The Wagar Cup Appeal

August 26th, 2014  ~  Bob Mackinnon  ~  15 Comments 

When committees continuously modify a basically simple set of rules to accommodate narrow self-interests, one ends up with a tangle that defies logic and confounds the ordinary man. The tax laws with all the loop holes are an example of self-interested tinkering carried to extremes. Judges aim to uphold the laws, but juries are not compelled to honor them. Everyman’s nightmare becomes a lawyer’s enchanted dream.

As is well known in the ACBL enforcement of the rules, justice is not always well served by the jury system in the form of an Appeals Committee. Awareness has been raised by the ruling that gave the China Red victory in the recent Wagar Cup. The subsequent heated, personalized discussions by experts on Bridgewinners revolved around how much a player must reveal about partnership tendencies. Is it enough to clarify agreements that are written on the convention card, or must a player bend over backwards to disclose everything relevant that has occurred in the past under similar circumstances? Has an opponent the right to know everything you know (without reference to the cards you hold)? Does that include what partner had for breakfast, which may have a bearing on his level of aggressiveness? Later we’ll look at the mathematical implications, but first here is the deal that raised questions.

Precision 1♦
In my experience the troubles began when the ACBL rules were modified piecemeal to bring Precision in under the fence, as it were. Some aspects were allowed, others prohibited, but once in, Precision methods began to undermine many of the Goren-based concepts and the more naïve players were burdened with bids that had one meaning in Standard and another in Precision. The auctions sounded the same, but they weren’t, and some opponents to their regret failed to make the necessary adjustments. Gradually the old standards fell, but the tinkering with the rules didn’t reflect the collapse, resulting in further confusion. The ruling in the Wagar Cup Final revolved around a Precision 1♦ opening bid and possible misinformation. Here is that deal.

The 1♦ opening bid is systemically correct as the hand contains at least 2 diamonds and at least 11 HCP. Coincidentally the hand also constitutes a standard 1♦ opening bid where 4 diamonds are the norm. Levitina’s takeout double, like the Precision 1♦ bid, is a noise from which not much can be concluded with regard to distribution. Redbl is understandable – 10+HCP, a flat shape and 2 suits covered defensively. However, because of the nature of the nebulous opening bid, a non-standard complication is that clubs or diamonds might provide the best fit for either side.

Sanborn’s pass is understandable. When one has nothing to say, don’t say anything. However, pass is descriptive – normally a balanced hand. Partner can add up the points, subtract from 40, and have a good estimate of the upper limit of her partner’s holding. Sanborn can stand by Levitina’s choice.

When I have doubts about standard practice, I refer to that superb reference from 1981, Modern Bridge Conventions by Root and Pavlicek, a book praised on the back cover by many late, great American players: Jacoby, Kaplan, Roth, Sheinwold, Stayman, and Truscott. The authors note that a takeout double of one-of-a-suit opening typically shows a minimum opening bid with support (three or more cards) for each of the unbid suits. So Levitina’s call is mainstream. After a redouble, they point out that a pass ‘merely expresses the lack of any clear-cut preferences among the unbid suits.’ It appears that Sanborn’s pass falls neatly into the category of standard practice. No problem, then?

One must take into account that the 1♦ opening bid did not promise more than 2 cards in the suit, so there is an additional reason for Sanborn’s passing the redouble –  maybe Levitina actually held length in diamonds. That raises the question as to whether diamonds is an ‘unbid suit’. In the Precision system responder cannot support diamonds, so if he bids diamonds, it is treated as a ’new suit’ in which he has length himself. If that is the way the Precisionists treat diamonds, then isn’t it logical that the opponents should have the same treatment, so that a takeout double does not suggest support for clubs nor guarantee shortage in diamonds? Thus a straightforward bidding sequence under the Standard regime is less informative and more complex when Precision 1♦ is involved.

At this point we ask ourselves, if there were no alerts, were the American pair obliged to answer questions as to the meanings of their bids? Certainly they are a long-standing partnership and similar situation must have come up a few times in the past. On that basis they know something that the opponents don’t know, but unless they have a prior agreement, the knowledge they have is of a statistical nature, hence uncertain to some degree. No matter how long a partnership has played together, their bidding won’t converge to perfection. If Levitina were asked, ‘based on your experience does your partner deny a 4-card major?’ the answer might be, ‘this situation may have arisen a few times in the past, but not enough times to merit expressing a firm conclusion.’

Estimating Probabilities from Data
There are mathematical procedures available that are used to estimate probabilities from data. Consider the problem in a simple mathematical context. When Sanborn claims her pass means nothing, she is implying that her pass means nothing more than what is to be expected with standard practices. With a 5-card suit she would take preference. Say there are 2 possibilities: A: Sanborn will pass without a 4-card major, and B: Sanborn will pass with at least one 4-card major. For purposes of our argument we take a narrower view and assume she is saying in effect that P(A), the probability of A, equals P(B), the probability of B. It is a coin flip whether or not she will pass with a 4-card major.

Suppose they have played in 4 similar situations and 3 times Sanborn didn’t have a 4-card major, and once she did. So we have 3 A’s and 1 B. If Levitina says that in her experience it is 3 times more likely Sanborn doesn’t have a 4-card major than not, she drawing a conclusion from a limited set of data.  In fact, Sanborn’s claim that P(A) = P(B) = ½ may still be correct, because AAA and B will occur at random with a frequency of  1 time out of 4. So, saying A has occurred 3 times more often than B, doesn’t rule out they have equal probability before each decision is made. Even if there were 6A’s and only 2B’s, there would not be enough evidence to rule out a 50-50 agreement with conviction. (normally rejection requires a less than 10% chance of being a random occurrence.) So Levitina’s statement based on her experience, that usually her partner has no 4-card major, and Sanborn’s implication that there is maximum uncertainty as to whether she’d bid or pass can both be true. Furthermore, Sanborn needn’t strive to even out her decisions by consciously adding more suit bids; she should continue to make decisions independently on the merit of each hand as she has always done. Levitina may adjust her thinking based on the observed short-term trend, but that doesn’t make it correct. At roulette it would be like betting on black because black has been coming up recently, or doing the opposite because red is overdue.

We can’t judge our own actions objectively. We may be aggressive or passive and still consider ourselves to be unbiased. Logic may be applied as a justification to move us in our preferred direction, so we mistakenly believe ourselves to be purely rational decision makers. On the South hand I would have bid 1♠ rather than pass, changing the whole complexion of the deal. For me the quality of the suit, not merely the length, is an important consideration.  Others might say, ‘change a few cards around and I could agree, say, change the ♠4 to the ♠9.’ Such changes are insignificant statistically, but they may lead to different decisions which are based on the hand as a whole and the relationship of one suit to another. Toss in the additional fact that one may react differently under different circumstances against different opponents, and we conclude that the sampling of bridge results is a mathematically flawed process, especially where the auction involves competition. Juries shouldn’t convict on such slim evidence. So it boils down to statements of prior agreements, but one can’t write down everything on a convention card. There must be allowances made for freedom of choice and table feel. Bridge bidding is information transmission subject to uncertainty of various degrees. So if one is revealing a tendency and not an agreement, an opponent must not assume 100% conformity to a trend which is subject to random variation. Levitina’s offered opinion based on experience concerning what Sanborn might have for her pass should not have been taken as a certainty. One shouldn’t be in a position of having to guess for the opponent’s benefit, then being held account if one has guessed wrong.

In a recent local game I balanced with a double of a vulnerable 2♠ opening bid on the following fine collection with 18 HCP: ♠ KJ ♥ AJT5 ♦ KT6 ♣ AQ64. Partner bid 3♣ and played there. Naturally I wished we were playing Lebensohl over doubles of weak two’s and was apprehensive that we might have missed 3NT. My RHO led the ♠A and continued the ♠T to dummy. Partner cashed the ♣A dropping the ♣K from the preemptor. Later the defenders got it wrong by assuming partner didn’t have 4 hearts. Partner’s 130 scored 80%. The preemptor had begun with ♠ Qxxxxxx ♥ Kx ♦ Qxxx ♣ K, an abomination sanctioned by the ACBL. 

One might say this was bizarre but not uncommon.  The opening bid was nothing out of the ordinary, although I detest it. I asked partner why he had bid 3♣ and not 3♥. He replied, ‘I knew you wanted me to bid 3♥, but my clubs were better than my hearts.’ The question arises, should I alert his 3-of-a-minor next time because it is an agreement that he might have 4 of a major? Isn’t that a ridiculous question? If he thinks bidding clubs is better than bidding hearts, good luck to him. There were many who didn’t agree with our bidding methods, but they will have to wait until next time to get even.

In the Wagar Cup deal, if Sanborn thought passing was better than bidding a 4-card major, good luck to her, too. When Levitina escapes to 2♣, it is a bit of a disappointment for Sanborn as this is her worst suit. At this point Wang could have doubled with ♣KQxx and beaten 2♣ by 1 trick, possibly 2 on very sharp defence, an optimum double dummy result. Wang passed, allowing Ran to takeout to 2♦ – an opportunity lost against vulnerable opponents. Really, what did Wang expect? There may have been some frustration expressed by her jump to 3NT. Deep Finesse tells us this contract can be defeated on any lead except a spade. After the ♣8 lead, defeat was in the cards on a natural defence of attacking spades from the North side, however, at the table, North rose with the ♣A and attacked with the ♥K, establishing the ♥J in declarer’s hand.

The Appeals Committee faced a task harder than that of King Solomon when faced with 2 complaining women over the custody of a baby. In his case, there was clearly a right and a wrong, but here both sides had failed to take full advantage of the opportunities presented to them.  It is not uncommon that perfection is not achieved at the table, so it should not be expected when evaluating a result on a double dummy basis. In this case despite the helpful defence Wang went down in her 3NT contract by not approaching the diamond suit with sufficient caution. The Appeals Committee, perhaps disappointed in the expectation of perfection from both sides and reluctant to reward either side’s errant card play, in effect cut the baby in half in order to appear to be fair to both sides. One can only hope that AC decisions do not carry the weight of precedence.

