The Zen Mind at Bridge

-Don’t be foolish, be stupid!

-The Zen Mind is like a mirror that reflects whatever comes before it.

– Bankei Y_taku (1623-1693)

The samurai class of ancient Japan adopted Zen as a way of thinking to help them cope during centuries of warfare. Bridge is an intense competition, war-like in some of its aspects, so can Zen thinking help the bridge warriors of today cope with the stresses we encounter at the bridge table? Absolutely.

On the Internet bridge players are often judged by the number of conventions they claim to understand. Conventions that help one communicate accurately with one’s regular partner are fine, but it is foolish to adopt conventions with an unfamiliar partner whose treatments may be different from your own. It is usual with cluttered convention cards that the whole is less than the sum of the parts.

The true expert out for a fun game may present a blank card that states, ‘I’ll play what you play’. In that way he is acting as a mirror that reflects partner’s state of mind. Two admirers of Bankei Y_taku meeting for the first time might agree to play KISS –Keep It Simple, Stupid, a statement that expresses the essence of Zen. They would realize that vague understandings cloud the mind as hot breath clouds a lens.

Zen is not against science; it is not a religion, you see. The Zen Mind seeks to see things as they are, not as they should be. One may occasionally come across a comment on BBO along the lines that, ‘she played the hand perfectly, but the cards didn’t lie right.’ To the Zen Mind such a comment is misguided, for uncertainty rules the game. There is success, there is failure, and perfection is unattainable. What is true on one hand may be false on the next. As a result the Zen Mind is comfortable in making decisions as there is no fear of failure through ‘doing the wrong thing’.

If one were to say, ‘many people believe Man is descended from the Ape’, a listener with the Zen Mind might reply ambiguously, ‘I’m not surprised.’ If pressed to elaborate, he may comment, ‘the history of science tells us that the more we learn the more there is to learn; theories come and go; Darwin’s Theory merely reflects our current state of ignorance’. So it is with bidding systems – they evolve and reflect the current state of our inability to communicate efficiently. Expect continual change, embrace basic change, but don’t continually adopt new conventions to patch over deep-seated problems.

It’s bad to be thinking about one’s bidding system during the game. Rather, think about the cards. Better still, don’t think about the cards, either. Card counting and registration should be automatic. Train the mind in order to free it. Consider the opponents. Sometimes they’ll win, and you won’t like it, but if it were otherwise, where’s the fun? Don’t be afraid to lose. At the bridge club, your enemies are your friends, for without them there would be no game.

We never do anything well until we cease to think about the manner of doing it

– William Hazlitt (1778-1830)

In a long-term partnership aim to play a complex bidding system that exchanges information in an efficient manner, without the expectation that everything will always turn out as one hopes. Bids should reflect without distortion the cards one holds. Sometimes this will prove counter-productive when the opposition is able to take advantage of the information volunteered. So be it – nothing works all the time. Don’t practice deception. Who is more important to your success, the opponents or your partner? When asked how to get more money, Master Ry_kan replied, ‘to get more, pay what you owe’. By giving partner the respect he deserves, you’ll gain in the long run.

A complex system requires continual practice – a few minutes taken every week to refresh the memory is time well spent. To do great things attend to small things. During the game let your actions cascade naturally like a clear mountain stream. Submersion in the game as it is being played is known as ‘being in the zone’ and you won’t stay in the zone if your mind is constantly twisting and turning because of trivialities that impede the flow.

The Role of Intuition

There are 3 stages of learning. The beginner thrashes around randomly without technique. His actions are instinctive and unpredictable. Consequently he may lose regularly to mediocre players who lie in wait while occasionally defeating experts who actively draw the wrong conclusions from his actions. In the second stage, he becomes aware of his mistakes, acquires correct technique, whereupon he himself becomes mediocre, losing less frequently to the average players, but losing more often to the experts. By immersing himself in the crowd he has become predictable. In the last stage of learning the player frees himself from slogans and generalities and plays according to what the current table conditions dictate. Intuition takes over. Acquiring freedom of thought he becomes unpredictable like a beginner but without being inaccurate.

Intuition is more than wishful thinking. The golfer does better if he imagines the flight of the ball towards the green. The body then tries to provide the swing to accomplish it. If the body has been trained, the chances of success are improved. One has spent a lot of time and energy building up a mental store house of experiences at the bridge table. Don’t keep that treasure locked away; draw on the experiences that only you possess. Imagine a solution; make a plan. Two experts may play the same hand differently because of their different experiences. Which one is right? (Often in a marital quarrel a couple argues from different points of view. Each is right and both are wrong.)

One needn’t stick to the standard opening lead if it doesn’t rate to be effective. The validity of standard leads is based on a broad range of situations, but not all situations are the same. As long as one doesn’t deceive one’s partner, deviant plays are acceptable. Most often partner will recognize that you have departed from standard practice, and later may even congratulate you on finding the killing lead.

Enough generalities, it’s time to give an example from my own experience at the local club that demonstrates why this works, even at matchpoints. The declarer in 3NT had bid confidently to game on the following uncontested auction:

1♣ – 1♠; 2♣ – 3NT.     I held:  ♠ KJT83 ♥ 9764 ♦ Q6 ♣96.

As I considered my lead the thought came to me that several years ago I had read of a clever someone who led a king and pinned a singleton queen in the dummy to devastating effect. Ever since I had aspired to such brilliance. Was this my chance? Well, I am not going to follow Larry Cohen’s advice about winning it on the next hand; there’s no time like the present! The ♠K flew out of my hand. What do you know, the ♠Q was singleton in the dummy! My joy was not complete, however, as partner held ♠A94, so any spade would have been equally effective with the possible exception of the ambiguous ♠8. Be that as it may, by taking the first 5 tricks in a suit declarer had bid, we achieved the only defensive plus score on the board, a common result being 3NT made with an overtrick. Results are transitory; it is the process which is of interest.

We can go back in time and consider the circumstances in a logical context. My first impression was that declarer did not hesitate to bid 3NT and his partner showed no signs of concern. In fact, both players looked rather pleased, although neither one could have had great expectations of tricks in the spade suit. I expected dummy to contain a healthy diamond suit, which put my ♦Q in jeopardy. Partner, with 8+ HCP had not overcalled in hearts, so there was no reason to believe that a heart lead would be successful. In fact, a heart lead makes it easy for declarer to take 10 tricks off the top. I suspect that was the reason behind the most common result. After a heart lead would partner later see the advantage of switching to spades? Unlikely, unless I led an attitude-laden ♥9, but that in itself might prove dangerous. Finally, if I were to lead the ♠J, top of an interior sequence, would partner read it to good effect or might he think that declarer held the protected ♠K and look elsewhere for tricks? True, in a worst case scenario declarer could hold the ♠AQ, but if he held the ♠A it was likely that the ♠Q was held elsewhere.

It is a question of probability. An abnormal action is justified if the chance of gain outweighs the risk of loss. In this field the most frequent lead against 3NT would be in hearts, the unbid suit, but there was no guarantee that all pairs would play in game. A passive heart lead holding my opponents to 400 might minimize my loss and yet could result in a below average score.  My chance of success needn’t be greater than 50%. I could go on justifying my hunch with specious arguments, but this is enough to make my point that what appears to be instinctive at the time may have behind it a string of logical steps that the subconscious mind grasps in an instant. What feels so right must feel right for a reason. My experience is that I have lost more by suppressing my intuition that by obeying it and from the number of times I have heard an opponent moan, ‘I knew I should have …’, I gather that it must be true of most experienced players. As a group we are too risk adverse. I think of it this way: ‘After 30,000 errors what’s one more of the same?’

