Minor Suit Slams at Matchpoints

A local Grand Master examined the scores and shook his head sadly after my partner and I bid a cold 6♣ against him. ‘People just don’t bid minor suit slams anymore’, he moaned. Yes, it was an unfair result, but that is matchpoints where many players are happy to dumb-down and go with the field. Why is that, after we have been taught that one should bid a slam when the chance of its making is better than 50-50? Let’s have a mathematical look at this situation. Here is a simple example with which to start.

Opener is in the middle of the 15-17 HCP range and responder can add 14 to 17 and come up with 31 HCP, not enough for slam. He expects that opener’s diamonds are longer than his clubs, and he hopes that those diamonds include a stopper. Rather than explore the situation and pinpoint his weakness, he bids what the field will bid content in the belief that he is sure to have lots of company whatever the end result.

In 3NT there are 11 tricks to be taken, no more, so in that respect when playing in a NT contract one needn’t go beyond the 3-level. The trouble with this auction is that it is based solely on HCP ranges. The West hand contains 6 controls which are equivalent to 20 HCP and the East hand 5 controls which are equivalent to 17 HCP, so the hands have amble power to justify exploring slam in a minor.

West might open the hand with 1♣. Responder bids 1♥, and what next? A 2/1 instructor once told her audience of eager matrons that ‘sometimes you have to lie’. So a jump to 2NT would reflect the potential strength of the hand in a club contract, but it is a couple of points shy of the system definition geared to NT bids. This time with a club fit it works like a charm, provided responder knows what to do next.

The hands are a lot easier to bid in a Precision system provided that there is a distinctive response on a flat hand with 14+HCP. I play that a response of 2♠ shows such a hand, in which case we bid the slam by cuebidding as follows. After the first exchange the bidding is easily understood with both partners contributing.

If the clubs and spades are interchanged, there would be little change in Precision and even with 2/1 methods slam would be reached, perhaps as follows.

 

2NT is Jacoby 2NT and cuebidding gets you there. It would be foolish to open with 1NT with 6 controls and miss the opportunity to explore a spade slam.

The Field Effect
A bidding system, like cheap insurance, doesn’t cover all contingencies. There is a built-in bias of spades before hearts, hearts before diamonds, and diamonds before clubs, which applies to partials and games, but is less relevant to slams. If one chooses to bid a slam, normally one chooses the safest strain. Trying to get to a minor suit slam involves swimming against the current of popular practice.

If the previous blog we noted that in a team game one scores a zero if one ends up in the same contract as the opponents, so it doesn’t appear superficially one has anything to lose by bidding a higher scoring contract when the probabilities favor it. At matchpoints, there is the tangible loss of a near-average score that one gets by playing in a common contract. Under such conditions some players think as follows: A final score is an accumulation of matchpoints won over several rounds; winning bridge entails never risking a bottom score; if I end up playing in 3NT, I will have lots of company and may score an average; if I end up in slam, I will have little company, and may score a bottom, in which case I will fall badly behind the field; rather than trying to win matchpoints on this hand, I will wait for a situation where I can profit without risk from my superior playing skills.

Doing the Math
We assume that there are just 2 alternatives: to bid a small slam or to stop in game. Let these symbols take on the specified meanings:

SS Small Slam
PM the probability of the SS making
PG the probability the opponents will stop in game
YB You Bid the SS
YD You Don’t bid the SS
TB the opponents Bid the SS
TD the opponents Don’t bid the SS

Here are the expected scores under the various conditions.

When the SS makes
YBTB   ½ x PM x (1 – PG)
YBTD    PM x PG
YDTB    0
YDTD   ½ x PM x PG

When the SS fails
YBTB ½ x (1 – PM) x (1 – PG)
YBTD 0
YDTB (1 – PM) x (1 – PG)
YDTD ½ x (1 – PM) x PG

The difference between expected scores when you bid the slam and when you don’t gives the result: YB – YD = PM – ½ > 0, when PM> 1/2.

The condition for achieving on average a better result by bidding the SS is independent of whether or not the opponents bid it. On that basis one should bid slam when the probability of making is more than 50% just like the books tell us.

