The Golden Rule at Matchpoints

Most play bridge for the fun it provides, and the most fun comes from the quick thrill of a lucky play. That’s a dangerous approach in the long run, so don’t say I didn’t warn you, but, hey, missed opportunities are just as bad, even though you don’t feel them as acutely at the table. To pursue immediate pleasure or to avoid future pain? As with many dilemmas of a philosophical nature, it’s your choice, no matter what Epicurus (341-270 BC) may have claimed. There is a third way, play with equanimity, free from anxiety, and always go with the percentages.

Parents set down rules for their kids, ‘brush your teeth after meals’, ‘ go to bed at nine’, etc. Parents don’t say to a 4-year old, ‘do what you think best’. (Although the trend appears to be in that direction.) Kids respect the rules, and the world might be a better place if everyone was home in bed at nine o’clock, but as time goes by kids learn from experience to make exceptions. A distraught mother may admonish a daughter not to scream in public, but if the daughter grows up to be an opera singer, the rule goes by the board. When the prima donna plays Tosca about to jump off the Papal parapet, her mother may urge, ‘scream as loud as you can, dear, the audience will love it.’ Whether it’s the opera house or the super market makes all the difference.

So it is when beginners are taught bridge. They are not told directly to do what they think best, rather they are taught rules, rules which will stand them in good stead in most situations, but rules that should be broken as the circumstances dictate. Beginner’s rules are for beginners. Take the finesse, for example. Students are shown how a declarer can create an extra trick by taking a finesse and are given numerous examples how this works. They are taught, ‘take your finesses and don’t fist-pump when the desperate ones succeed.’ Students are not told how to avoid a finesse by employing a strip-and-endplay, because that is a topic for the master class, and it may be hard to spot the possibility in any case. It’s easier for the average player to keep on finessing, regardless. Only advanced players can follow the golden rule: choose the path mostly to lead to success.

In order to judge whether a given bid or play is likely to be successful, one needs a working knowledge of the probabilities of the success of various options. At matchpoints especially one should not make a play that is against the odds. In many cases it is better to play for a plus rather that hope that a finesse will work when you feel it won’t. How can one expect to win by playing against the odds? Before one can think in these terms, one has to learn how to estimate the odds at the time of decision, which may be when the dummy first appears, or near the end when more knowledge has been gathered.

The knowledge one seeks is to what extent the current deal departs from normality. One has to gauge the state of affairs and decide what is most probable. Sometimes one has a rule that covers the situation and sometimes one may decide instinctively guided by previous experience on other hands of a similar nature, but often one has the clues available to make a decision based on the current probabilities.

The Golden Rule when Bidding

Differences due to system are most strongly felt in the bidding of slams. In a mixed field many players are content to end up in 3NT rather than in a minor suit slam simply because the field will not be confident enough in their methods to attempt the higher scoring contract. This approach feeds upon itself, as even superior players will play down to the field. Slams are becoming rare, whereas previously the bidding of slams was considered to be the keystone to good bidding practices. Now failing to bid a cold slam may result in only a small loss as the vast majority will be stuck in the same boat. Using Precision on the following hand I am ashamed to relate that I fell into the trap of bidding down to the level of the field.

The initial response to the Precision 1♣ showed a game-forcing hand with 5 or more spades. Using a series of asking bids I was able to discover that partner held at least 5 spades to the king, 3 high-card controls, and second round control of the clubs. By bidding 5♣ I could find out whether the club control was a singleton or the ♣K. If John held a singleton club I would stop in 5♠ with work to be done with the field stuck in game with 17 HCP opposite 9 HCP. If he held the ♣K I would bid 6♠ with good chances of making 5 spade tricks, 6 club tricks and the ♦A. Playing to minimize my loss if I were wrong, I stopped abruptly in game when it would have been better (although not optimal) to go directly to 6♠ over 4♣ because the odds were greatly in favour of finding the ♣K opposite. In a field of 11 pairs, fully 10 pairs stopped in game so ostensibly I was not punished for my bad bidding. Nonetheless it was a mistake to defy the Golden Rule by rejecting an action that was more likely to be right than wrong.

Maximize the Gain or Minimize the Loss?

There are two common approaches to decision-making: minimize the loss if you guess wrong, or maximize the gain if you guess right. Let’s consider the scores one would receive by bidding for the higher score regardless of what the field is doing. Assume 11 tables with eight pairs in game, two in slam. Here are the splits in matchpoints resulting from the decision on whether to bid slam or stay in game.

Bid slam and it makes 9 Bid game and slam makes 4

Bid slam and it doesn’t make 1 Bid game and slam doesn’t 6

With 10 matchpoints available there is greater variability when one goes against the majority and bids the slam. There is less variability when choosing to bid with the majority, even if they are wrong. Say P represents the probability that the slam makes, M represents the number bidding slam and N, the number resting in game. The average score for bidding slam is (M+N) x P/2 and the expected score for bidding game is (1-P) x (M + N)/2. The average score for bidding slam will be greater than not bidding it, if P>1/2, regardless of how the field has split. This is the origin of the Golden Rule.