Lessons We Can Learn from Watching BBO

The bidding sequences of our top players are so different to the sequences played at our local clubs that it is very difficult for aspiring players to learn from the experts.

– ‘Cliveo’ on BBO

Of course, the aspiring players know that the bidding at the local club is inadequate. What they learn from watching experts in action is that the difficulties they have experienced are not all of their own making. There are better ways of doing things than they have been led to believe. The major lesson involves concepts. Expert bidding is a language that one should attempt to learn. Hearts don’t always mean hearts, and there are good reasons behind it. BBO commentators want to inform the aspiring player, but by catering to the prejudices of the mediocre and propagating false doctrines in the interest of accessibility, they are doing a disservice to bright beginners. If parents always talk baby talk to their child, how can that child learn to speak properly?

I could watch Chinese TV for years without learning how to speak the language coherently. To learn it, I would have to do more than watch. So it is with the language of bidding. It requires effort away from the screen. However, it would be a great help if someone could explain to me in simple terms its structure, where the verbs and nouns are placed, for example. So it is with bridge bidding. One wishes to know the structure and how in the main it differs from the language with which one has grown up. Vocabulary can be added later, so there is no need initially to get stuck on all the fine details.

The concept that ’hearts doesn’t necessarily mean hearts’ is easily taught. Start early with Jacoby Transfers to 1NT. Even beginners catch on to the advantages and love to play those beautiful bids. They like structure and find nothing wrong in it. For advocates of a scientific approach to bidding, victories over regulators have proved hard to win, and there is still a lot of foot dragging by those would advocate ‘hearts means hearts’ – a totally unnecessary limitation in my view. And we still have these meaningless ‘Scientists vs Naturalists’ contests, which are akin to re-fighting the Battle of Hastings.

Here is an illuminating example from the recent match in the 2009 Norwegian Premier League featuring Glenn Grotheim’s highly complex Viking Precision Club. What can we learn from one of the most complex relay bidding systems currently in use?

Tundal        Grotheim

♠ T3        ♠ AK9

♥ KJ532   ♥ A8

♦ T9        ♦ AK5432

♣ AKJ4     ♣ 87

Tundal	Grothiem
1♥	1NT*
2♥*	2♠*
3♦*	4♦
4♥	4NT
5♦	6♦

Natural 2/1?	_____________
1♥	2♦
2♥	2NT
3♣*	3♦
3♠	4♥
Pass

First we observe on the right the opponents in action reaching game in hearts, making 13 tricks, on an auction to which many can relate: hearts shows hearts, diamonds shows diamonds and so on. Nonetheless, there are mysteries. 2NT appears odd, but one mustn’t bid spades without the implication one wishes to play in that strain. 3♠ asks for a stopper, and responder has 2, but chooses to raise on a doubleton rather than bid 3NT. Why?

With the Big Club auction on the left I am not sure we got all the asterisks in place, but it doesn’t matter; it is the structural design that is important, not the vocabulary. 1NT is not an attempt to live on the cheap, but a trigger to a game forcing relay sequence in which Grotheim is the master and Tundal is the slave. The master asks a series of questions and the slave answers as best he can under a strict regime of responses that allow no deviations. As the BBO commentator noted, the system can pinpoint jacks, shape, HCP concentrations and controls. It can also revert to natural bidding. I should think that this example may serve as an eye-opener to the neophyte who doesn’t particularly aspire to making 13 tricks in a wrong game contract.

One could argue that ‘master and slave’ concept is unappealing to those who love individual rights and freedom of expression, but that goes against my experience that weak players love Blackwood more than any other bid and tend to use it indiscriminately against friend and foe alike. We all love being a master and hate being a slave, but why not take turns according to the lie of the cards? That’s democratic.

Another lesson to be learned is one of evaluation. The above pairs holds all 12 controls, yet some may argue, ‘you can’t bid a slam on 30 HCP and no shortages’. Think again. Even a well-endowed responder has to work hard to get a partner to admit to 2-card support for a minor suit. In fact, I have played with some who would rather die than do so. Rather than being a slave to a system, they prefer to be slaves to habit, on the grounds that minor suit slams don’t come up very often and when they do, no one bids them. Such an attitude can kill one’s interest in bridge as an intellectual pursuit.

The End Product of Learning is Discipline

This brings us to the next lesson, which is, when bidding stay cool and transmit reliable information through your bids. Don’t get caught up in objective orientated bidding where one player imagines a desirable outcome (say, 3NT) and blindly steers the bidding in that direction. That approach is akin to turning news into propaganda. At best it is a matter of ‘spin’, at worst, a matter of deceit.

More Cliveo Observations

I once played in a 48-board match against an English International who opened 1NT against me 6 times and he was never in the range on the front of his convention card.

I once opened a 7-6 hand 1NT in 3rd position in a match against Yorkshire.

Much as we are drawn to success, we can’t accept the idea that sloppy bidding practices represent a winning strategy. As for the unnamed egocentric internationalist, we have grave concerns regarding his potential for generating happiness long-term.

The recent 2009 NEC Cup was won by the Chinese Women’s National Team who play Precision. But even Precision players can come to grief if they lose their cool and try to spin the result in their favor rather than to maintain an informative, neutral approach that serves well on most deals. Here is a deal that shows them at a disadvantage against free-wheeling Canadians. An unnecessary loss of discipline nearly cost them their victory.

Dealer: West Vul: N/S		Larry Mori
		♠	Q97
		♥	Q52
		♦	QJ987
		♣	T2
Wang Wenfei				Liu Yiqian
♠	–			♠	K65432
♥	A643			♥	T98
♦	KT53			♦	A6
♣	KJ976			♣	83
		Vinkatrao Koneru
		♠	AJT8
		♥	KJ7
		♦	42
		♣	AQ54

Wang	Mori	Liu	Koneru
2♣	Pass	2♠	2NT
Pass	3NT	Dbl	All Pass

Silver	Sun	Carruthers	Wang
1♦	Pass	1♠	Pass
2♣	Pass	2♠	All Pass

First we observe the Canadians in action. Joey Silver opened an off-shape 1♦ as he would have a rebid problem after opening 1♣. John Carruthers showed his spades and Wang Hongli passed with a good hand. The oppositions’ actions were unlimited at this point and gave the appearance of a misfit. When leading a match with 4 boards to play is not the time to court disaster in a live auction. Silver then limited his hand and Carruthers gave his preference. Even more so than before, Wang had reasons to pass. The Canadians had stolen the hand due largely to the uncertainty of the strength of their bids.

Wang Wenfei might have followed the same path as Silver and opened 1♦, in her case limited to the range of 11-15 HCP. Liu would respond 1♠ as had Carruthers, but it not certain that Koneru would have let this pass him by. There was less danger involved in competing when the number of diamonds in opener’s hand was unknown. NS could have a workable club fit. We will never know as Wang chose to open 2♣.

Those who play Precision know that opening 2♣ shows a hand whose primary assets lie in the club suit, usually 6 cards in length. It is difficult if not impossible to reach a diamond partial after opening 2♣ as subsequent diamond bids are artificial and used as enquiry bids. So opening 2♣ was not a constructive move, rather it was an attempt to preempt NS to some extend. It was possible that NS would be bidding spades if given an easy opportunity to overcall. This 2♣ bid was putting some spin on the ball in anticipation of competitive action. Negative thinking is bad. It was partner, of course, who bid spades, 2♠ being nonforcing, and the plan, such as it was, fell through.