Watching Meditation at Work

August 6th, 2014  ~  Bob Mackinnon  ~  3 Comments 

I was delighted to see Allan Graves come out a winner at the 2014 Spingold as a member of the Richard Schwartz team. I have played against him several times at our local club while he was a resident of Victoria for a brief period. It is always a pleasure to lose to a gentlemanly card shark as one comes away thinking one has been given a free lesson. His comments on BBO are always thoughtful and to the point. He now lives in Vermont, plays bridge professionally, and teaches at the Shambhala Meditation Center.

I hope Graves writes a book on his fifty years of bridge experiences, one that includes how his meditational exercises have helped him at the table. Meditation is often portrayed as an otherworldly endeavor when the practitioner shuts himself up and contemplates his navel. I think not. Otherworldly to me is hoping for divine intervention in a situation that appears to be beyond one’s control, whereas meditation is a means for attaining self-reliance. Paradoxically, self-control leads to greater freedom of action. The basic technique is to train diligently and do what you feel instinctively is right at the time.

Descartes famously conjectured, ‘I think, therefore I am’. Buddhists decline this approach, preferring the more mundane assessment, ‘I am what I am.’ Self knowledge is an important element. Once you discover you are a fool, you can work hard at becoming less of a fool. (Well, that’s the theory behind it.) It is not a question of right or wrong. One learns to observe one’s own actions dispassionately, which tends to prevent an emotional over-reaction. Accept the fact you won’t always do the right thing.  Remember,

‘Even monkey fall from tree’ – Munenori Kawasaki ?

Allan could do a better job at this than I can, nonetheless let’s look at him in action at the recent Spingold, as reported on BBO. Board 43 in the Semi-Final against Team Assael showed the value of partnership trust in a competitive auction. Such trust is developed over many boards, and sometimes one may be criticized for being overly cautious during the process, but there can be a payoff if one is patient and maintains a high degree of awareness so that caution doesn’t become the overriding approach. With none vulnerable the German opponents began with a minimal 1♣ bid on 4=4=1=4 shape with a singleton ace.

Schwartz had a decent (that is, old-fashioned) overcall in diamonds. Piekarek had a modern transfer response of 1♥ which allowed Graves to show values there cheaply. Smirnov was able to jump raise to the 2-level, but that was not high enough to shut out Schwartz. Now Piekarek took up some more space with his mediocre hand, but not enough to prevent Graves from getting in a cue bid at the 4-level. The enemy bidding had helped him in his evaluation, and EW did little to impede the NS exchange of information. Schwartz was no doubt delighted to show his club controls, and Graves took the hint.

A good carpenter plans ahead and makes best use of the tools available with the result that it all looks so easy when everything fits together nicely. At the other table the workmanship had a somewhat slap-dash quality, so the end result was a bit wonky.

Sementa showed his diamond support and shortage with a jump cuebid in spades. Tokay liked his hand a lot, and went into ace-asking, rather than cue bidding the club controls. Apparently he customarily overcalls on much less. Sementa probably regretted having taken up his own bidding space, so he bid a simple 5♣ without confirming the spade void. Tokay counted 2 losers and stopped in game. As it turned out the wrong player made the final decision. Shutting out the opponents can be profitable, true, but shutting out one’s partner is bad when it’s your hand. It is a matter of perception.

Here is a hand from the third session of the final. Allan didn’t do anything, so a Zen-like  non-happening, but as the Chinese say, ‘when nothing can be done, do nothing.’

Schwartz led the ♥K which was allowed to hold, Graves following with the ‘encouraging’ ♥2, Zimmermann with the ♥4. The sight of the dummy’s minor suit honors sitting behind his is disheartening to a defender who had revealed his all. It appeared that if he played a second heart he could later be endplayed successfully. If so, nothing could be done about it, but rather than ‘do nothing’ and continue with the ♥T, Schwartz precipitated the action. He cashed the ♠A and unblocked the ♣K hoping for a miracle. We see this kind of ‘give up’ play often enough at the local matchpoint game, especially when the cookies are being put out just before the coffee break.

It was unlucky that the game could have been defeated and that teammates accurately bid only to 3♠, making 140 for a loss of 10 IMPs. Monaco had taken the lead when 2 boards later Graves again turned the tide in the third quarter of a match by bringing home a vulnerable game that was defeated at the other table.

At the other table Nunes as West opened a weak 1NT, Fantoni bid 4♣ as a transfer to hearts. Against 4♥ Lindqvist led the ♣3. Nunes ruffed in dummy and played of the ♥A and ♥K, applying the familiar rule of ‘Eight Ever, Nine Never.’ Down 1 appeared to represent a normal push.

Schwartz-Graves has a very American 2/1 auction to a vulnerable game. As we learned from the Davy Crockett Show, don’t show fear when facing a bear in the woods. Zimmermann had questions to ask about this simple auction. Eventually he chose a spade lead and hit pay dirt. North took 2 spade tricks and exited with a safe diamond, the ♦7.

Declarer won the ♦K with the ♦A, played the ♥A, then finessed Multon for the ♥Q, making his game, gaining 12 IMPs, and putting his team back in the lead. What led him to the successful line of play? I see 3 possible factors at play:

• the bad result 2 boards earlier,
• the defender’s actions, and
• table feel.

Personally I don’t like a teammate who tries to swing a result by taking an action chosen specifically for being different from what is expected at the other table. In this case, that would entail finessing for the ♥Q rather than playing for the drop, the expected out-of-sight action. I don’t think Graves would consider himself to be in a situation where he would choose that alternative in the hope of creating a swing. His partnership, playing against the Monaco sponsor, was the senior pair in a team with 4 young guns, so his role was to come through the session without major damage, leaving the swinging actions to the likes of Brogeland and Co who come by them naturally.

The BBO commentators made much of the fact that the opening leader was marked with 4 spades and 3 diamonds. Multon was criticized for returning the ♦7 after taking 2 spade tricks on the opening spade lead, thus giving away the distribution in that suit. One might conclude that with 5 cards in spades and diamonds in the North hand, and 7 cards in those suits in the South hand, the difference of 2 was enough to justify the trump finesse. This argument ignores the possibilities in the club suit. It is more likely that the NS distribution is North: 3=2=2=6 and South: 4=2=3=4 than it is North:  3=3=2=5 and South: 4=1=3=5. That is to say, the difference of 2 vacant places is more readily filled by a 6-4 club split than by a 3-1 heart split. The appearance of the ♥T doesn’t affect the odds.

The third factor is table feel. We are told that Zimmermann asked Graves several questions about the bidding sequence, which appears to us to be quite straightforward. Why would the opening leader feel he has to ask for hidden meanings unless he has a problem? This in itself raises suspicions, especially when the defenders have not entered the auction. The same applies when a defender comments on the suitability of the dummy on first inspection. This is invariably a tip off of an exception circumstance. Expect bad breaks, provided that one is playing against honest and/or naïve opponents.

We won’t ask Allan why he finessed, but remain happy in imagining that all three factors may have had a cumulative effect leading to the winning decision.

Information Changes Perception

August 5th, 2014  ~  Bob Mackinnon  ~  No Comments 

Information Changes Perception

In a recent Swiss Teams I was dealt the following potent collection: ♠ AKQT6 ♥ AJT8 ♦ — ♣ AQ43. If I could make just one bid it would be 6♠, but slam was possible in 3 suits, and courtesy demands one lets partner have his say. Admittedly it would be nice to find out whether I would find an entry in the dummy. How? I was playing a democratic Standard American system, where in principle everyone has the right to express an opinion regardless of what they know for sure. Facts are often a source of embarrassment that become revealed when it is too late to do anything about it. Under such conditions one may have to work hard to get partner to cough up precise and relevant information. My forebodings were interrupted by an opening bid on 1♦ on my right. Great!

Some might consider double at this point to be the correct bid, but a double very often gives partner too much latitude because it is not immediately clear where the auction is heading. It appears as if one is seeking an opinion, thereby yielding the captaincy, which is often hard to regain. I decided to put the club suit aside at least temporarily and to cue bid 2♦ asking for partner’s better major, a simple question he should be able to answer unambiguously. The bidding proceeded as follows:    1♦    (2♦)    3♦    (3♠);   pass (6♠) pass   (pass). When my partner saw my 6♠ bid he nearly fell from his chair. He had recently been fitted with a pacemaker, which happily withstood the test. The club lead was not trying, and 13 tricks were easy taken as he held 3 useful HCPs in the form of the ♠J and the ♥Q.

You see, the problem was one of creating a perception – how to get partner to see his hand within a particular context – my context. From his point of view he was merely competing for a part score, so he could risk a 3♠ bid under duress with the assurance of support for his 6-card suit. His perception of the deal was different from mine, but there was enough overlap that he could express a relevant opinion. The opponents had helped out by bidding and supporting diamonds, adding clarity, which is what one hopes for in a competitive auction, but what one doesn’t always get. Let’s now look at some ancient history for guidance in perception management.

Hideyoshi’s Ploy
Toyotomi Hideyoshi (1536-1598) was Japan’s most successful warrior, beginning life as a peasant and rising in times of civil war to be the country’s absolute ruler before the age of 50. Naturally, he was a master of strategy. , Kitami Masao in his book, The Swordless Samurai, purports to give lessons to businessmen drawn from the master’s actions during his rise to power. Of course, lessons on strategy can be helpful to bridge players as well.

One such lesson is: Information Changes Perception. In 1582 the warlord whom Hideyoshi served was assassinated by one of his top generals. Hideyoshi quickly gathered his troops, defeated the assassin’s army within 4 weeks before the others ranked about him were able to coordinate their efforts. Rather than let matters stand in abeyance while his rivals made alliances and took their sweet time in assessing the state of affairs, Hideyoshi sent each an urgent message calling them to an emergency conference on the succession for which he would set the agenda. He wrongly stated that everyone else had already agreed to come. Some may have doubted this claim, but they couldn’t afford to be left out, so they accepted his invitation individually, which put him in the driver’s seat before anyone realized what had happened. Kitami’s conclusion is that one must strive to control the perception of the situation regardless of the true state of affairs. Well, of course, that’s what competitive bidding is all about these days.

Double Rhymes with Trouble
A double is a poor way to project the image of a strong distributional hand. Partner will imagine the doubler is asking for an opinion. If he has a flat hand with a stopper he will be only too pleased to head doggedly towards 3NT played by himself, imagining the doubler is otherwise well stocked for that purpose. This tendency was recently displayed in the Challenge the Champs feature of the July 2014 issue of The Bridge World. Here are the hands where slam was missed by both pairs.