A probability of ½ represents a state of maximum uncertainty. It follows that if one has some reason to suspect slam will make one should bid it. Trust your instincts, especially when they are right. Clearly, I was wrong not to bid 6♠. I might excuse myself by saying that near the end of a successful run I was happy to minimize my potential loss knowing I would have lots of company in game. In the long run this thinking is bad. One is playing to surpass the good players in the field. It is to be expected that you will outscore the bad ones. How would my partner have felt if we had come in second overall by a couple of matchpoints? Not good.

The Matchpoint Anti-Finesse

The Golden Rule applies equally when making a play decision. Very often this reduces to fishing for a queen. Many feel they must take all the tricks available in a common contract, so will finesse at every opportunity. Play may degrade into a frenzy of finessing, declarers being unwilling to forego the extra trick obtained when the finesse happens to succeed. They are playing to maximize the number of tricks taken, and if the finesse fails it won’t cost that much with most playing in the same manner. However, one shouldn’t take a finesse that is more likely to fail than not. The following hand recently played at the local club represents a situation where declarer does best by taking an anti-finesse.

West overcalled the opening bid of 1♥ with a call of 1NT, not everyone’s choice. Partner evoked Stayman then left him in 2NT. The opening lead was the ♥T and questions were raised at the table as to why East didn’t raise to 3NT. However, it appears his caution was justified as 8 tricks may be the limit as the cards lie. South took his ♥A and continued a low heart to the ♥K, LHO following with the ♥9. At this point South had 3 heart tricks to take if and when he gets in again.

One of the main advantages for declarer is that upon seeing the dummy he immediately knows the division of sides. When the division of sides is 7-7-6-6 it often pays declarer to go passive and give up the obvious losers early rather than trying to create an additional winner by force. Sometimes pressure is applied in this manner. The active approach is to overtake the ♠Q in dummy in order to take the club finesse. If it wins, continuing clubs will create 9 tricks provided the RHO holds ♣ Qx(x). If the finesse loses, there is still an excellent chance for taking 8 tricks, via 2 spades, 1 heart, 1 diamond and 4 clubs.

The question to ask is whether or not the club finesse is likely to succeed. By overtaking with the ♠A the number of spade tricks is reduced from 3 to 2, so declarer has to make an extra trick in clubs to make up for the loss. What are the chances the finesse will succeed? For his first seat opening bid South needs the ♦K and at least one minor suit queen. With 15 HCP he might have opened 1NT. North has 11 vacant places to South’s 7, so the chances of South holding the ♣Q is less than 50%. That indicates declarer should avoid the finesse. Let’s look at the most likely division of suits.

The two main candidates are North 4=2=4=3 opposite 3=5=2=3 and North 4=2=3=4 opposite 3=5=3=2. If clubs are split 3-3, it is 50-50 whether the finesse succeeds or not. If the clubs split 4-2, the finesse will probably fail. As the shapes are equally likely, declarer is unlikely to maximize his score by taking the club finesse.

What is the alternative plan? Declarer can cash the ♠KQ and play the ♣J hoping that North must take the ♣ Q. If so, declarer has 9 tricks easily. North must duck the ♣J if he holds four to the queen in order to destroy the communication with dummy and hold declarer to 8 tricks. But some might win at the first opportunity and exit ‘safely’. That is an edge that can be exploited. On the other hand if South has the ♣Q, declarer is held to 8 tricks immediately. It would be a cause for general merriment at the table if South held a singleton ♣Q, nonetheless 8 tricks would still be taken with declarer’s communications still intact.

What was the situation at the table? Not surprisingly North‘s shape was one of the two most likely candidates, 4=2=3=4, and he held the ♣Q as expected in that situation. This is exactly what declarer might have expected at trick 2 following the suggested line of reasoning. By not taking a losing finesse West might still have scored 9 tricks on the extra chance of bad defence. It is hard to guess how many matchpoints the overtrick would be worth, but we do have the results for this occasion.

The 14 tables in play produced 8 different contracts and 9 different scores. Only 3 pairs played in 2NT, 2 making 120, one making 150. Making 9 tricks in 2NT instead of 8 would have added 5 matchpoints to the score raising the percentage from 42% to 80%. That shows one needn’t bid a close game to be successful at matchpoints, even if you would have made it if you had bid it. Two pairs were in 3NT, but both declarers failed, as they should have done, for a shared bottom, the highest EW scores were got by defending against a vulnerable 2♥*. The Law tells us it doesn’t pay to stretch on 13 total trumps, one of the most neglected rules in bridge.

Sometimes when the dummy first appears declarer realizes he is in a minority and is pretty sure that this is a very good contract or a very bad one. Don’t be too happy or too displeased when you find yourself in that situation. It’s silly to hope to gain matchpoints by playing against the odds. What little you may lose on the play in such situations could make a difference in the final standings.