Koneru was in a situation where both opponents were limited, and, most important, West had shown a poor hand with 6 spades. Mori could be expected to supply some values in diamonds and the hearts appeared to be well stopped. Consequently the danger of bidding 2NT was small, and the possible reward was high. The Precision system had failed, but Wang by opening 2♣ rather than 1♦ had not followed the precept:

Let the System Make the Mistakes

The loss on the board was due to be 300 points, -400 versus +100, but Liu went mad and doubled a contract that was cold, so the loss was changed to -650, or 12 IMPs instead of the 5 that charitably might have been attributed to a difference in systems. Suddenly China was behind by 1 IMP with just 3 deals to be played. A 3NT contract might have been defeated if Wang had a good club suit as advertised, but an unattractive lead from ♣KJ9xx gave dummy a trick with ♣T, a justly deserved humiliation.

Bid with Your Head Not with Your Whatever

Another lesson for the attentive is: once you have described your hand fully and accurately, let it go. Don’t bid on. Here is the part score hand that decided the match.

Dealer: East Vul: None		Larry Mori
		♠	AJ875
		♥	Q52
		♦	A8
		♣	K72
Wang Wenfei				Liu Yiqian
♠	T42			♠	Q963
♥	KT96			♥	A84
♦	K5			♦	J974
♣	T986			♣	AQ
		Vinkatrao Koneru
		♠	K
		♥	J73
		♦	QT632
		♣	J543

Wang	Mori	Liu	Koneru
—	—	1♦	Pass
1♥	1♠	Dbl*	Pass
2♥	All Pass

Silver	Sun	Carruthers	Wang
—	—	1♦	Pass
1♥	1♠	1NT	Pass
Pass	Dbl	Pass	2♣
Pass	Pass	2♥	All Pass

Liu opened the nebulous Precision 1♦ and later employed a ‘support double’ over Mori’s 1♠ overcall. Koneru wisely stayed out, and Wang was forced to bid an uncomfortable 2♥ on a known 4-3 fit. Good defence would beat this contract by 1 trick, meaning North must lead the 4th highest from his longest and strongest, not unheard of, and South must switch to a club into the teeth of the ♣AQ tenace in dummy, a passive play that doesn’t give up anything that declarer can’t achieve by herself at a time more to her convenience. The brilliant lead of an unsupported ace (♦A) was suicidal, as Wang made 2 tricks over par and scored 140. (After all, bridge teachers aren’t always wrong.)

At the other table Carruthers didn’t avail himself of the dubious advantages of a support double, rather he opted for a descriptive 1NT. Good bid! That contract was bound to make. Sun made a balancing double forcing the partnership to a 2♣ contract that was doomed to a 2-trick set on a trump lead. Cutting down on spade ruffs would be the key move, and we expect that Silver would find it. That result would win the board for the men, with 5 IMPs up and 2 boards to go. Of course, if EW had been able to double for penalty and make it stick ….but now we are dreaming again.

However, Carruthers hadn’t yet shown his 3-card heart support and it is the mark of an expert that he is always willing to bid one more for the road. That might have been OK as the same contract was being played at the other table, but Sun made the second best lead in the suit she had forced her partner to bid and that proved awkward. The contract drifted off 1. China won 5 IMPs,  and with those, the match.

Those who seek perfection might conclude that in the end the Chinese women won on better defence playing in the same contract at both tables. I don’t think so. If you can take IMPs on defence, take them, but it is the uncertainties of the bidding processes that largely determine winners and losers. If Wang had (shudder) passed on Board 28, all this wouldn’t have mattered. Liu would pass instead of bidding 2♠ on a ratty suit, and NS would play peacefully in 1NT. Dream on.

What was right yesterday is wrong today. – Zen Master Ry_kan (1758-1831)

Opinion: Why Meckwell Bid Well

It is surprising to me how many players at my club are ignorant of the  continuing success of the partnership of Jeff Meckstroth and Eric Rodwell, known to aficionados as ‘Meckwell’. It is something of a mystery to many why there are players, like myself, who haven’t joined the crowd and switched to 2/1 Game Forcing methods. Now I can excuse my persistent deviation by pointing to the recent success of Meckwell, who in November spear-headed the Nickell team that won the Reisinger Trophy.

This has been a banner year for Eric Rodwell who won both events in the Cavendish playing Precision with Geoff Hampson and 3 national events in the recent Boston NABC with regular partner, Jeff Meckstroth, as well as placing second in a pairs event with a third partner. He is the ACBL Player of the Year, just ahead of Meckstroth, a frequent winner and the leading candidate for Player of the Decade. I wonder how much weight will be given in the ACBL Bulletin to the fact that Precision must have played a key role in these successes.

I can remember when, before Meckwell became Meckwell, an article in the Precision Newletter in which they stated that their favorite convention was Precision 2♦ . This bid primarily shows 11-15 HCP with a 4-4-4-1 shape, singleton diamond. It does not come up very often and there is a long list of follow-up bids that must be maintained in the memory banks. Thirty years ago that preference struck me as odd, but today I feel it gives good insight into the approach that has made them so successful. The keys are aggression (opening light, competing vigorously) and discipline (keeping to their agreements). The world now has come to see the advantages of a light opening bid, but they have not yet fully embraced the idea of discipline.

Larry Cohen, who maintains a successful Precision partnership with David Berkowitz, has written that consistency is more important than system in determining success. I can see his point, but consistency is no more than assurance that one’s bids are informative to the highest degree possible within their definition. An informative system will outperform a vague system in the same way that a consistent bidder will outbid one who bids what he feels best fits the current circumstances known only to himself, a ‘master-mind’ in common parlance. As I often advise an erring partner, ‘let the system make the mistakes’ but many continue to try to improve on the results by adjusting their bids as they see fit without informing their partners. The vaguer the system, the more freedom they feel they have to adapt unilaterally to circumstances, a practice which only serves to reduce the information content of their bids. Tight definitions increase information by imprisoning the wayward will, and that is one of the advantages of Precision as it demands partnership cooperation.

Meckwell are not entirely mechanical. Jeff Meckstroth will step out occasionally, if for no other reason than to introduce uncertainty in the minds of the opponents. It doesn’t pay to be entirely predictable in a long match against good opponents, however, partner should always act as if the bid is genuine. This is where discipline comes into play. Here is an example of a disaster that resulted from an undisciplined overcall, during the WMSG in Beijing. One is reminded of the debacle created by the so-called ‘The Best and The Brightest’ when they began a war they couldn’t win.

Dealer: East Vul: EW		North: Rodwell
		♠	QJT6
		♥	T62
		♦	A82
		♣	742
West: Pazur				East:  Zawislak
♠	5			♠	A972
♥	KQ764			♥	3
♦	J95			♦	KT74
♣	KQJ5			♣	AT93
		South: Meckstroth
		♠	K843
		♥	AJ98
		♦	Q63
		♣	86

West	North	East	South
		1♦	1♥
Pass	2♥	Pass	Pass
Dbl	All Pass

Losing 500 against a game that was going down in the other room cost 12 IMPs. What did Meckstroth think he was doing? Perhaps he was creating a diversion, or maybe he thought it was Rodwell who had opened a nebulous 1♦ . Rodwell made his normal aggressive raise on 3 small hearts without exploring other possibilities. Once having committed to a contract arrived at using normal procedures, Rodwell did not attempt to correct. Partnership trust must be maintained.