If you were West you’d be thinking, ‘nice collection for a slam in either diamonds or spades. I wonder if partner has a control in clubs.’ If you were East you’d be thinking, ‘nice collection for playing in NT – love those ten’s and nine’s. The hearts are particularly well stocked.’  How can they get together?

If West had one bid to make it would be 4♠, but a bidding system should be able to do better than that.  It is disheartening to go through several rounds of bidding only to be left in your best initial guess. That happens when responder has a flat hand and nothing significant to add, which is the normal expectation. Using a 2/1 system West opens 1♠ hoping not to be left there. After a 1NT response one is judged not strong enough to jump to 3♦, a natural bid, so a patch is necessary, that patch being an artificial 2♣ (Gazzilli) to avoid being passed out in a partial. It’s all very murky, but West has shown great values.  The basic problem arises because the strength of opener’s distributional hand shouldn’t be measured in HCPs, the central guidelines of the 2/1 system.

The Bridge World problem had North open the bidding with 1♣, passed around to West who doubled. Israeli stars Michael Barek and Yaniv Zack gave it a good try thereafter.

Although each player bid correctly within their system, it is obvious that they didn’t share a common perception of a slam in the offing. Zack showed his 4-card heart suit, and his stopper, then was left in the position of deciding on the final contract. That should have been Barek’s prerogative. Zack’s limitations were already evident from his initial pass. The problem lay in the use of a double to cover a 2-suited hand.

Do as the Romans Do
In general terms the greatest amount of information is conveyed by a bid that describes an unusual circumstance. The more specific the bid, the more information it contains. As a flat distribution is the most probable, bids that guarantee distributional hands are highly informative whereas bids that show flat hands are less so. A double that says little about shape is not efficient in this regard. It is normal for a partner to assume initially what is most probable, that is, a flat shape with support for the unbid suits. First impressions are hard to overcome. Commonly one may double and bid a suit as a means for showing a hand too good for a nonforcing suit bid, but this may not convince partner he should adjust his means of evaluation. It is natural to assume a 5332 shape opposite, or 5422 after a second suit is revealed, as these are the most probable.

A solution to this deficiency is to employ 2NT as a strong 2-suited takeout, in the manner of a Roman Jump Overcall. American experts suggest that for the lack of anything better a balancing 2NT should be a natural call with 19-20 HCP. This type can be incorporated in the double where it fits the preconception of a balanced hand. 2NT as a 2-suiter presents a totally different set of circumstances, so prepares partner for a different set of priorities and a different means of hand evaluation.

To be classified as strong, at a minimum the 2-suiter should have 6 controls and 4 or fewer losers. The method is general. Because the opening bid was passed by partner, 2NT may work better in a constructive mode in the balancing seat than as an immediate jump overcall when partner has not yet had a chance to bid. This is especially so when one of a minor is passed as partner could have entered the auction cheaply with an overcall and failed to do so, indicating high potential for a fit in at least one of the balancer’s suits.

Appearances Are Important
When bidding in competition one must keep in mind the effect of one’s action on the other participants. In a part score battle a minor suit may serve better than a major suit to distract opponents who think primarily of the majors. Here is an example of a competitive deal during a Sectional where two very good players were led astray.

It was matchpoints, so West risked his neck on a balancing double. In this situation East is sure that the doubler holds 4 hearts and a decent hand. He could have balanced with 2NT as a takeout to a minor. In the East seat I considered the effect of bidding 3♥. Experience has taught me that if one does the obvious, the opponents will do likewise, which was, from my point of view, to bid 3♠. I have also learned that if one opts to play in a lower scoring minor, they are more likely to leave you alone, thinking you may be in a misfit and have missed your best spot. The minors appear less threatening.

Deep Finesse tells us that EW can make 4♥, 4♦, or 2NT, so I missed my best possible spot, but my pitiful +110 scored 34 out of 38 matchpoints with the result sheet full of -140’s. I am sure that if I had bid 3♥, South would have balanced, even though he is a firm believer in the Law of Total Tricks. Over 3♦ there were too many chances I had got it wrong. Indeed, I did get it wrong, but that didn’t matter in practice, so let’s give West high marks for his brave balancing double.

When Image Outweighs Reality
Deception has always been an accepted strategy in bridge, however, in the long run reliance on deception is a losing strategy, for one begins to lose sight of what’s real and what isn’t. There is always the danger you’ll begin to believe your own phony hype. The Wagar Cup Final gave us so many examples of deceptive and misleading bidding, that it was ironic that the match was decided on a committee ruling on misinformation. What is legal and what is not is a moot point. Appropriately the venue was Las Vegas.

Accuracy was not a top priority; appearances counted most, so it was not surprising that the outcomes very often didn’t match up well with the double dummy results. Let’s not belabor the point with many examples, merely state the obvious: image has come to outweigh reality. Here is one example. On Board 22, EW vulnerable, both Easts (Yu and McCallum) opened 1♥ in first seat on: ♠ 7 ♥ KJ864 ♦ 32 ♣ KQ432. (Alert! She usually has an opening bid.) This doesn’t even qualify as an opening bid based on ZAR Points, which I tend to favor (must promote the ♥J to the ♥Q). The vulnerability increases the (in)credibility. With spades and diamonds instead of spades and clubs, I might be tempted trailing late in a match, but here it was early and close.

So what happened? Yu and Wu competed to a cautious 3♥, prompting Levitina to stretch to 4♠, off 1. Baker competed to 4♥ thinking a vulnerable game might be in the offing, doubled by Lu, the only one with an opening bid, for -500, a loss of 11 IMPs. As so often happens the gross deception worked against the perpetrator, but the effect is random. History teaches us success is everything, so bid on and let the chips fall where they may.

Bridge Beyond Reason

July 4th, 2014  ~  Bob Mackinnon  ~  3 Comments 

Some people like to think of bridge in deterministic terms: find the correct solution and you win. This is the textbook approach. In practice there is uncertainty, in which case, the correct solution entails finding the most probable construction, which does not always provide the winning solution in the short term. Losers are left with the consolation that they will come out ahead in the long run. Some are disturbed when perfectly logical approach falls short in practice. One sometimes reads a complaint along the lines, ‘If the ♣2 and the ♣3 were interchanged, he would have made his slam by overtaking in dummy. It’s a pity such a small change makes such a big difference.’ Well, it’s not a pity at all, it’s a fact of life: a small change can make a big difference. It’s not a question of probability because the ♣2 and ♣3 can be interchanged without changing the probabilities. The effect is chaotic in that a small, apparently insignificant, change can have an unpredictable huge consequence. Furthermore, it is futile trying to refine the bidding to the point where one can distinguish a winning placement from a losing one. I short, there are limits to what one can achieve through reason alone.

Uncertainty is at its highest when competitive bidding is involved. In his book, The Contested Auction, Roy Hughes notes that it is impossible to cover the many variations that may come up during a contested auction.  Having made that point, he devotes the bulk of the book to a discussion of a multitude of methods along with his personal preferences. One may agree or disagree on each suggestion, but in the end the sheer weight of choices presented dulls the brain. It is satisfying to think that every sequence can be refined to provide the greatest advantage, but I ask myself, how much disclosure is optimal? I maintain that too much refinement can be counter-productive, and not just because of the memory load. What is needed is a flexible general approach to competitive bidding. This is not the case for constructive bidding where practice makes perfect.

Consider the situation where the opponents have used a bid, say Multi-2♦, that requires a written defence. Would you prefer a half-sheet or several pages? Through its sheer bulk the most detailed defence may cause confusion, even though all the possibilities are clearly defined, and the half-sheet defence may be criticized for being suboptimal. However, it can be better to keep it simple and let general principles guide the action. If one opts for the more detailed definition it may well be the opponents, who are familiar with the subtleties, will benefit more. Being specific may play into their hands.

Experiments with stock trading practices have shown that decisions tend to get worse when the amount of information available is increased beyond a certain point. This is counter-intuitive, but the figures don’t lie. With regard to bridge, we can expect an even worse effect when all players are active in the auction often providing conflicting information. That in itself adds stress which compounds the problem. Promoting uncertainty by entering the auction can be useful if it increases the chance the opponents will make a mistake. Keeping the pressure on may pay off late in a long match. 

A Takeout Double in the USBC Final

The normal expectation before the bidding begins is that the hands are balanced. Once an overcall is made the perception may change. To double on a balanced hand is more dangerous as the initial expectation has not been altered greatly. On a bad day one might get redoubled. So I would not double an opening bid of 1♠ on this hand: ♠ A5 ♥ Q652 ♦ Q985 ♣ KJ8. The red suits are defensive in nature, and most of the points are in the shorter suits. I count 9 losers. Partner will have to bid at the 2-level, and a double two of a minor puts the odds in the favour of the opponents. I can’t imagine a takeout double being recommended by a bridge teacher, but experts think otherwise.

Lead: ♦K for down 3, -500.

Although the light double was within the bounds of a normal action under NS partnership agreements, it was misjudged under the circumstances of having a 17 IMP lead with 4 boards to go. As noted on BBO, there was considerable amount of table talk taking place, which I have concluded added to the stress of an already stressful situation. Hampson’s worst error was his subsequent redouble which re-enforced Levin-Weinstein’s inclination to go for the throat. Why redouble when the ♣KJ8 represented good support for partner’s chosen suit?

My criticism of the double turns out to be totally wrong when judged in the light of the overall result. EW can make a vulnerable game, so a loss of 500 represents a virtual gain on the board. Unfortunately or otherwise the bidding proceeded as follows at the other table:

Rodwell made the same bad double, but Moss was intent on reaching the best game for his side. Choosing to play in hearts showed a distrust of the double. Rodwell led a low heart. Bathurst made the fatal play of going up with the ♥ K. Meckstroth unfailingly found the club switch, and the contract was down 1 for a loss of 12 IMPs. If the contract had been 3NT, Bathurst could afford to lose 4 tricks so might have been more inclined to play the ♥ J and make his game for a gain of 3 IMPs.

Thus a garbage bid that defies common sense may yield unexpected gains when the opponents fumble the ball. Logic doesn’t apply, so what are we left with? Let’s not resort to the ‘bad luck’ excuse. One might conclude that the bad takeout double gave the impression that Rodwell held the ♥ A. The misplay was a logical consequence of that reasonable assumption. Or one might think that psychological factors took over in a moment of stress, perhaps increased by the disappointment that the contract was not 3NT.

