bidding contests. It would be important to score well in the first round before such partnerships got their rhythm, and in the last round when mental fatigue and disappointment may become factors for those who relied on inspiration and deceit hand after hand.

Commentators are there primarily to guide the viewers with regard to the play on a hand-by-hand basis. Similarly, in books readers are presented with a number of deals with which to sharpen their bidding or play. The emphasis is on developing a sound technique. Less attention is given to an overall strategy, the idea being that if one plays each hand in a theoretically optimum fashion, one is bound to come out a winner. Technique helps immensely, of course, but in practice a bit more is needed. Some would say the rest is ‘luck’, but in this world one often makes one’s own luck. At bridge the best way to become lucky is to overbid.

Here is a list of the top 7 finishers with their final scores and average per session.

One can see that if one wishes to be in contention one needs to score over 350 IMPs per session. If one bid and made a slam when half the field played in a vulnerable game, one would score 117 IMPs on that board. If on defence one beat a vulnerable game that half the field made, you would score 108 IMPs. The scores are close, but which is easier to achieve? Reaching a close slam is easier because one may develop the necessary skills beforehand and it may not depend on what the opponents are doing. Out-defending the field is harder, as it requires specific, unpredictable circumstances that include the uncontrollable actions of the opponents. Through the development of a solid bidding structure a partnership controls what is controllable.

Winning requires consistency. As noted in previous blogs, the best strategy in a marathon is to get off to a good start, stay in a bunch close to the front runner, and sprint at the end. This is easier than getting ahead and staying there to the finish. This tournament provides us a perfect example of how this works at bridge. Here is a table of the scores over the 5 sessions for the 7 top finishers. The average score of the leading pair is given on the right.

The numbers tell the tale. The German Scientists got off to a good start and led the field after 2 rounds. Thereafter they faded to average results and finished a far seventh. The seasoned pro pairs who finished 3rd through 5th started poorly over the first two sessions, put on a big rally in the third session, averaged over 400 IMPs over the last 2 sessions, but fell short coming from behind. Hurd and Wooldridge produced steady results improving with time and were in second place after 4 sessions. 690 IMPs behind the leaders, Bobby Levin and Steve Weinstein. With youth on their side, one might have expected they would have maintained their pace and consolidated their ranking, but it was not to be – the last session was a big disappointment.

Levin and Weinstein had produced a terrific score over 4 sessions, averaging 645 IMPs per session and many thought the game was over, the race was run. They would be worthy winners, highly respected for their adherence to their well-practiced bidding system and their skill as declarers and defenders to see through the cards. If the game had been just 2 boards shorter (or 2 boards longer?) they would have held on to win for the 4th time in 5 years. Lurking behind in 4th place behind Billy Cohen and Ron Smith were the veteran pair, Kit Woolsey and Fred Stewart, who had won the Cavendish between them a total of 5 times, but in other partnerships. They knew what it was like to win. The light preemptive style for which they are known had done them no damage on this occasion as they produced the sequence of good sessions one might expect from a disciplined precision pair who were bidding aggressively and keeping their noses clean. Here from the 3rd session is an example of their Wabash Cannonball style where Woolsey stokes the boiler and Stewart strives mightily to keep the train running on the tracks.

Stewart          Woolsey

♠ 2                ♠ KQ93             1♣*           2♦

♥ AT83         ♥ —                3♣            3♠

♦ A9             ♦ QJT764          3NT          4♣

♣ AKQ643     ♣ J85                 4♦ 4♥

4 losers         6 losers              6♣            Pass

After the Big Club opening bid the auction proceeds along natural lines with each player able to show a long minor. Woolsey provides the shape and Stewart provides the controls along with an excellent 6-card suit. 3NT appears a bit limp, but after Woolsey completes his picture with the 4♥ bid, Stewart bids a descriptive 6♣ leaving it to partner to carry on if he holds better controls. Purists may ask what would have happened on a trump lead. Answer: it goes off 1. So is this a 0% slam? Not at all. As in many cases, even when the players bid descriptively, the killing lead does not materialize. Here the opening lead from a ‘rubber bridge expert’ was the tricky ♠4 from ♠A54. Needless to say, Stewart was not tempted to put in the ♠9. The deal provides contrary evidence to those who would devalue the jack in a high card point scheme. (I am joshing, as usual. Jacks are important attendant cards, that is, when attached to higher honors in their suit. Their value is relativistic, not absolute.)

Probability calculations should take into account the various options that arise during the play. On a cursory look at the 2 hands in isolation, one might conclude that 6♣ depends on the diamond finesse and a 2-2 club split, whereas neither conditions materialized. When declarer is playing in a 9-card fit with the top trumps, the cards often allow for a variety of plays, such as eliminate-and-throw-in, that reduce the number of losers by one. Add to that the possibility that the defence may not be perfect and one sees that bidding up with distribution and a good trump suit comes with its own share of good luck.