As with the sinking of the Titanic, the result was entirely predictable with hindsight, but it is human nature to plow on regardless always prepared to shed copious tears of regret when the inevitable happens, as it inevitably will. The trick lies in minimizing the long-term damage from our reckless pursuit of short-term gain.

I myself would have jammed on the breaks by bidding 1NT with the North hand, because I don’t like raising on a poor tripleton with 4-3-3-3 shape and no ruffing potential. Meckwell think otherwise. Support with support! The immediate raise is intended to keep the pressure on the opening bidder who is prevented from rebidding in a minor at 2-level. The single raise is both informative and in keeping with the Law of Total Tricks. Partner will know better how to react if the opponents do compete further. Next hand.

Dealer: East Vul: EW		North: Meckstroth
		♠	AT852
		♥	6
		♦	965
		♣	AJT9
West: Berkowitz				East: Cohen
♠	9			♠	KJ76
♥	AJT43			♥	Q5
♦	432			♦	QJ8
♣	7542			♣	K863
		South: Rodwell
		♠	Q43
		♥	K9872
		♦	AKT7
		♣	Q

West	North	East	South
		Pass	1♥
Pass	♠	Pass	2♦
All pass

Another example of partnership discipline shows Meckwell playing in a poor contract that one of them must have felt was wrong. The scoring was BAM, so playing in 2 of a minor with a combined total of 23 HCP doesn’t looks far from promising. Rodwell may have been tempted to raise immediately to 2♠ as he has good support under the restriction of his limited opening bid. However, system requirements are such that he must not raise on just 3-card support, so he bid descriptively in his second suit. Meckstroth must have wanted to correct to 2♠, but he made a disciplined pass, even though there was little hope that Larry Cohen would come to the rescue in clubs.

The result was a disaster. In the other room, ironically Zia, playing unlimited opening bids, felt free to open 1♣ on his aceless 12-count, whereas Cohen, playing limited opening bids, passed. This resulted in Stansby playing the contract in the correct strain, making 170 after the following auction in which the lengths of the major suits were better defined.

Hammam	Stansby	Zia	Martel
		1♣	1♥
Pass	1♠	Pass	2♠
All Pass

So far the reader might consider this the faintest of faint praise and not a very good advertisement for Meckwell methods, but the examples show the restraint they apply which allows them to bid their hands to the full when the appropriate opportunity comes along. Players who are always making adjustments on their own will often fall short in situations when trust is required. Finally, here is an example from the 2008 Reisinger where restraint paid off. Rodwell is our hero.

Dealer: South Vul: NS		North: Meckstroth
		♠	T
		♥	KQT52
		♦	—
		♣	AQJT843
West: Kujarski?				East: Kujawa?
♠	Q965			♠	J732
♥	AJ98			♥	754
♦	AK976			♦	J
♣	—			♣	K9765
		South: Rodwell
		♠	AK84
		♥	6
		♦	QT85432
		♣	2

West	North	East	South
			Pass
1♦	2NT*	All Pass

On misfit hands the side that passes first is the winner. Rodwell had a hand that somewhere in the world is deemed an underbid at 2♦ , but the Precision system wasn’t prepared for the risk. West had a good opening bid and Meckstroth chose to show the 2-suited nature of his hand with a rather heavy unusual 2NT. He must have been surprised and greatly disappointed to end up as declarer in that contract. Minus 200 on good defence was not a hopeful outcome, but all was well as it ended well for the Nickell team. In the other room, NS played in 5♣*, down 800.

The Beautiful Mind    Is there a thin line between insanity and genius? No thinner than between normality and insanity. If one looks at the world objectively, one might observe that even actions that are widely considered to be normal are actually self-destructive and based on false doctrines. A mild example is the current economic crisis based on the proposition that greed is a virtue, not a sin as previously thought. The aspiration at the bridge table as in the stock market is to achieve maximum profit at the expense of gullible victims, the difference being that at the bridge table one needs the cooperation of a capable partner. It is enlightened self-interest to keep partner well-informed so that he or she can make good decisions in the face of the ‘natural’ uncertainty that is part of the game. Huge gambles can pay off in the short term, but in the long term self-indulgent bidding practices set up conditions ripe for disaster.

The beauty of bridge is that it is an exercise in logic and self-discipline. But just look at the results which are spread far beyond the bounds of the ‘natural’ variability that is dealt with the cards. Genius is said to consist of 10% inspiration and 90% perspiration. I’m sure as a boy Mozart practiced night and day. At bridge the perspiration comes when one practices bidding with one’s partner. Those who practice and keep to their agreements will do well enough. The inspirational part comes when one plays the hands at the table. Meckwell are often inspired to take better advantage of the lie of the cards than their opponents, but that would count for little if they hadn’t the discipline needed to maintain an informative bidding style.

Michael, Me, and Information

Michael Rosenberg has always been known for his technical correctness and analytical capacity. For years he was the perfect partner for the glamorous Zia, well known for his immensely successful intuitive plays. The bridge world reveres the Stoics, but loves the Epicureans, so when his book came out, Michael’s title was chosen to be Bridge, Zia and Me, rather than Bridge, Me and Zia. Isn’t it rather ironic that in this year’s Reisinger Cup, the dour Scot got to play on a team with 3 charming ladies who all strike me as John Updike material, world champions Debbie Rosenberg, Sabine Auken and Daniela von Arnim, whereas Zia, the erstwhile ladies’ man, had to sit opposite a grim-faced Bob Hamman throughout, and endure post mortems with Coach Kokish and ‘the boys’. This year coming in third had more than its fair share of compensations.

I have been an admirer of Debbie Rosenberg ever since her appearance on BBO when she commented wisely and wittily on her husband’s bidding habits. Michael is a lucky man. Well, now that they play serious bridge as partners, I am looking forward to Debbie’s book.

Here is a hand they defended in the Reisinger Cup Final in which many felt Michael did less than was possible to help his partner in a tight defensive situation. The question is this: should one sometimes sacrifice technical correctness in an attempt to be helpfully informative to the partner you love and cherish?

Dealer: East Vul: None		North: Casen
		♠	53
		♥	QJ5432
		♦	87
		♣	543
West: Debbie				East: Michael
♠	KJ6			♠	QT742
♥	7			♥	98
♦	KQ96			♦	JT53
♣	KT762			♣	J9
		South: Schwartz
		♠	A98
		♥	AKT6
		♦	A42
		♣	AQ8

 

West	North	East	South
Debbie	Casen	Michael	Schwartz
		Pass	2NT
Pass	4♦*	Pass	4♥
All Pass

 Opening 2NT with a hand containing 9 controls is a good way to miss slam, but there was no problem this time as apparently NS is one of those partnerships where one player bids game and the other partner is expected to make it. The ♦K was led, ducked, and diamonds continued. Declarer drew trumps, ruffed a diamond in dummy and led a spade from dummy. Obviously 2 club losers needed to be compressed into 1.

Some BBO commentators pondered the possibilities of an elimination of spades and diamonds with an endplay in clubs. Schwartz didn’t see the ♣8 as sufficient backup for such an attempt. Instead he decided to play immediately on the defenders’ uncertainty. When Michael played the ♠4, Schwartz covered with the ♠9, and there was Debbie on lead and facing a guess in the black suits. A return of the ♠K defeats the contract, but she got it wrong when she played a fatal club. From her point of view, declarer might have been playing from the combination of ♠AQ9, in which case his clubs would be skimpy. To sympathetic observers it was rather obvious that Michael hadn’t been of much help in the endgame.