In such cases the player who made the wrong play shouldn’t be relied upon to give his reasons. It may be that he himself does not know why he took the action he now regrets. Hormones may have provided an unconscious reaction. On the other hand, he may remain defiant and may not want to reveal his thinking at the table which included some extraneous considerations. There is always a next time. Actually the game is more interesting when it takes on an additional psychological dimension.

Consider what to do when called to an appeals committee. When asked to give one’s reasons for taking a disputed action, the truthful answer might be, ‘because I felt like it.’ Of course, this is frowned upon, because the committee is there to bolster the concept of bridge as a game of logic. They distrust emotion. So, when called upon, one has to be prepared to give pseudo-explanations that more or less fit the hands which are now fully on view. This may require some overnight preparation. Giving several reasons gives rise to doubt, so pick the most plausible and go with that. Be convoluted if you must, but keep emotion out of it. This is yet another situation where it may not pay to tell the truth, the whole truth, and nothing but the truth. 

The Topless Suit

A fairly safe way to enter the auction is to bid a suit. The hope is that partner may be able to raise, so that one can compete on the basis of the Law of Total Tricks. The expectation is that if one bids a suit and partner raises, we hold some control of the suit. This may be so, in which case the opposition will do well to avoid declaring in 3NT. Thus, unlike the takeout double, a suit bid does fundamentally change the perception of the opening side. The antidote to this kind of bidding is for the opening side to bid NT if they have a stopper. Partners can be surprised to find both have stoppers. In such cases I assume the opposition have our suit as well stocked as we have theirs, which makes 3NT all the more attractive. Recently I was able to put this theory to the test.

Lead ♠Q, 3NT making 430

I had my usual misgivings about opening in a suit with a flat 19 HCPs, however, with 2 aces and 2 kings (6 controls), trying for game in a suit looked appropriate, so I resisted the temptation to open a light 2NT. Partner gave me a raise in hearts, after which my RHO got into the action with a 2♠ call. As my controls were in the suits the opponents had bid, I felt 3NT would be a better contract than 4♥, so I bid it on the assumption that partner had help in clubs. I half-expected a club lead, as certain opponents get into the auction for the purpose of finding out which suit to lead –not spades, not diamonds, not hearts, ergo, a club. Not this time. The opening lead was the ♠Q.

Once again letting the opponents into the auction paid off . I felt further satisfaction when the RHO showed out on the first heart lead towards dummy. The field was in 4♥ going down on the bad breaks, sometimes doubled. I could afford to set up 3 tricks in hearts, ending up with 10 tricks for a 90% score.

I can see the temptation to bid 2♠. The 2♦ overcaller must be very short in hearts, so if he holds a few good spades the chances of pushing the opponents too high is good. Unlucky, then, that I held such a good hand and that the 2-level overcall was rather skimpy. However, when one knows partner is short in their bid suit, one must recognize that such shortness motivates light actions. And if you hold strength in their suit, they must be bidding on strength in yours. It works every time, but players keep missing the inferences, so the practice persists. Whenever you can, make them pay. 

Hormones and Bridge

June 23rd, 2014  ~  Bob Mackinnon  ~  No Comments 

Does Wall Street make sense? John Coates, a former trader, doesn’t think so. In his 2012 book, entitled The Hour between Dog and Wolf, he maintains he doesn’t believe in Mind over Matter, in fact, he thinks just the opposite: that our actions in moments of stress are governed by unconscious bodily reactions in which reason plays a small part. He maintains that decisions made daily by stock traders are made under stress, so are largely attributable to hormonal fluids triggered by the hypothalamus, so cannot be explained largely in rational terms. He accepts the view of John Maynard Keynes who observed in the 1930’s that market activities are spurred on by ‘animal spirits’ that trigger spontaneous optimism rather than by coolly derived mathematical expectation.

It is obvious that the same arguments could be applied to decisions made under pressure at the bridge table. This brings into question much of the tournament reportage which acts as propaganda in support of bridge as primarily a cerebral exercise. Bridge is more than that. There are purely physical reasons not apparent to the naked eye that make bridge the exciting, pleasurable, and addictive game that it is.

Coates feels certain that endocrinology provides the clues as to why women act differently from men. He suggests that stock markets would be better constituted to avoid boom and bust trends if more women were traders, these days the almost exclusive domain of young males who (he claims) snort drugs and spend their leisure moments at the computer screen viewing porn. It struck me that Coates is doing little else than reviving the age-old concept of Yin and Yang, but nowadays to convince the non-religious American reader, authors have to toss into their texts a plentiful dose of scientific references much in the way that James Bond novels were sprinkled with posh brand names. Bear with me as I illustrate the technique with this encounter in Monte Carlo after Bond having cleaned out a hated enemy at the card table is about to dine with a super Russian spy of the opposite sex.

‘So pleased to meet you at last, Mr Bond,’ she oozed, her black satin gown clinging enticingly to her generous curves. Everything about her spoke of estrogen levels of epic Marilyn Monroe proportions.

‘Shall we order now ….or later,’ suggested Bond. In precisely the manner described by Bruce McEwen and his colleagues at Rockerfeller University, his hypothalamus was issuing urgent orders to his kidneys for an increase in his level of testosterone. Consequently the rising levels of steroids in his hemoglobin increased his blood’s capacity to carry oxygen and reduced his evaluation of risk to negligibility.

‘It’s our first time together, so let’s enjoy it slowly,’ she proposed smoothly.  ‘What are we drinking?’

‘Dom Pedro ‘12, chilled but not shaken.’

‘Lovely. I could watch the bubbles for hours and it’s sweeter than most champagnes.’

‘I go for the full-bodied, myself, but this shad roe could do with some perking up. Waiter, bring us a bottle of Heinz 57.’

‘It’s true what they say about you, James – you have impeccable taste. May I call you James?’

‘I always feel the world could do with more intimacy.’

‘My name is Harmony. My father was Anton Korsokov, chief conductor of the Moscow Philharmonic until Putin had him fired for refusing to record the 1812 Overture with live ammunition. Oh, bother, do you have the time? I love my Vuitton Tambour but it’s impossible for telling time and I promised myself I’d get to bed early tonight.’

‘Now that’s what I call a happy coincidence.’

Her soft fingertips touched his wrist as he showed her his Q-modified Jaquet Droz.

‘Careful not to push any buttons – GMT is on the top left dial.’

His dopamine content, already at an extraordinarily high level, went through the roof. Meanwhile her cortisol level had taken a dive triggering the memory that she had neglected to refill her prescriptions after a recent prolonged stay in Saudi Arabia. Her ghrelin production increased sharply as her glucose levels plummeted.

‘Right now I’d love to have a great long chocolate éclair filled with whipped cream,’ she mused, ‘followed by a vanilla flavored Nescafe, black and very hot. What would you like to finish with, James? Let me guess: Pantysgawn and a stiff Dalwhinnie. Don’t act so surprised, it’s in your file, James.’

I like to believe there is a limit to what one can learn about human behavior by studying animals in a laboratory, and that the interpretation of experimental results can lead us in bad directions. For example, Coates informs us that with repetitive exposure to freezing conditions rats learn to remain calm as the temperature drops precipitously. The survivors don’t panic as a consequence of their hormonal production having adapted to a repeated experience. The conclusion can be drawn that Northern Europeans are best equipped to make decisions as their physiology has been trained over the centuries to cope with the heat of summer followed by the cold of winter. Residents of the Equator tend to overreact in a crisis – their testosterone levels get high quickly and stay high, leading to burn out, whereas a James Bond type can engage in life threatening activities, splash some cold water on his face (to desensitize his valus nerve), change a shirt, and be fresh for new challenges as they arise. This idea comes under the heading of pseudo-science in support of racism. Coates wonders whether central heating will reduce the Northerners’ natural advantage in decision making. The next generation will need toughening up. Could it be that future studies with monkeys will serve to revive the notion that the ideal family consists of a harsh, distant father and a forgiving, ever-present mother to cling to, the hairier the better? (Remember this: it is not survival of the fittest, it is survival of the most adaptable – there are more poodles in the world than timber wolves.)

Envy the Japanese who have learned from childhood not to panic when their houses shake and their dishes start to fall from the shelves. They are not easily stressed. But let’s not forget Pearl Harbor, a foolhardy decision if ever there was one.

With regard to bridge the USBC Finals should provide a good experimental environment from a stressful situation where rational thought gives way to subconscious physiological reaction. Unfortunately this year the players were not wired up, so lacking real data we’ll have to judge from the external evidence only. When I sat down to watch the last 15 boards on BBO, Diamond led Nickell by 27 IMPs. I concentrated on Meckwell, a pair noted for coming from behind at the last moment to snatch victory from defeat. They faced Moss and Bathurst, an infrequent Precision partnership, whereas as at the other table teammates and natural bidders, Weinstein and Rubin, faced Greco and Hampson, Meckwell disciples. I anticipated fireworks all around.

I was disappointed as Meckwell were about their business playing a steady game. There was no stretching to get to games that might not be bid at the other table. On one board they played quietly in 1NT, making 4 overtricks. Nickell trailed by 25 IMPs with 7 boards to play when this board came up, providing the opportunity for a slam swing. Meckwell bid to 4♥ unopposed; Rodwell, South, with a stong hand suggested slam, but Meckstroth declined his invitation with an ill-fitting hand. This was frustrating as 12 tricks were clearly available. Here is what occurred at the other table.

Logically Weinstein’s vulnerable overcall doesn’t make any sense, even if we recognize that the chances of getting doubled for penalty are slim to none. Levin’s raise is scary, but Hampson, in a game-forcing situation was intent of reaching his side’s best contract. With a minimum for his 2♦ game forcing bid Greco opted to get out quickly. For all the activity NS reached the same contract as played at the other table and made the same 11 tricks. This then was a board easily forgotten in order to clear the mind for the next challenge. No harm was done, so relax, let the testosterone levels subside, and get on with it. However, that is not what happened.