When in the later stages of a pairs tournament one is having a good game, in order to win it is especially important to score well against a pair who is having a bad game. One cannot avoid to score averages against them and fall behind the rest of the field. It would be bad strategy to go against the grain and attempt to swing points against them, after all the card probabilities don’t change and the opponents are no fools, but if an opportunity arises one should be resolved to make full use of it. I think this is what accounts for Fred Stewart’s strange double on the following deal from the later stages, which also serves to illustrate the Woolsey –Stewart normal competitive style.

1♣ was strong and Woolsey’s initial pass showed he held at most 4 HCP. Players are keen on interfering with a Precision 1♣ auction, on the assumption that the auction will be more efficient than one normally expects against ‘natural’ bidders. This tendency to interfere works best when the Big Clubbers hold the balance of power, so the normal advice is to interfere on bad hands and pass with good ones, planning to come in later. The 1♦ overcall seems to have been deliberately ambiguous, possibly showing 2 suits of the same rank (CRASH). Woolsey was temporarily silenced, and North’s 2♣ showed clubs and a major. Stewart passed. South showed he held the majors, choosing the lower ranking suit, not the longer suit, to allow for a pass from his partner. Armed with the knowledge that his partner knew he didn’t have anything, Woolsey now took advantage of his limited bid structure by bidding his fine 6-card suit, headed by the jack, please note. The opponents’ bidding had revealed that he was sure to find a fit in that suit.

North knew his side had a double fit in the majors, so it was quite normal to bid 3♥ . Now comes the strange part – Stewart doubled this, even though the opponents had a better fit in spades to which they could have escaped. He knew they had a better fit, but he gambled that they wouldn’t find it. Going for the maximum, he was not content to leave them in a failing contract undoubled. So it came to pass that NS gave up 500 in a part score deal.

This shows the great advantage afforded to a Precision pair when the opponents are overly eager to confuse the auction. To some this result may inspire the addition of a Reverse-Flannery to their overcall scheme, however, if South could have been content to follow the simple procedure of overcalling 1♠ planning to follow up with a 2♥ bid, none of this would have happened. Vulnerable versus not, he was too good to overcall ambiguously when it appeared that the Big Clubbers could not make a game their way.

Finally, we come to the next-to-the-last hand that put Woolsey and Stewart in front. This time it was played against the German Scientists who had done well at the start, but who were struggling at the end. Again it demonstrates the readiness of Stewart to risk an abnormal action in order to achieve a good result. In fact, it was a most extra-ordinary action in today’s bridge environment.

Today the emphasis is upon stealing from the opponents. Smirnov would have been more descriptive if he had contented himself with a bid of 3♥ , but he was hoping to destroy the opponents’ auction. The damage such bids do often accrues from a growing suspicion on the part of at least one opponent that his partner must necessarily hold the perfect hand.

One might think of it as ‘the stampede effect’. The more aggressive the opponents, the more likely they will fall for it. We prefer the assumption that an opponent’s undisciplined preempt doesn’t necessarily improve one’s chances to make a game or slam.

Fred Stewart would agree. To many BBO commentators there was no question but that a call of 4♠ was the normal action by North. Stewart is made of sterner stuff, besides which he has the fearless Woolsey there in the pass-out position to balance if required when holding 4 spades (giving a total of 10 trumps for each side.)

Now the bridge gods rewarded Stewart for his courageous pass. Piekarek saw his hand represented slam potential. The preempt without the AQ of trumps left open the possibility Smirnov had some help in the diamond suit, and he did, but not enough – the ♦ J would have been nice. (Further evidence of just how valuable those jacks can be.) Just how Pierkarek planned to find out about the ♦ J has not been disclosed, but he felt an exploratory move might lead to a good guess later. He got underway with a cuebid of the ♠A. It may seem strange to some that for a pair whose system is full of artificial bids, one of them would think 4♠ was natural.

Even a young genius will find it impossible to make 4♠ on a 3-1 fit missing the KQJ, but this was not the time to double with vicious intent. Stewart by passing throughout had generated a swing of 12 IMPs against every pair that reached a normal heart game making 450, even those who were pushed to the 5-level.

The summary by Andrew Robson on BBO was interesting – ‘Shame, not really bridge….but that’s the game.’ We know what he is getting at, but is it a shame, or is it just part of the game? Would we say that it is a shame that Beckham shot one over an open net or that Mickelson hooked one into the drink? No, we would realize that mistakes are an integral part of the game, as they are with human activity in all spheres of endeavor. This week I have to live with the fact that in a team match I lost my concentration, drew an extra round of trumps ‘just to be safe’, and went down in a cold 7♦ . I may resolve never to do that again, but it is probable that I shall. We move on and try to keep the flagrant mistakes to a minimum. We do not conclude, ‘I’ll never bid another Grand Slam when the opponents are resting in 3NT, making 6.’ That is the stuff of which pessimism is made. The proper conclusion is: never let concerns about safety overrule the primary need to make the contract, and, if circumstances demand, to bid it in the first place.