David Burn, whose comments I find insightful, thought that Michael couldn’t risk playing the ♠T on the lead from dummy as he would give away the show if Schwartz held ♠KJ9. I wasn’t convinced this time, as it was quite possible that Schwartz would have played the ♠9 from that combination. Furthermore, is KJ9 the most likely holding one can attribute to declarer?

Experts aren’t all strong on signals. Rixi Markus once famously said to a younger, inexperienced partner, ‘Don’t signal, Dear, I know better than you what you’ve got’ (or words to that effect). Maybe she felt that her neophyte partner’s signals contain an element of outrageous condescension. I suppose someone like Zia could feel the same way. Although I hope it wasn’t so, I can imagine Michael saying to Debbie, ‘I think you should have been able to work it out.’ Who has the better excuse? I look at it from the point of view of who has the more relevant information. It is that partner who is under an obligation to share what he knows, even if that requires a play that in isolation may not be otherwise optimal. Here East holds key honors in the black suits, so is in a better position to place the cards. Here is a reasonable construction of the black suits from East’s point-of-view where declarer has an entry to dummy in trumps.

		♠	53
		♣	543
♠	A86			♠	QT42
♣	KT6			♣	J9
		♠	KJ9
		♣	AQ8

When East plays a low spade on the first lead from dummy, declarer can duck to West by playing the ♠9. Whether West wins with the Ace or not, it is game over. If instead East puts up the ♠T, actually his worst choice, declarer certainly covers with the ♠J, and the same result is achieved. The ♠Q from East presents a problem. When declarer covers with the ♠K, West can duck smoothly knowing partner doesn’t hold the ♠J. On the next round of spades, declarer may be tempted into putting up the ♠J and lose the endplay position. Being known as somewhat unreliable would help East here. Of course, there are other possibilities, so let’s concede without proof that Michael’s play was correct technically, but still condemn him for not putting up the informative ♠Q.

It is acknowledged that a defender with a weak hand should signal, but I carry it a bit farther. If I am defending with a partner who can use a little help from time to time, I consciously make a play that should provide useful information especially when the endgame looms large. When defending a doubled contract I aim first to assure putting it down 1. Although as a result I sometimes take valid criticism, I have found that in the long run it works, especially on close doubles, because declarers these days by design or fault are not reliable bidders. Recently I was told by a partner, ‘why didn’t you lead a trump? I thought you wanted a ruff, but she was short in clubs, not you!’ What could I say? I was only trying to help. (Secretly I think he should have worked it out!)

Can we extend the principle of disclosure to lead-directing doubles? Not without reservations. Once the opponents have started cue bidding towards slam, any information provided without cost by the defenders is only going to help them make the right final decision. There are some examples of backfiring doubles in my upcoming book Bridge, Probability, and Information.

The Shifting Sands of Probability

Although it is certainly not the best of all possible worlds, it might be the most probable

– Jules Henri Poincairé, French mathematician and philosopher (1854-1912)

As a schoolboy I was trained to think in terms of numbers, the very bases of scientific knowledge. Do they still teach that way? I wonder. Maybe not as much as before, but the numerical way of thinking is certainly useful when it comes to following presidential elections, and more importantly, to playing bridge. During the recent elections we have heard repeatedly the results of opinion polls and have been constantly warned about their unreliability. The statistics changed with time, but they have proved to be an accurate gauge of how things were going to turn out in the end. Well, the same applies to bridge probabilities – they may change during the play of the cards, but they are usually a good guide to what will happen, baring the occasional nasty surprise.

In the world of bridge we have probabilities fed to us by the writers and commentators. I had always accepted these percentages at face values, but once I had the time to look more deeply into the whole concept of probability, I discovered the assumptions that lie hidden behind the figures and that all too often are lost in discussions which lead to misleading conclusions. The idea that ‘probabilities never change’ was one of the first assertions that fell by the wayside, as, of course, this is contrary to common sense. The correct way of thinking is ‘probabilities change according to what information becomes available’. If they didn’t, we’d be living in a strange world where ignorance would surely be bliss.

Some are reluctant to admit that bridge is a game of guesses, but it is that because it is played in an atmosphere of uncertainty. ‘Guess’ is not a dirty word. Our lives are governed by chance. Probability is a way of organizing our guesses and assigning them proportions. Of course, at the end of the hand when all 4 hands have been revealed one may realize that there were clues along the way that should have pointed us in the right direction. (By the way, did you dump your stocks in a timely fashion?) The skill of an expert is to adopt his play to what has been revealed as the bidding and play proceed. The main theme in the following blogs is that probabilities change with circumstances.

There are very successful players who haven’t mastered Probability Theory, although they apply it in a practical way based on experience. Sabine Auken in her great memoir I Love This Game has described how her curiosity has been piqued at a later stage of her career. The question arises, why should we ordinary players be interested? If one is to use probability successfully then it is necessary to understand how hidden assumptions come into play so as not to be distracted unduly by the numbers lifted from textbooks. Probability should be a way of expressing common sense in numbers. Of course, once one has mastered the basics, there are many applications to be found away from the bridge table.

One foundation of analysis is the table of suit combinations to be found in The Official Encyclopedia of Bridge and elsewhere. Expert players are expected to know these backwards and forward. If they don’t play accordingly, they are open to criticism from the pundits, but maybe the expert had his reasons. Well, I am nothing if not critical, and in many situations there can be arguments both ways. We begin by looking at expert play in an 8-card suit missing the Ace and Jack when the 2008 bridge championships of the world were at stake.

About Five Missing the Ace-Jack

The English Open Team that reached the finals of the 2008 WMSG was formed after

trials involving teams of 4. A third pair was added to the winning foursome on the basis of current form. The added pair were Tom Townsend and David Gold who were judged by some to be the best English performers in Beijing. Let’s see how this pair fared against their future teammates in the trails where under different circumstances 2 experts played differently a heart suit of 8 cards missing the ♥AJ.

Vul: East/West		North
		♠	J73
		♥	AJ
		♦	8753
		♣	J972
West				East
♠	A96			♠	K42
♥	KQ9653			♥	T8
♦	AQJ			♦	K642
♣	T			♣	AK54
		South
		♠	QT85
		♥	742
		♦	T9
		♣	Q863

The bidding without interference took different routes at the 2 tables, one EW pair reaching a slam in hearts played by West, the other game in diamonds played by East. The key at each table was the play in the heart suit.

Townsend-Gold reached 6♥ played by West. The lead was the ♦7 won by declarer in hand. He went to dummy with the ♣A. The problem is straightforward –  what is the best play to avoid more than 1 loser in trumps. Declarer immediately suffered defeat by running the ♥T to the ♥J. This is the safety play for 4 tricks as it picks up 4 cards with the Jack in the South hand but the references will tell you that the best play for 5 tricks is to go up with the ♥K on the first round.

Of interest is what to do on the second round of trumps if the ♥K loses to the ♥A. An imprecise short-cut argument based on Reese’s Rule of Thumb leads to the correct decision on this hand as follows. Suppose North takes his Ace on the first round. With AJ he would be obliged to do so, but with Av he might hold off the Ace. This affords the assumption he played the Ace of necessity from AJ.