In a Bond movie, 007 and his implacable enemy face each other at the card table with gentlemanly composure. The confrontation is intense, but they do not engage in frivolous banter. “Your move, I believe’, is as far as the provocation goes, even when playing Texas Hold’Em. All very stiff upper lip, the raised eyebrow, and all that. Apparently this is not how it was going at the USBC Final, where the voracious table talk became an essential element of the competition. Speculating on what might have happened keeps the pressure on, and does not allow for recovery of the hormonal balance. However friendly the tone, table talk becomes a psychological weapon, the result being to induce mental fatigue and cause mistakes. Similarly, salesmen are friendly when they have something to sell, but they know it is a mistake to let you go home and think about it.

According to the BBO report, after Board 54 Weinstein accused Greco of habitually making unusual and deceptive bids (the pot-versus-the-kettle gambit) and Hampson speculated on how far 2♠ would have gone down if he had doubled (hollow threat). This was not a harmless exchange for blowing off steam, but a way to keep the pressure on.  The effects were felt on the next 4 boards when Weinstein-Levin gained swings of 9, 12, and 13 IMPs to win the match going away. I conclude that if Coates is correct in assuming the critical decisions are governed by physiological imbalances, in future bridge reports must include the punk table talk as part of the bidding process. If this trend is allowed to continue, irrational decision making is bound to increase, and bridge as an intellectual exercise will deteriorate further into a form of two-handed poker.

Coates suggests that markets would be more stable if the hormonal composition of stock traders were to be balanced by the addition of more women and older men to the profession. Of course, those who profit greatly from ups and downs may not welcome the change. Is the collapse of ’08 bad when the market has doubled since to the benefit of those capable of taking advantage? We don’t need experiments on monkeys to verify the effect of a balanced approach, as local bridge clubs, replete with ageing men and women,  can provide direct evidence on how hormonal changes affect human performance. The club is a socially mature, stable environment where all players, winners and losers, can pass the time in pleasant surroundings due to a strict enforcement of a zero tolerance policy, but we don’t expect to find technical advances there. Trying too hard to win is taboo, which inhibits innovation. The ACBL does its part in that regard.

Endocrinological evidence may explain why certain club players consistently perform better against some opponents than against others, irrespective of the hands dealt. The top players certainly get more gifts than the also-rans, which I attribute to the stress felt by the lesser talents. Husbands may consistently score well against their wives and fail miserably when facing aggressive male rivals. This is due not only to inferior technical skill, but also to self-generated stress that compounds the problem. The question is: how can a player overcome this loser’s habit short of surgical intervention? Unfortunately, there is less free will involved than one might hope for, nonetheless, the essential first step is the development of self awareness. Denial doesn’t do it.

I have a tip about table talk: don’t engage in post mortems, especially those that clothe naked self-justification with tattered rationalizations. The complainers will not follow the good advice you could give them, rather, they will continue to make the same irrational mistakes over and over again, always seeking justification in the wrong places. Walk away from the table, look out a window, and say hello to a passing cloud. Be happy.

What Do I Need to Know?

May 28th, 2014  ~  Bob Mackinnon  ~  8 Comments 

Why, might we ask, is 2/1 a popular system? Primarily the concept is easily grasped: ‘you open at the one-level, I respond at the 2 level, and we can’t stop below game.’ This doesn’t mean it always works, but bidding bad games sometimes pays off when the defenders slip up after an uninformative auction. The requirement of having 12 HCP for a 2/1 response is a restriction that implies 3NT will be played in preference to 5 of a minor, where distribution may be a critical factor. Guided by this general principle, players continually aim for 3NT from the start and neglect minor suit contracts. The average player benefits from this simplification, but good players don’t need to be continually reminded of the facts of life. To aim for a minor suit contract under unusual circumstances is to bend the system so as to overcome its built-in bias.

When one plays a system diligently one is accepting the priorities set by the system designer. This means one accepts the predetermined limitations based on prior probabilities. There should be no crying over spilt milk. If one bids against the system because of particular circumstances, one is more flexible and judgment comes into play, for better or worse. Bending the system to better fit what one sees in one’s hand degrades the information content of the exchange, because partner is misinformed. Let’s examine some examples of where judgment overcame systemic restrictions.

The Effects of Uncertainty
In a recent Swiss match I played Standard with a veteran who prefers a primitive natural style. Basically he bids what he thinks we can make. A consequence of this approach is that he never temporizes. That can work well at Teams where one wants to play in game whenever it is remotely possible to make it. The less information exchanged, the better the chances. The effects are familiar to club players and are becoming more so among experts.

I upgraded to 1NT mainly on the basis of my 5 controls, partner applied Stayman, and not finding a 4-4 heart fit, bid what he thought I should be able to make. He felt there was nothing to be gained by passing information about the long diamond suit with at most 29 HCP available in the 2 hands. The ♥2 was led, to the ♥Q, ♥K and my ♥A. I lost to the ♦A on my left and the spade shift was obvious. In the time honoured manner I ran off the diamonds, cashed the top clubs and, based on the discards, finessed in hearts successfully to collect 12 tricks after my LHO had been forced to choose to guard either the ♥T or the ♣Q. I hoped to gain an IMP.

The overtrick didn’t matter because the opponents had stopped in 3♦, making 150. Their auction had begun 1♦ – 1♥, both bids being ill-defined, making it easy to overcall 1♠ in fourth seat holding ♠KJxxx and ♥Kx. Interference of any quality changes perceptions. Neither opponent was confident enough in his spade holding to suggest 3NT. Thus, a simple overcall, even on a bad suit that takes up no space, can be damaging when neither player has expressed his strength. Uncertainty here made it unnecessary for me to bid a close minor suit slam at the other table.

. I would have preferred to play in 5♦. If I had held ♦AT75 in a hand with 16 HCP, 6♦ would have been the correct contract. Partner’s bidding was crude, but what I didn’t know didn’t hurt me this time. Here is an example of our successful slam bidding style.

This time I was within the 15-17 NT range, but too many missed slams have convinced me that a control-rich 17 HCP is too strong for a 1NT opening bid. With a wonderful fit in diamonds Pard expresses the hope that I could make 5♦.  As I held an extra ace, I bid 6♦, my fear being that we might be missing a grand slam. I was right there, but it didn’t matter that much as the opponents stopped in 3NT, after the auction 1NT – 2♦*; 2♥ – 3♦; 3NT – pass. The opening bidder preferred to show his club stopper rather than raise diamonds to the 4-level, which might get passed.

One might say the gain had nothing to do with system and was due simply to superior hand evaluation, but both auctions are ugly. If I had been playing Precision and opened 1♣ I am sure I would have reached 7♦ after a largely natural auction in which diamonds got to be bid along the way, but what is the need if the opponents stop in 3NT?

Here is one more example from the same Swiss Teams event. I employ a weaker-than-usual strong 2♣ bid with control responses which allows me to open 2♣ on hands with good distribution. It always has worked for me, this time in a strange way.

Fearing that I might be asked to pass a 3NT bid while holding a 3-loser hand, I decided to take control with a 2♣ opening bid despite having only 5 controls. The possibility of 6♠ loomed large. Pard showed 4+controls, which usually is enough for slam if a decent fit emerges. Subsequently he thought he could make 6NT, and who was I to say 7♠ would be better?  He made an overtrick after the ♣J lead. Diamonds were never mentioned. I am not proud of my 2♣ bid, but it served the purpose of putting me (temporary) in charge of the auction. The control response served to set the goal. Playing Precision I would be able to open a normal 1♣ without having to distort the system, and a natural sequence thereafter would put 7♦ on the map at the 3-level.

At the other table they did stop in 3NT after the auction: 1♠ – 2♥; 2♠ – 2NT; 3♦ – 3NT. I suppose responder thought 3♦ was suggesting 3NT without a club stopper, consequently he had no comfortable response. The trouble is that the system is unstable. It is very difficult to carry on after a partner signs off in 3NT. Usually, next stop: Slam. Surely it would be an improvement if 4NT were treated as natural and invitational, and 4♣ were treated a slam try in diamonds with 4NT a possible resting place.

Who Decides?
If partner opens a strong 2♣, what are the options for the responder? Some play that 2♦ is waiting and unlimited. This means the opener must now describe his hand in detail, giving the responder some authority in the subsequent auction, even if the pair adopts a Kokish 2♥ relay. That is the wrong way around, although one might recover if opener limits his hand with a 2NT rebid. Others play that responder initially shows controls. That is better as it passes specific information and keeps the opening bidder in control.

I have often claimed that in a complex auction the stronger hand should make the final decision. From the weaker side there appear to be too many things that can go wrong. In the spirit of democracy many have disagreed with me – thinking that the weaker hand has a right to make his opinion known under all circumstances. They are wrong, of course, which was made obvious by the comments that arose during the following hand played in Segment 5 of the 2014 USBF Semi Finals. It demonstrated that bad bidding is not confined to the local clubs. In 2 matches the same result was achieved: the Big Clubbers in each match gained a slam swing when the weaker hand in a 2/1 auction decided to stop in game without describing his primary asset, a 6-card club suit. Here is one auction.

Rosenberg was able to describe his shape and responder promised non-minimal values with his 2NT bid. As he put down the dummy, Willenden apologized for possibly missing 6♣, but an apology wins no points. The player with the weak hand made the final decision without conveying essential information about his shape.

The BBO commentators missed this point entirely. They excused Willenden because from his side the ♠KJxx appeared to be wasted. They speculated whether 6NT was makeable on double dummy play that overcame the lack of entries to the long clubs. The ♦Q seemed to hold great significance, whereas it was irrelevant in a 6♣ contract. In fact, all that the opener needed to know was responder’s shape. Lew Stansby and Bart Bramley showed how it could be done in a Precision context.

When Bramley bid 4♣, it appeared to be ambiguous to the commentators. Were hearts set as trumps with 4♣ merely showing a control? No matter, Stansby simply showed clubs, and Bramley, with ♣AKQ was sufficiently informed so as to be able to make the correct decision. It is wrong to argue that the same information was available to Willenden as to Stansby, and that he, too, might have bid 5♣, as clearly he was thinking of doing. The point is that the 2♣ auction was fundamentally flawed, putting the shoe of the wrong foot and keeping it there.