PM is a concept of convenience. Ideally PM can be calculated with a computer program once we feed in declarer’s hand and the dummy. The calculation involves the probability of the various card combinations for the opposition. One assumes perfect defence and perfect play. That is not realistic as the opening lead is often critical, but it is dangerous to bid a slam on the assumption one will benefit from imperfect defence.

At the table we have available only an estimate of PM. As the auction progresses our estimate changes as more information is received. This also affects PG as the higher the estimate of PM the less likely one is to prefer game to slam. The estimates depend on the nature and quality of the information being processed. That in turn depends on the structure of the bidding system.  It is an over-simplification to assume that PM depends solely on the HCP total, but some believe that one should bid slam only when holding at least 33 HCP, because that was what they have been taught.  Usually in a cooperative slam auction the estimated PM is related to the number of bids being made, on the basis that one player or the other will end the process if he thinks game is the limit.

In a matchpoint game, the one hand is played at several tables by different pairs, so the average score is in reference to the distribution of scores across the field on that particular board. If the field is playing the same simple bidding system it may be easier to estimate PG than PM. In a good field, the two are closely related.

In reference to the club slam given above, after a 1NT opening bid responder does not even consider the possibility of a minor suit slam because the player can judge the field is unlikely to go that route. With some confidence he can estimate PG to be at least 75%, in which case he will still score 47% when stopping in 3NT. If he were to bid the slam, he risks losing 47% for a doubtful gain. Of course, when he chooses to jump to 3NT without further exploration he doesn’t know the probability of slam making on this particular hand, but he does know the initial odds are against taking 12 tricks with most 1NT hands opposite. This woeful thought process is aimed towards minimizing the loss when one has made the wrong choice. If he stays in game when slam makes 75% of the time, clearly he has made the wrong decision, but he still scores near average.  If he bids slam but it goes down, he has made the wrong decision and scores a bottom.

The Effect of Superior Technique
PM is the theoretical probability that 12 tricks can be taken, but taking them may require a certain delicacy of technique, such a squeeze or a dummy reversal. Perhaps not all players in the field will be capable of reading the situation, so one can gain matchpoints against the inept pairs when one wrongly stays out of slam, but manages that elusive 12th trick. Let’s assume that a player knows he is a better technician than one-quarter of the field.  In the YDTD category when slam makes on a squeeze, say, he will make 12 tricks in a game, but one-quarter will hold themselves to 11. Against those he scores a full matchpoint, so the overtrick is put on the same footing as the slam bonus. This favours individual effort. Now, the break even point is achieved when PM equals ½ + (1/8) x PG.  If PG is 3/4, the slam is unlikely to be bid across the field in the ratio of 3:1, and the justification for bidding the slam requires PM to exceed 60%, even though a good player is quite capable of taking the necessary 12 tricks when conditions allow it.

Some players consider this effect to be a contamination. To deliberately play against one’s better judgment because the field contains a few inept players, and, moreover, to profit from it, degrades the game.  So say some, but is that the case? Luckily bridge is not politics, so one needn’t dumb-down to be successful. One may choose to ignore the effect of the field and imagine one is playing against the best at all times. That noble approach is not optimal. It makes good sense to vary one’s play according to what the field is likely to do on any given hand. That adds an intriguing extra dimension to the matchpoint game.

Major Suit Slams
The same mathematics applies to major suit games and slams, but there is less need for adjusting to the field. The fact that so few players reach a good minor suit slam indicates either: (1) everyone is convinced they are better players than most, so don’t need to bid slams, or (2) the 2/1 system is deficient in this aspect. I strongly suspect the latter, because the problem does not occur to the same extent with major suit slams. The system is geared towards major suit contracts and most responders know when and how to look for slam possibilities right from the beginning. That was the whole idea behind 2/1.

An exception is when opener bids 2NT with a control rich hand and a 5-card major. Puppet Stayman is available to sort out the major suit fits, nonetheless, bidding space is restricted and the onus is on the weaker hand to do the slam exploration.  With few controls he may opt to play safe and stop in game unaware of how well the hands fit. This is understandable when the field will have the same self-inflicted difficulties.

If West opens 1♥, East hasn’t sufficient values even to bid 2♣ to force to game. Some might respond 1♠ on a bad suit happily planning to bid an invitational 2NT next. Here comes Gazzilli riding to the rescue.