Of course, each case should be considered fully on its own merits. The key decision needn’t be made until declarer plays the second round from the dummy and South follows with a second low card. Let the low cards be denoted by the letters u, v, and w. Here are the 2 conditions remaining that afford a winning position after the sequence of u-A-w:

	I		II
	South	North	South	North
	Juw	Av	uvw	AJ
Plausible Sequences	4		6
	u-A-w		u-A-w	u-A-v
	w-A-u		w-A-u	v-A-u
	u-v-w		v-A-w	w-A-v
	w-v-u
Probability Weights	1/4		1/6

With Av North might hold up the Ace on the first round, giving him 2 choices, so Condition I has at most 4 plausible sequences available. Under Condition II South has 6 ways to play 2 insignificant cards from a selection of 3, whereas North has no plausible play other than taking his Ace. If under Condition I one judges that North is equally likely to take the Ace as not, the 4 plausible sequences are equally probable. The probability that the defenders chose to play in a particular observed sequence, u-A-w, has the probability of choice of 1 out of 4. As a consequence the probability of Condition I is subject to a reduction of 1/4 once the given sequence has been observed. A similar deduction is that the initial probability of Condition II must be reduced by 1/6 once the sequence u-A-w has been observed.

Reese’s Rule would give the correct theoretical answer if only 2 cards had been played, u-A, say. Condition I has 4 plausible plays at that point, while Condition II has 3. Thus, the probability weights are 4:3 in favor of AJ doubleton. It is the random choice of play of the insignificant cards that determines the weights.

Quantification of North’s Choice

From the bidding the North defender has a good idea of the lie of the heart suit and could very well be inclined to hold up the Ace depending on the circumstances. The question is how his inclination alters the probability weights. Declarer cannot be certain of how North would play from his holding of Av, but he may (should) assume a particular tendency. An assumed frequency of hold up on the part of the North defender gives an indication of whether or not to finesse for the Jack on the second round, as the following table shows.

Hold-up Frequency	Weight I	Weight II	Decision
4 out of  5	3	5	Drop the Jack
3 out of  4	3	4	Drop the Jack
2 out of  3	3	3	Toss up
1 out of  2	3	2	Finesse
never	3	1	Finesse

The hold-up frequency of 1 out of 2 assumes that North will play the Ace at random on a 50-50 basis. The fractional weights given previously are expressed in integer format for convenience, the ratio of 3:2 being preserved. If North would hold up the Ace 2 out of 3 times, it would be a toss up as to whether or not to finesse for the Jack. Any greater frequency of hold-up would favor an attempt to drop the Jack. If North would never hold up the Ace, there are 2 possibilities under Condition I and 6 under Condition I, so the odds becomes 3:1 that the finesse will succeed, based solely on the number of permutations in play of insignificant cards in the South hand.

All’s Well That Ends Well

At the other table the lead against 5♦ by East was the ♠5 won by declarer in hand. Immediately he began the heart suit by leading the ♥T to the ♥K, losing to the ♥A. The ♠7 was returned to the ♠A in dummy, creating a loser in that suit. The temptation for declarer is to return to hand with the ♣A, discard the spade loser on the ♣K, and finesse South for the ♥J if he judges North would hold up his Ace fewer than 2 times out of 3. On the other hand, if declarer thinks North would hold up at least as frequently as 2 times out of 3, under the circumstances he can save time by playing the Queen immediately with the additional chance of dropping the bare Jack in the South if the cards had been dealt Ju opposite Avw (Condition III).

The declarer, Nick Sandqvist, didn’t lose his focus because he might have missed reaching a makeable slam. He drew two rounds of trumps with the ♦A and ♦Q, South following with the ♦9 and ♦T, cards of significance. He could judge that South’s diamonds were more likely to have been played from a doubleton ♦T9 rather than from a tripleton ♦T98, leaving North with ♦87 remaining. This is another example of restricted choice in action where with ♦T98 South would have had 6 choices in the sequence of his plays, whereas with ♦T9 doubleton he would have had just 2 choices.

We don’t know whether Sandqvist had Reese’s Rule in mind, but at trick 6 he made the right decision when he played the ♥Q from dummy dropping the ♥J in the North, so was able to continue the established heart suit to embarrass North who couldn’t afford to ruff even though the ♦87 were equals in front of the ♦K6. By not blindly following the standard advice and making the right play in the wrong contract led to a 13 IMP gain early in the match, which the Sandqvist team went on to win by a large margin.

More About Five Missing the Ace-Jack

The final of the women’s 2008 WMSG Championships was won by England over China by the slim margin of 1 IMP over 96 boards.    The purist might say that the difference was a vital overtrick, implying that missing an overtrick can be a critical play even in such a long match. Well, yes, but the difference could be more than made up by avoiding many of the simple errors one observes in the bidding and play. In that regard England was the more steady team throughout and deserved their win, although they almost blew it in the last 16-board segment. To me the lesson is this: bid aggressively, avoid major errors in the play of the hand, cooperate with you partner, and your team will be hard to beat. There is too much variability built into the results to be worried about overtricks.

One of the sources of percentages in play are those related to how a declarer should play combinations of cards in a given suit. An abundant source of this type of information is available in The Dictionary of Suit Play Combinations a great reference book written by J.-M. Roudinesco. If that is not enough, there is the compute program, Suit Play, created and made available on the Internet by Jeroen Warmerdam. In the following segments I continue to look at the recommended play in suit combinations where 8 cards are missing that include the Ace and the Jack. If the Chinese Women had got one of these right they would have gained enough IMPs to win their final match handily. By examining the hands in detail, we should get a deeper understanding of how probability analysis should be applied under changing circumstances.

Going with the Odds

The first combination we shall ponder is QT opposite K97652. The textbook play is low to the Queen, and regardless of whether that wins or loses, to run the Ten on the next round. The chances of this providing 4 tricks is close to 96%. That figure is derived from considering the suit combinations in isolation from the full deal. As this is based on the prior expectations of how the cards were dealt, the approach yields a valid approximation when very little is known about the defenders’ hands. If they have passed throughout, one may assume that the suits are likely to split more evenly than expected a priori, but that may not greatly affect the calculation of odds. Here is the hand from the final where the Chinese declarer went against the odds and lost 6 IMPs as a result.

Dealer: East Vul: Both		North (Wang)
		♠	A94
		♥	QT
		♦	862
		♣	QJ974
West (Brock)				East (Smith)
♠	T832			♠	Q765
♥	83			♥	AJ4
♦	A975			♦	43
♣	K32			♣	AT86
		South (Sun)
		♠	KJ
		♥	K97652
		♦	KQJT
		♣	5

West	North	East	South
		Pass	1♥
Pass	1NT*	Pass	2♦
Pass	2♥	Pass	3♥
All pass
	*forcing

Sun held a good hand in the context of a  Precision opening bid, only 5 losers, so she raised herself to the 3-level where others holding the hand were content to stay put in 2 hearts. The lack of aces is a defect not overcome by the distribution, and perhaps the diamond suit is overly rich with honor cards while the heart suit is rather sparse in that regard. In the Open Final where Italy faced England neither South was allowed to play in 2♥ as West balanced and EW played in a contract of 2♠ , going down 1. At the other table in the women’s final, Nevena Senior played undisturbed in 2♥ making 3. So Sun did the right thing in theory as her 3♥ contract appears to be solid and prevents the opposition from balancing into their optimum contract of 2♠ .