The Bramley-Stansby auction was not ideal as too much discretion was allowed the weaker hand. Bramley did the describing early, leaving Stansby to make the critical bid of 5♣ in uncertain circumstances. Well done Stansby, but was it necessary to put the pressure on responder in this way? Does opener need a self-preemptive 2♥ jump to describe his hand to the weak 1♦ responder? In classical Precision Bramley could have bid 1♥ as forcing, possibly canapé. This saves space, and allows for exploration with asking bids of responder’s size and shape. Clearly this is the way to go. The 2♥ bid should be specific, setting trumps in a 4-loser hand while asking responder to bid a control. In this context responder need not consider other alternatives, leaving the Big Club opener in charge.

You Gotta Have Style

April 30th, 2014  ~  Bob Mackinnon  ~  8 Comments 

It was good to see Meckwell return to the top at the 2014 Vanderbilt. Things have not gone as well as expected for the Nickell team after the addition of the highly esteemed Levin-Weinstein partnership, although it is hard to feel sorry for a team seeded #2. Given their outstanding success over the past 30 years it is surprising that Meckwell’s influence on American bridge players has not been greater. To understand why this is so, we take a look at recent history.

American heroes generally are the lucky ones who succeed by overcoming steep odds. True, there are a few charismatic losers tossed in, such as Bonny and Clyde, and the like. In the latter half of the 20th century 2 men rose from humble beginnings to become Presidents of the United States: Dwight Eisenhower and Ronald Reagan. Americans liked Ike, but they loved Ronnie, still do despite all the scandals. It is a matter of style. Eisenhower spent a lifetime behind a desk learning the ins and outs of the administration of a large, diverse organization. He coordinated the Allies’ victory over Nazi Germany. As President he sent the 101st Airborne into Arkansas in a just cause, but he gave the impression a dour grandpa whereas Reagan was the rich uncle from Out West. Ronnie was a cardboard cowboy who learned as an after-dinner speaker how to spin dubious tall tales that nonetheless appealed to his well-heeled audiences. He created a winning style out of little other than unlimited ambition. Reagan’s policies did more to bring down the American middle class than to bring down the Berlin Wall. It leads me to wonder whether the Supreme Court in future might pass a law so that Mickey Mouse can become the first corporate-sponsored cartoon character to occupy the White House, despite his advancing years. (On the plus side Mickey is black and speaks fluent Spanish, rare for a Republican candidate.)

We see a similar trend in bridge history. Meckwell have developed an elaborate, tightly defined system that depends for its success on accuracy, yet the playing public persists in playing a 2/1 system that resembles those of Meckwell’s frequently defeated foes. I characterize 2/1 by its 4 F’s – for Fuzzy, Fussy, Fudgey, and Fanciful. The underlying approach is individualistic with each partner being enabled to take charge and make decisions irrespective of relative strengths. It’s the freedom loving style that appeals to most. It is an American belief that the general good is best served with everyone acting in a spirit of narrow self-interest, so they cherish the right (or even the obligation) to make decisions without restraint based solely on their personal perception of what is best. That is akin to believing America would be a safer place if every law-abiding citizen carried a concealed firearm to discourage purse snatching, abrupt lane changing, and the like.

Levin and Weinstein are more to the popular taste, so it will not be surprising if they are proclaimed the heroes of the day in the next ACBL Bulletin. Let’s look at 3 examples of them at work against Monaco in the Vanderbilt final. What would you open with this hand: ♠ AKQJT73 ♥ 9653 ♦ Q3  ♣ —? The Eisenhower approach is to open 1♠ and proceed cautiously from there step-by-step to a successful conclusion just as in the European campaign. After all, seven hearts could be the correct contract. The Reaganesque approach is to open 4♠, which represents an irrational expenditure of limited resources on an ill-prepared plan that has no obvious pay out, characteristics in common with the dreamy Stars Wars missile defence system.  Here is the full Weinstein-Levin auction.

Levin was not happy stopping in a small slam with 13 tricks available off the top in 7NT. He commented, ‘well, I certainly didn’t think you had any kings.’ Weinstein replied.’ I’m not showing queens unless we discuss it.’ Obviously opening 4♠ had an inadequate follow-up plan. Levin has commented that he is averse to incorporating conventions into his system, preferring to rely on experience and superior judgement. (The upshot of this off-the-cuff approach is that his partnership needs 200 pages of system notes to cover the special agreements for situations that have proved awkward in the past.) At the other table Fantoni opened a limited 1♠ and Nunes took charge with a 2♣ response. He had the room and the methods available to uncover the ♦Q, so they reached 7♠ and gained a rather easy 11 IMPs. I suspect Ike would have got there, too, as it is not especially difficult to reach to uncover the prime assets while conserving bidding space.

Grand Slams are not eagerly pursued in cold climates, although Alan Truscott thought that they should be bid if the trumps were solid and the 13th trick depended at most on a finesse. That implies that there should be 2 ways to succeed, and that failing the one, there is a finesse to fall back on. Here is a board where both declarers avoided the Grand, but made 13 tricks in 2 different ways.

BBO commentators exchanged views on whether 7♠ should be considered a good contract.
Kit Woolsey: ‘very easy small slam to reach, it’s the grand that’s in question.’
Joey Silver: ‘These boys bid too well to get to 7.’

This proved ironic in the light of the subsequent winning action by Levin which we shall get to later. Ira Chorush saw that there were 2 chances to make the 13th trick: first play off the ♣AK to see if the ♣Q dropped, then take the heart finesse. This seems to satisfy the Truscott criterion, but are we convinced? Alternatively, Woolsey suggested, one might try to drop the ♥K tripleton, keeping the club finesse in reserve. So there are ways to succeed on a double dummy basis, but none is as good as what happened at the tables. Nickell led a club, giving up the 13th trick immediately. Against Levin a diamond was led, but Helness covered the ♥Q with the ♥K for the same result. These actions are quite possible even among world champions, so they must be considered in the light of the information exchanged during the auction. Maybe Truscott knew that being close often proves good enough in the presence of uncertainty.

Now let’s consider the actions taken on Board 58 on which Nickell, down by 16 IMPs, gained 17 to take a lead they didn’t relinquished.

At one table scientific bidders faced one another. The information exchanged was extensive and accurate. Meckstroth considered his hand worth a vulnerable preempt on a 7-card suit – we can recognize it as such. Nunes showed the black suits with a leaping Michael’s jump and Rodwell got his diamonds into the picture cheaply. Fantoni showed a good raise to 4♠, and Rodwell was able to emphasize his long suit without danger. When the bidding came back to him at 5♠, he was in a position of being able to make a logical decision based on what was known. He had shown his values, he had a good idea of Meckstroth’s values, and he knew that if he bid 6♦, the result would be he would have to make another guess over 6♠. His pass of 5♠ avoided further problems. Was it courageous, or middle-age prudent? No matter, it was logical based on the evidence.

At the other table the auction was much less informative. Levin opened the bidding with a standard 1♣. Helgemo had to choose whether to bid his values directly, or double to elicit more information from his passing partner. A bid of 5♦ might work, but that would give up on 3NT which might be the best place to play. His double gave Weinstein the space to make a weak 1♠ response. Helness forced the action with a supposed 11-card heart fit, but this didn’t discouraged Levin. Having hidden his main asset Helgemo had to come clean with a 5♦ bid, which encouraged Weinstein. Levin had undisclosed extras in clubs, so momentum pushed him to 6♠, and Helgemo was forced to take the sacrifice in 7♦. To double and collect 1400 would have been good bridge, but it wouldn’t have been winning bridge. Instead, Levin bid 7♠ more or less on general principles and table feel.

 In theory there was zero chance of success, so Helgemo’s badly defined takeout double seemed to have been a brilliant stroke, until BBO commentators began to wonder if this wasn’t a good move as it left Helness with the problem of what to lead. This is what they should have been thinking on all the previous close slams, but here a critical point at been reached for all to see. Did Weinstein’s pass of 7♦ show a void? Of course, we would have led partner’s bid suit, but Helness led from his Broken Heart suit. So a huge swing resulted from the uncertainty in the auction. Often aggression pays off, especially when it puts the opponents in the position of having to make a critical decision on the basis of little solid information. Their decisions become more psychological than logical, and harder to explain.

It helps to be a brilliant card player like Bobby Levin, but he knows that winning bridge requires more than what meets the eye on the double dummy sheets or on the convention cards. Sports heroes are not afraid to take chances late in the game. Think of Bubba Watson on the 17th fairway leading the Masters by 3 shots, but refusing to play safe and taking a big risk because he was ‘in the zone’ and couldn’t imagine failure. You gotta have heart to win, sure, but you gotta have style that stands out a mile to catch the public’s fancy.

Visualizing the Ending

April 3rd, 2014  ~  Bob Mackinnon  ~  1 Comment 

After the Vanderbilt comes the Masters. Golf and bridge have much in common. Pro golfers are taught when addressing the ball to imagine it hitting the green and rolling up to the cup. Even a fleeting memory of ball striking water, rock, wood, or spectator invites disaster. The same method applies to playing a bridge hand. One must form a plan and envision success, not fear failure. No golfer, even Phil Michelson, plans to hit the ball into the trees so as to get a lucky bounce on the green, so why should bridge players close their eyes, swing wildly, and hope for the best? What’s the hurry?

Krythoff Martens in his book, Calf, notes that most defenders play automatically according to a fixed set of rules rather than think independently and take the action appropriate to the circumstances at hand.  Sometimes a defender can avoid a bad result by foreseeing the end position at an early stage, sometimes at trick 2. This is the hard part for those who tend to see only the cards before them. They have no plan.

It is easier for a declarer to anticipate the end game.  Generally he has greater control of the sequence of plays and may benefit from early disclosures from the bidding and opening lead. The declarer’s point-of-view is well represented by the deals discussed by Chien-Hwa Wang in his book Practical Bridge Endings (1997), a collection of hands that occurred at the table in which success was achieved through either a squeeze or a throw-in. In forming a plan a player must envision the location of the significant cards. One may say that he ‘reads the cards’ or that he ‘places the cards’. The difference is just a matter of degree. Reading the cards implies there is strong evidence that indicates what is most likely. Placing the cards means one assumes the cards are in the positions that allow for success, regardless of how improbable that may be. As Terrence Reese put it, it is a not only a question of where the cards lie, but also where I want them to be. It is ascetically pleasing if what you want is also what is most probable given what is known. This makes it most likely your plan will succeed.

If the defenders are silent throughout the auction, it is normal to assume the cards are distributed evenly between them. With nothing much to go on, declarer should assume tentatively that the card distribution are the single most likely distribution given what is known at the time. It is better than playing blindly and hoping for later inspiration. Here is an example from Wang’s book.