The opening lead was an innocuous ♠2 won by the ♠K when Nicola Smith played her ♠Q. The play in the trump suit was now front-and-center, and if Sun had gone with the percentages, China would have won the championship. A point well made by Linda Lee in her blog of October 19 was that there was some urgency in the trump play as the lack of controls for the declaring side made it a race to the finish line with declarer hoping to prevent the opponents establishing the setting trick before declarer makes sure of her 9 tricks.

Sun didn’t feel the urgency even though the defenders held minor suit aces that provided them with transportation. This wouldn’t have mattered if Sun played the trump suit optimally according to the a priori odds that is, low to the ♥Q, planning to run the ♥T next. The ♠A was still there as a safe entry to dummy to allow this sequence. Unfortunately for China, Sun chose to play a heart to the ♥T and the ♥J. Nicola Smith had defended well throughout the Final and here she was quick to take the opportunity of obtaining a ruff in diamonds. She led the ♦4 and Sally Brock took her ace to returned a diamond immediately just in case that ♦4 was a singleton. Not so, but it didn’t matter as Smith on winning the ♥A underled her  ♣A and got the ruff that set the contract and brought 6 IMPs England’s way, a critical swing late in the match.

When 2 high honors are missing, it is a great temptation to finesse against the lower honor first. The motivation is that this guards against one defender holding A-J-x in front of the queen. Another reason for adopting this approach would be that declarer places the Ace behind the QT, in which case the odds usually favor the honors being split. We shall examine this argument in the next segment.

Placing an Ace

The following hand played early in the Final matches of the Open, Women’s and Bronze Medal series. It involved declarer play in a suit with the following construction:

♣ K9765 opposite ♣ QT3.

The textbook play for 4 tricks with the suit taken in isolation is to lead to the ♣Q and if that holds to pass the ♣T. That assumes declarer has no information on how the cards clubs may be distributed. The odds of success are 57%, but the bidding may change the a priori odds. Let’s see the whole hand and how it was played in the Open Series where Italy faced England.

Dealer: East Vul: North/South		North
		♠	A65
		♥	K
		♦	K532
		♣	K9765
West				East
♠	94			♠	KQJ75
♥	QJ8753			♥	T64
♦	87			♦	Q96
♣	A84			♣	J2
		South
		♠	T82
		♥	A92
		♦	AJT4
		♣	QT3

West	North	East	South
Townsend	Lauria	Gold	Versace
		Pass	1♦
1♥	2♣	Dbl	3♣
Pass	3♦	Pass	3♥
Dbl	5♣	All Pass

Gold led the ♠K and Lauria held up. Gold switched to the ♥4 after which Lauria won to run the ♣9 around to Townsend’s ♣A. The heart return did no damage as a losing spade could be discarded on the ♥A. Obviously Lauria’s play in the club suit was predicated by the bidding and the opening lead from a high honor sequence which placed the ♣A in the West hand. He assumed the ♣J was in the East. He could have taken the necessary finesse in diamonds at trick 3 and led the ♣3 from dummy, guarding against ♣AJ doubleton in the West.

In his book Playing with the Bridge Legends Barnet Shenkin makes the point that when amateur analysts (like myself, I admit) criticize experts, they are usually wrong – even with the help of Deep Finesse, I am willing to concede. Who are we to question the great Lauria? Nonetheless no player is perfect and we amateurs mustn’t give up on trying to understand the mental processes at play. We shall explore this later.

In the Open Bronze Medal match, Germany against Norway, Kirmse played in 3NT after West showed values and a heart suit. Here was the bidding at his table.

West	North	East	South
Aa	Gromöeller	Molberg	Kirmse
		Pass	1NT
2♦*	Dbl	Rdbl**	3♦
Pass	3♥	Pass	3NT
All Pass

The German declarer won the heart lead in dummy and followed Lauria’s line of running the ♣9. That doesn’t seem right even though it succeeded in gathering in 10 IMPs. The danger is that the opposition may find the spade switch if given 2 tries when West wins the  ♣J without holding the ♣A. So now we have evidence of 2 experts going against the conventional wisdom of ‘low to the Queen.’

Child’s Play?

The term ‘Chinese finesse’ is a derogatory one referring to a play that depends on an error on the part of defenders in not covering an unsupported honor played from the hidden hand. The declarer runs the unsupported honor and makes an undeserved winner. It is the defender who has erred. I now propose that the term ‘Chinese Drop’ be applied to a play that also appears to be ridiculous, except when it works. The Chinese women could have won if they had employed a play that on the surface appears to be one that only a novice would make: low to the Queen, then low to the King.

When it comes to the replay of the hand in the Women’s final, I cannot get rid of the feeling that something was definitely wrong in declarer’s approach of making the standard percentage play in the club suit. Let’s see if you agree.

West	North	East	South
Dhondy	Wang	Senior	Liu
		Pass	Pass
2♦*	Dbl	2♥	3NT
All pass
*Multi

Heather Dhondy’s lead was the ♥ 7, won by Liu Yi Qian in dummy. She led the ♣ 5 to her ♣ Q and Dhondy ducked that as the ♣ A was her only entry. Liu led a second club from her hand, Dhondy following with the last outstanding low club, the ♣ 8, and here Liu missed the seemingly ridiculous but winning play of going up with the ♣ K to drop Senior’s now bare ♣ J. Let’s see the most probable possibilities when Dhondy followed to the second club play.

	Dhondy	Senior
Situation #1	8-4	A-J-2
Situation #2	J-8-4	A-2
Situation #3	A-8-4	J-2
Situation #4	A-J-8-4	2

                                                                       

In Situation #1 there is no winning play, so we can rule that out, as we must play for success. Situations #2 and #3 are equally likely on the deal, but isn’t it more likely on the bidding and play that Situation #3 holds? Without an entry in clubs, West might have led a spade hoping to hit her partner’s suit, whereas with the ♣ A she would rely on setting up her own suit.

In my experience when an opponent enters the bidding with a flimsy suit, and leads that suit against 3NT, it is more likely that the bidder holds a top honor in my long suit. So, here when NS holds ♥ AK, it is more likely that West holds the ♣ A. With regard to the dealing of the cards alone that would have no mathematical foundation.

The Division of Sides

One of the most useful pieces of information available to declarers is the division of sides. It is also the most neglected. When the dummy appears a declarer knows how many cards are missing in each suit. One can link this to the probability that a particular distribution exists in one hand or the other. Here the question is whether Situation #4 is a live possibility, and, if so, how to take that possibility into account. That would give West 6 hearts and 4 clubs. Let’s look at the possible divisions of sides when the opponents hold 7 spades, 9 hearts, 5 diamonds, and 5 clubs and the hearts are split 6-3 and West holds at least 2 clubs.

	I	II	III	IV	V
	♠ 3 – 4	♠ 2 – 5	♠ 2 – 5	♠ 3 – 4	♠ 2 – 5
	♥ 6 – 3	♥ 6 -3	♥ 6 – 3	♥ 6 – 3	♥ 6 – 3
	♦ 2 – 3	♦ 2 – 3	♦ 3 – 2	♦ 1 – 4	♦ 1 – 4
	♣ 2 – 3	♣ 3 – 2	♣ 2 – 3	♣ 3 – 2	♣ 4 – 1
Weights:	100	60	60	50	15

The Probability Weights given along the bottom are easily calculated from the assumed splits. I’ll show you how in a later blog if you’re interested. By far the single most likely is Condition I, but we see that this is a losing configuration corresponding to Situation I. The same is true of Condition III. That leaves Condition II as the most likely winning position, corresponding to Situations #2 and #3. Condition V, representing Situation #4, is only 1/4 as likely to have been dealt.