The ♣Q is led, overtaken by the ♣A and the ♣3 is returned to declarer’s ♣K. It appears the defenders’ clubs are split 5-2. What is the most likely distribution of their suits? Declarer notes the division of sides for the defenders is 7=5=7=7. He plays off 3 rounds of hearts and finds West was dealt a doubleton. The single most likely split is West: 3=2=3=5, and East: 4=3=4=2. Place East with 4 spades and 4 diamonds and West with 3 of each. Furthermore, it is most likely that the king and queen in each suit are split between the two defenders. No guarantees, but it provides the basis for a plan.

Declarer can concentrate his attention on West. With 5 clubs held, when declarer runs off 5 hearts, West is likely to come down to 3 cards in spades and diamonds, and these should be, according to our preliminary assessment, Hx and H, one way or the other. So declarer watches West’s discards on the run of the hearts, and if he sees 2 cards from either diamonds or spades, he plays that suit towards dummy expecting to see the king or queen pop up. He can then safely establish his ninth winner in that suit.

The assumption of a particular distribution simplifies the problem. As it happens the most likely distribution of the cards is what occurred in practice on this occasion. Very often this is the case when authors write up successful endplays. It is not luck but good management if one succeeds when the cards are in the most likely mode.

A final note on this deal: in practice West did not bare an honour, rather he discarded a club to remain 2-2 in spades and diamonds. The club discard was a strong indication of which way the wind was blowing. As Wang points out, the easiest counter is to finesse safely in spades losing to East who has no clubs left.

Here is another deal from Professor Wang in which it appears that West has given away too much information in his bidding and play. West opened 1♦ and South played in 4♠ on the ♦K lead. West took his 2 top diamonds and exited safely with a third which was ruffed by South. Once again the defenders hold 7 cards in 3 suits.

One sees that West has done most of the work for declarer, even to the point of setting up the ♦9 as a threat card against the ♦T. He played like a calf. There were 9 tricks available off the top so just one more was needed. As West would have opened 1NT with 14 HCP, declarer could place him with either the ♣Q or the ♥Q, but not both. Declarer placed the ♣Q in the West, rather than the ♥Q, presumably because the ♣Q would result in one less loser in an obviously substandard opening bid. He eliminated West’s side suits by running off 5 spades, cashed his top hearts, ruffed the ♦9 and endplayed West with a club. Once the ♣KQ were placed with West, the play became more-or-less automatic.

Early Recognition
In this example the opening leader made it easy for declarer to find the winning play. Generally, declarers will get less help from the defenders, so should be aware of the possibilities of an endplay at an early stage. The Law of Total Tricks predicts 15 tricks with an 8-6-6-6 division of sides. To overcome this barrier, declarers have to make up some tricks in their 6-card fits, and thrown-in play is a way of achieving a promotion without relying directly on a finesse. In order to succeed in a throw-in one must hold a suit which the defender has to break and give declarer the advantage of scoring a trick not available without help. In his article on throw-in plays in the Official Encyclopedia of Bridge, the late Monroe Ingberman listed several suit combinations that provide this advantage. One combination we have seen above: ATx opposite Jxx, where an extra trick is assured. Upon seeing this combination shared with the dummy declarer should be prepared to take advantage of its existence.

We note that most the combinations listed by Ingberman involve 3-3 splits, making 7 cards held in the defenders’ hands of particular interest. Seven of the 10 combinations listed contain a jack, a lowly honour that can be promoted with help from the defence. Qxx opposite Jxx is often encountered when playing 1NT contracts, and most declarers recognize the advantage of not breaking the suit. Potentially Kxx opposite Jxx is just as useful, although there is the temptation of leading towards the king hoping the ace is onside. In addition declarers should be alert to the extra chance obtained with Axx opposite J9x. Recognition is the key to throw-ins.

Replay the Deal
On the above deal, suppose West, prompted by his weakness in the majors, had decided to pass in first seat, giving up on playing in 1NT and South again reached 4♠. West stays consistently passive by leading the ♠3, usually a rotten choice. The opening lead gives rise to suspicion, otherwise the information provided is scant. The most likely distribution of the 7-card side suits has West holding two 4-card suits to East’s one. It is also most likely that the two missing courtly honours in each suit are split between the defenders, just as in the previous example. The situation is not hopeful, but it is not hopeless, either.

Declarer can see the useful combination in clubs, so that suit can become the target for a throw-in play which can function even if the club honours are split, however, the communications between the defenders must be severed or they can escape the trap. With this in mind declarer plays 2 more rounds of trumps, keeping 3 hearts as dummy decoys. It is to be expected that East will keep parity with the dummy by discarding from the minors. West may find 3 discards, one from each side suit. The paring down of the minors is a hopeful sign, while the ♥5 from West provides the clue that West has come under pressure in the minors. Declarer plays off ♥KA to strip West of hearts and runs the ♦9 to West who is endplayed into breaking the club suit. The effect is similar to that achieved when West was active, but the timing is different and the solution much less obvious. Other possibilities exist, and reading the discards is of paramount importance.

On this construction it appears that it would be better to play a passive game leaving declarer to find his way in the dark. That was the old way of playing in Teams where great reliance was placed on balancing. Also, it is possible that if West passes NS will not reach game and a calf-like declarer will be content with his 9 easy tricks off the top. Not bridge at its most exciting. Most modern experts opt for the impatient approach. Partial scores are important and the evidence shows that there is more to gain by aggression rather than by passivity. So, don’t start underbidding, but, as declarer, be resolved to make use of what the opponents have told you. As Sherlock Holmes might say, ‘Watson, I never guess. The most miraculous solution may be no more than a reasonable deduction based on the known facts.’

On Being a Calf

March 10th, 2014  ~  Bob Mackinnon  ~  3 Comments 

Imagine what it would be like to play with Don Rickles for a session during which you were the doomed defenders on each and every hand. After your third miss in a row Don looks across the table and says, with a crooked smile,

‘I feel like a lamppost at a dog show. If you were any smarter you’d be a hockey puck. Why I am doing this when I could be having my prostrate examination? Even your mother won’t play with you, otherwise, why am I here? Hey, Director! Is it too late to change my name?’

If a game with Don appeals to you, I can recommend ‘Calf’ a book of 60 problems from the self-style professor of The University of Defence, Krzysztof Martens. ‘Without pain there is no gain’ is a philosophy of education that has all but died out in North America, but which apparently still holds sway in Poland. It is painful in the extreme to be constantly told one is a halfwit, but maybe the lesson sinks in eventually. I hope so.

The deals are clearly presented. The bidding is easily interpreted, the opening lead has been made, the reader is shown the dummy, and the question is simply, ‘how do you go about beating this contract?’  What more hints does one need? It is easier than a multiple choice, yet, if one is honest, time and time again one will go wrong out of habit. That makes you a calf, a player who follows the rules blindly without regard of the particular circumstances at hand. Of course, I was aware that some of my partners are calves, but until I did the quizzes in this book I never realized that I, too, am a creature of habit.

In the initial stages of the learning of how to play bridge, the novice is presented with a number of rules to get him over the rough spots. By adopting these rules he is able to play a respectable game. Here are some rules for defensive play that we live by:
– Return partner’s suit;

• Give count when dummy wins a trick;
• Cover an honour with an honour;
• Second hand plays low;
• Keep parity with dummy;
• Switching suits costs tricks;

– Lead through strength.
The Professor observes that some players are interested in rules and some are interested in exceptions. Experts study the exceptions. Martens goes so far as to state emphatically, ‘thoughtlessness is the regular state for most defenders.’ He advocates active participation at all times, noting, ‘meekness and passivity are not the way to victory. There is no excuse for failing to think.’ One agrees, and yet, besides being hard to break, habits form the basis of modern civilization; traffic jams are clear evidence of our passive submission to the dictates of the mindless clock. Routine is the enemy of creativity. You can believe the skinny guy with the bald head when he tells you on TV that giving up bacon and eggs can improve your sex life, fine as far as it goes, but the next morning staring at your empty plate, you should ask yourself, shouldn’t I be looking for a better way?
 Probability plays little part in the decision making process when one must defeat the contract at all costs. Often we have to go against the probabilities. Here is a rare example where the reader can use probability to justify his decision.

EW have reached game in hearts via 1♦ – 1♥; 2♣ – 3♥; 4♥ – Pass. The lead is the ♠ Q. Declarer leads the ♥9 from dummy and South ducks, reading West for having started with 2 spades (♠ Kx) and 6 hearts. The question arises as to what is declarer’s distribution? Is it 2=6=3=2 or 2=6=2=3? The author states, ‘there is no evidence to suggest that one is more likely than the other.’ This is not so. South can see that the most likely distributions of the missing cards in the minors are the following:

This assumes all minor suit cards are equivalent, however, it is reasonable on the bidding to place the ♦ A with West in which case the remaining equivalent cards may have been dealt as follows.

It is 4:3 that West was dealt 2=6=3=2 rather than 2=6=2=3. If South accepts this assessment, he should go up on the first heart (breaking the second-hand-low rule) and play a club (leading towards strength), planning to repeat the play on the second trump lead, thereby cutting declarer’s communication with the dummy.

From Martens’ point-of-view the odds of 4:3 have little relevance to his recommendation as his is the unique series of plays will defeat the contract if the conditions are right. Under other conditions the defensive plays are irrelevant, so the choice is obvious. It is coincidental that the defender’s play is in accordance with the most likely splits.

The Justification for Being a Calf
General rules have validity in situations of maximum uncertainty. Like the Law of Total Tricks they are essentially statistical in nature and are subject to exceptions. Without a clear indication of the layout, players will normally follow the rules. Many players lack the confidence and/or ability to project beyond the horizon, so their decisions are largely based on what they can see in their hand and in the dummy. They continue to operate in a mental state of high uncertainty. In a local game there is the added uncertainty that declarers may not bid or play with accuracy. They may not be able to take full advantage when the contract is handed to them and will fail to find the winning endplay.

A better justification for doing the obvious is that defence most often depends on close cooperation with one’s partner. If one fails to follow the general rules, partners tend to misread the position. Plays transmit information, which is well and good if a partner recognizes the unusual actions and extracts the correct information from them, but more often they cause puzzlement. This is why, for example, brilliant leads often fail to produce the optimum results they deserve in theory. In Martens’ examples, partners play a lesser role, so individual flights-of-fancy will not cause short-term damage.

The commentators on BBO are told not to criticize a failed play merely because they can see all four hands. In this way players escape criticism for a near-sighted approach. On the other hand, in his book Martens criticizes defenders who do not place cards around the table in a way that will allow them to defeat of the contract. He expects a player with partial knowledge to project into the future and play as if he sees everything and anticipates the ending. It is not a sin to misplace the cards, but it is an error not to try. So it is part of the commentator’s task to point out how declarer might arrive at the double dummy solution based on the evidence he has at hand. This is a task Kit Woolsey, for one, is more than happy to take up. Usually there are inferences that point the way.

Protecting the Calf
The survival of organizations depends on its calves; it is the duty of organizations to protect them. In the long run calves will rise to the top. The ACBL Bulletin is aimed at the vast majority of players and continually pushes standard practices. Players who consistently come up with winning plays that go against the consensus rules are often subject to suspicion. This applies as well during the bidding phase. An example of this mentality occurred recently in the 2013 US Open Trials as reported by Kit Woolsey in the March 2014 issue of The Bridge World. Opener was blessed with this excellent 4=4=4=1 hand: ♠ AKQT ♥ AQ96 ♦ AK64 ♣ 4, a 3-loser hand with 8 controls. Standard methods require one to open 1♦ . The bidding proceeded:  1♦ – 1♠ ; 4♣ – (double) – 4♠ ; 6♠ – Pass. Responder made 12 tricks but the opponents appealed on the basis that he, a notoriously thoughtful individual, took his time before bidding a cautious 4♠ over the asinine double. They win their appeal and the result is rolled back to 4♠ making 12 tricks. This ties the board as the opponents also started with 1♦ and without interference got no further than game. What do you think of that?

The 4-4-4-1 shape is not unusual. A bidding system that requires one to open 1♦ without having a suitable second bid available is seriously flawed. The informative splinter bid is not a good choice as it puts responder in charge of what follows. What can the opener expect from him? Even club players know partner will have reservations because his spades are so poor, so I am willing to believe that the opener was planning all along to bid 6♠ over 4♠ as a Grand Slam invitation, in other words, a second descriptive bid, which would allow responder to go the whole hog with hidden extras. Not a good approach, I would say, but one possibly dictated by temperament.

Cooperation is the key word for 2/1 methods, but with a dominant hand opposite limited resources that approach is futile and misguided, not that opening 2♣ is an improvement. Don’t even try to describe this rock-crusher. Spare the anguish, take charge, and use RKCB over 1♠ – at least partner will know what to bid next. (Fans, how about 3♥ for that purpose? For every 2/1 problem there is a patch.) Here are the hands followed by a suitable Precision 1♣ auction that employs routine asking bids at a lower level.

There is no claim of perfection, but opener has enough information to bid slam with some confidence after the second response which shows that partner has at most 4 red cards. It is merely a question of 6♠ or 7♠ . Note that responder is just 1 HCP above the minimum for his bid. (In the event the anonymous ♣Q was to play an important role.) Responder has no problem answering the asking bids, and need feel no guilt that his trumps aren’t more robust. Note also the strong hand gets to play it, protecting the ♥AQ if necessary.

Doesn’t it seem unfair that the opposition can appeal after the fact rather than at the time of the hesitation? The rules are made for the convenience of the enforcers. If 6♠ had gone down, the result would stand, but when it makes, the appeal comes into effect at no cost. Crazy logic, isn’t it, unless the Appeals Committee feels its duty lies in protecting those who play by habit and bid without first taking the time to think it through.

Mystical Math

February 10th, 2014  ~  Bob Mackinnon  ~  23 Comments 

Some feel there is mystic power in certain numbers: 7 is lucky, 13 is unlucky. Scholars in the 10th Century calculated the world would end in the year 1000 AD, a nice round number, albeit a miscalculation. Some fans are attached to the number worn by their sports hero. Is it significant that Alex Rodriguez chose to wear number 13 which in hindsight appears to be an ominous tempting of fate?

I suppose everyone has a favourite number (mine is 5), but what do you think is the most beautiful number? Philosophers from Greek times have considered the most beautiful number to be one-half of 1 plus the square root of 5 (1.61803….). This is known as the Golden Ratio. Not beautiful in itself, perhaps, but Phidias designed the Parthenon using it. Euclid wrote of it. It appears in the design of the pyramids and great mosques of the middle ages and is a feature of the Fibonacci sequence introduced to Europeans in the 13th century along with the decimal system.  Mathematician Luca Pacioli called it The Divine Proportion (1509) and passed on his ideas to Leonardo da Vinci – an Italian bastard, whose mother should be praised for her judgment in choosing to produce such brilliant fellow (even though it is akin to praising the execution of an unintentional double squeeze.) Leonardo kept the concept in mind as he painted The Mona Lisa. The modern architect Le Corbusier thought of the number as an underlying feature of the mathematical order of the universe. Today industrial engineers use it in the design of consumer products. When I learned of this from a Japanese TV program I measured the attractive face of my TV cabinet finding it to conform closely to the Golden Ratio.

The number 13 figures prominently in the game of bridge. Consider 13 cards divided in the ratio of 5 to 8, a ratio of 1.6, a close approximation. The opening bid of a 5-card major reflects this split. The ratio of 8 to 13 is 1.61, an even closer approximation. If partners hold 8 of the 13 cards in a suit, the Law of Total Tricks indicates they are safe to contract for 8 tricks. Also, a 4-4 fit (8 cards) is often the best trump combination. So maybe there is a bit of magic in the division of 13 into the ratio of 5 and 8. If we add the prior number 3 from the Fibonacci sequence 3-5-8-13, we have the a priori expectation of the number of cards in a given suit having been dealt to a given hand.

Pythagoras thought the number 10 was divine. His faith is shared by bridge players who adhere to the Work Point Count. HCPs are used to draw boundaries in bidding systems which are considered sacrilegious to cross, but as with the Ten Commandments, temptation often overrides the inconvenience. It is a matter of the remote possibility of bitter punishment measured against the sweet promise of immediate satisfaction. Here is a hand where I had to break the rules to get to a slam everyone missed.

A bidding system is merely a language by which one conveys the tricking taking potential of one’s holding. The HCP content isn’t always the best indicator. My hand had 7 controls and 5 losers. It is the equivalent to a 2NT opening bid with 23 HCP, although, of course, it contains only 19 HCP. When partner transferred to 3♥, my hand was worth a jump to 4♥, counting AQx as the equivalent to 4 trumps with potential ruffing capacity in clubs.

Despite the fact that 13 tricks were available, my less than optimal achievement of 12 tricks was enough to score a clear top as 3 pairs played in 4♥, 3 in 3NT (Garrr) and 1 in 6♦, off 2. So, on this combination if you follow the standard bidding rules that depend on HCP evaluation you probably won’t reach the right contract. Responder will not be able to act if you don’t super-accept on 3-card support with ruffing potential. To me this goes to demonstrate that the consensus is often wrong. Have you noticed that groups make bad decisions? If my crowd debates which restaurant to go to, I feel lucky to get to dine at the second-best place and drink the third-best wine. Then there is Congress…..

Here is a second example where for the majority slam was hard to reach on just 30 HCP. Again, opener held the dreaded 19 HCP.

Two other pairs reached 6♣, 4 were in 3NT and 2 in 5♣. We began with a Precision 1♣, but the rest of the auction was natural and game forcing. Over 4♣ I thought briefly as possible about bidding 4♦ to show the ♦A, but chose a conservative 5♣ influenced the quality of my 2 long suits. John had 8 controls and did not hesitate to bid the slam, perhaps expecting to see the ♠K opposite. A spade was led to the ♠J and ♠A. The ♣AK dropped the ♣Q. Declarer played his LHO for the ♥Q and made 13 tricks for a clear top without the need for the diamond finesse.

Leonardo noted that truth comes from observation, but if you are too concerned with appearances and forget to count you make mistakes, as I did on the following hand.

My hand was worth a strong 1♣ bid and partner replied a natural, game forcing, 2♣. This gave my RHO the opportunity to enter the auction with a lead directing 2♥ without great fear of being doubled for penalty. My first mistake was to jump to game on what appeared to be, and nearly was, a misfit. The lead was the ♥3 to the♥4, ♥J and my ♥A. I entered dummy with the ♠K, returned with the ♦A and led the ♠A, dropping the ♠QJ from my RHO’s hand.

My second mistake to assume too hastily that I had 3 remaining losers, the ♦J, the ♥K and the ♣A. One of these might be discarded on the 4th diamond if the ♦J fell in 3 rounds. I tried this after drawing the 3rd trump, but my luck was out as I held myself to 11 tricks. This tied for bottom as 4 pairs made 6 and one pair bid and made slam.

First, I should have bid 3♠, not 4♠, giving my partner the chance of bidding 3NT, but once in the common contract, it was too easy to assume that our Precision auction had worked to our disadvantage in allowing a disruptive overcall, as it is so often claimed to do by those who don’t play the system. I even went so far as to congratulate my RHO on her brave action. (2♥* would have been down 4, vulnerable.)

Leonardo wrote in his notebook that clear thinking is best achieved in a small room by oneself. Later at home without distraction it became obvious I should have run the spades to this 5-card ending:

When the ♥7 is discarded on the ♠4 it is natural for my RHO to discard a diamond. Now I play on the diamonds and collect my 12th trick. If I had really thought ahead, I would have played the ♥Q from dummy at the first trick, leaving the ♥T hidden in my hand in the squeeze position. Now she might discard the ♥J fatally allowing for a progressive squeeze to 13 tricks. With no cost involved, it pays to try even if the odds are against it.

So, here is my advice. When playing the hand once dummy has appeared, put aside ideas of what could have or should have been and concentrate one’s mind on doing what’s best under the current circumstances. Books provide useful preparation, but the cards are what’s real, and the lie of the cards is what determines the outcome here and now. Imagine yourself alone at a desk in a quite room at midnight, when time is suspended between yesterday and tomorrow. There is only the timeless present, without thirst, without hunger, without regret, and (be careful) without triumph. Count the cards, and keep counting as those are the numbers wherein you’ll discover the magic.