How the Unplayed Suits Contribute to Probabilities

Probabilities are derived from ratios of the number of suit combinations. In the case at hand there remain 2 honors missing, 2 possible splits in clubs, and 3 distribution of sides. We can add together the number of suit combinations in the unplayed suits, diamonds and spades, to obtain an estimate of the probabilities of success of the 2 possible winning plays, namely, running the ♣T and going up with the ♣K.

Play	II	IV	V	Total	Weights*	Percentage
Run T	210	175	175	490	14	56%
Run K	210	175	0	385	11	44%
				*Weights are the number of combinations divided by 35

A calculation of the ratio of suit combinations yields the result that the probability of success for running the ♣T is 56%, very close to the a priori probability. An assumption that underlies both calculations is that we are not at liberty to assume that the ♣A is more likely to have been dealt to the West hand. Another way of thinking of this assumption is that we are maximally uncertain as to the location of the ♣A. However, as noted above, we should be surprised if the ♣A were not with the West player for the reasons stated. If one could say that the probability of ♣A being with West was 56% the 2 plays would have the same probability of success. Anything greater than 56% and rising with the ♣K becomes the preferred play. I would estimate that West would hold the ♣A and play the way she did as greater than 3 times out of 5 (60%), and that is my basis for stating that the Chinese Drop represents the best chance at this stage where all the low clubs have been played. Yes, the Chinese Drop is not so dumb as one might expect. It is even the percentage play, given the information that is available at the time of decision.

Luck lies not with the player but in the placement of the cards. Probability Theory, properly applied, is the best tool for extracting it.

 

The Maximally Likely Distribution of Sides

Returning our attention to the Open Bronze Medal Series we ask why did Kirmse play for the ♣J to be in the East? If you see him, ask him, and let me know. Ask Lauria the same question. I can see a connection between the choice of plays and the most likely division of sides represented by Condition I. In that configuration the clubs are split 2-3 with 3 in the East. Generally it is the better play to start a suit by playing through the defender holding the greater number of cards in the suit. Let’s see how the first card played affects the odds. Here are the possible combinations.

Constituents		Number	Possibilities
East	West
A-u-v	J-w	3	u,v, or w in the East
J-u-v	A-w	3	u,v, or w in the East
A-J-u	v-w	3	u,v, or w in the West
u-v-w	A-J	1	no possibility of a low card in the East

When a club is led from the North hand,  East follows with a low card, specifically card w. That eliminates the least likely combination. The probabilities of A-u-v and J-u-v are the same but have been halved as the low card v could have been as easily played as card w. (A consequence of Bayes’ Theorem). There is no winning option for A-J-u in the West, so, based on the dealing of the cards alone, it is a 50-50 choice as whether to play the ♣ Q or run the ♣ 9. However, the bidding has indicated the ♣ A lies in the West, so the odds clearly favor running the ♣ 9 with an edge given by the bidding.

One might say that this analysis is rather naive. It is certainly incomplete as we has considered only one possible division of sides. That being said, I am somewhat amazed by how often the maximally likely division of sides turns out to be a reflection of reality. The longer the defenders follow with low cards to declarer’s plays, the more likely that condition becomes. Those plays have eliminated the possibility of extreme splits.

When a declarer starts playing his suits, he should have a plan in mind. Taking into account the most likely division of sides makes sense. A simplification based solely on the maximum likelihood division is not rigorous, but it may focus the mind in a beneficial way. If the problem faced is a complex one, declarer may gain clarity through simplification. It is a start. By solving a simple problem, one hopes that the more complex problem has the same solution. Probability is on your side. If you can think more deeply, and consider more possible distributions, great.

What one can do in many situations is gather more information before making a critical decision. Every bit of information helps, and the probabilities change accordingly. When Liu played the second round of clubs from her hand and West followed with a second low card, she gained information. The most likely distribution of sides could be eliminated as encompassing a winning choice. Attention should then have been concentrated on the second most likely condition, specifically, the clubs splitting 3-2.

Probability and Information from a Surprise Action

The greater the surprise, the more information the action transmits. Let’s suppose that on Board 2 Dhondy and Senior had not entered the auction. In this day and age, that would have been a surprise as when the dummy came down Liu could see EW held 17 major suit cards and 16 HCP between them. There are 6 equally most likely distributions of sides for a 7-9-5-5 division, namely,

I	II	III	IV	V	VI
♠ 3 – 4	♠ 3 – 4	♠ 4 – 3	♠ 4 – 3	♠ 4 – 3	♠ 3 – 4
♥ 5 – 4	♥ 5 – 4	♥ 4 – 5	♥ 4 – 5	♥ 5 – 4	♥ 4 – 5
♦ 3 – 2	♦ 2 – 3	♦ 3 – 2	♦ 2 – 3	♦ 2 – 3	♦ 3 – 2
♣ 2 – 3	♣ 3 – 2	♣ 2 – 3	♣ 3 – 2	♣ 2 – 3	♣ 3 – 2

Based on the inaction of this normally active pair, one might downgrade Conditions V and VI for which one player holds 5-4 in the majors. Next consider the opening lead. If it is a heart, this is most consistent with Conditions I and II, as a player is most likely to lead from her longer suit. Note that a 3-2 split in clubs is as likely as a 2-3 split.

But suppose the opening lead was the 5 from the player on the left. That would be a surprise, and surprises greatly affect the probabilities. None of the above 6 conditions makes sense with this lead. Declarer might then consider other options, in particular, that the lead was from a singleton. She would then consider a distribution of sides based on that assumption and work from there. Here are some main candidates together with their probability weights relative to the above set.

	VII	VIII	IX	X	XI
	♠ 4 – 3	♠ 4 – 3	♠ 5 – 2	♠ 5 – 2	♠ 4 – 3
	♥ 5 – 4	♥ 6 – 3	♥ 4 – 5	♥ 5 – 4	♥ 4 – 5
	♦ 1 – 4	♦ 1 – 4	♦ 1 – 4	♦ 1 – 4	♦ 1 – 4
	♣ 3 – 2	♣ 2 – 3	♣ 3 – 2	♣ 2 – 3	♣ 4 – 1
Weights	50	33	30	30	25

The relative weights are based on the number of card combinations available on a random deal. The bidding must also be taken in account. As the opening leader has passed throughout, more weight must be given to Condition XI. It makes sense that with a 4-4-4-1 shape a player would tend to remain silent throughout the auction whereas with 5-4+ in the majors, she would be inclined to make some noise during the auction, so Condition X belongs at the end of the line and Condition XI moves to the top.

Nothing is certain, and that why we must revert to probabilities. It is possible that the opening leader decided to make a ‘safe’ lead from xxx in diamonds because of observed gaps in the majors. Some may even hope to make a deceptive lead. The general rule is that the best deceptions come from actions that appear to be normal. Such players will lead from worthless doubletons for no other reason that they hope declarer gets it wrong. That’s unusual, which is the reason why the technique is sometimes effective, but such occasions are rare. Based on likelihood considerations, what appears to be normal should be assumed to be normal. To be constantly suspicious of a normal action is to present yourself with one more way to lose. Be resigned to being deceived occasionally, and move on. That is the way to keep on the right side of probability, besides which, it’s easier on the nerves.

Sound Advice: If the opponents were sucessful taking a ‘wrong’ view, think that they gave your side a chance for a good score that didn’t quite pay off this time. Be patient. In the long run you will benefit from their poor decisions.