Grand Slam Percentages

I have heard that the world championships at Bali were an outstanding success. All the better, as it was a long time coming to this enchanting location. It has been said in the past of world championships that the winners are usually those who get the slams right. Perhaps these days the competitive deals have rather taken over in importance, but slam bidding is at least an indicator of how well the nerves have stood up after the week-long round robin.

Canada had a rather good run and met USA1 in the quarter finals before losing their grip in the late stages. I am not a fan of standard 2/1 bidding so it doesn’t grieve me greatly to report the following failure. Paul Thurston is a respected, popular bridge columnist who has written a book on 2/1 methods for the masses, so he might wish to reconsider the bidding on this deal from the 5th session.

One of the arguments for the method is that a bid of 2/1 saves bidding space for the full exploration of slam possibilities. But, keeping Twitter in mind, the fact is that given that both parties are saying a lot doesn’t necessarily mean they are having a useful conversation. Content is the key: some things you needn’t know, whereas other details are critical. In slam exploration the quality of the trump suit is essential information. I think, given the method, neither party bid incorrectly on a step-by-step basis. It was wrong only in its accumulative effect. Neither side had limited his hand. Smith’s trumps looked to be adequate and the fact that partner was bidding a lot encouraged him. Thurston was criticized for his 2♠ bid, and in similar circumstances Zmudzinski for Poland jumped to 4♠/2♥. That set limits to his holding, but it didn’t stop Balicki from bidding slam, and he made it on a passive misdefence, as given time the diamonds provided for ample discards. After all the bidding exchanges, Smith was less likely to get away with it, and, in fact, he went down 3. If it must be done, let it be done quickly.

Grand Slams
Some players avoid grand slams like poison. Once they determine a small slam has good chances, they jump to it, shutting out further exploration. As Kit Woolsey has stated on BBO, it is bad practice to jump to slams. Why the rush? Well, a grand slam is thought not to be a good gamble when it is unlikely the opposition will bid it, but this is not true. What is true is that it is not a good proposition if the opponents may be stuck in game as on the following deal from the Venice Cup Final.

On Bridge Winners there is a nice interview with Migry Zur-Campanile conducted by Christina Lund Madsen. After watching Charlie Rose interview Margaret Atwood, I am inclined to the view that women should be interviewed only by a woman. Charlie, a subconscious sexist, eventually got around to the subject of sexual stimulants, a subject on which Atwood was less than forthcoming and we were left in the dark as to whether her knowledge went beyond what one reads in her books. When asked what she does when she isn’t writing or twitting, Margaret replied sweetly, ‘I do the ironing.’ She explained that concentrating hard on doing a proper job to the best of her ability helps her brain solve hidden, more troublesome, problems. Whatever you do, concentrate hard and try to do it as well as you can. No task is trivial. Will Charlie eventually take up ironing?

Migry, we learn, has red hair, a big mouth, and is a great cook. In the interview she comes across as a vibrant teammate leaving no doubt as to why she was approached to replace Valerie Westheimer who withdrew from USA2 for health reasons. Her partnership with Jill Meyers was a first-time experience, so we can be sympathetic Jill’s precipitous jump to 6♣.

There are further considerations. Is it possible the opponents will get stuck in game? We might think that in the Venice Cup Final the answer would be ‘no’, but, believe it or not, Fiona Brown opened the North hand with a self-preemptive bid of 5♣, and there she rested. So, on this basis one might say that Meyers’ jump was justified even though 13 tricks are cold. We don’t know, we weren’t there, and I suspect Jill isn’t telling.

The Open Final was a grudge match between Italy and Monaco, a team that included erstwhile Italian stalwarts, Fantoni and Nunes. In that match both teams bid 7♣. One North decided to bid it (Fantoni) and one South (Madala). Let’s look at the mathematics of bidding a grand slam when you think the other team is sure to be in a slam.

Doing the Math
We assume that there are just 2 alternatives: to bid the grand or to stop in a small slam making 12 or 13 tricks. No doubling is allowed. Let these symbols take on the specified meanings:

GS Grand Slam
PM the probability of the GS making
PB the probability the opponents bid the GS
YB You Bid the GS
YD You Don’t bid the GS
TB the opponents Bid the GS
TD the opponents Don’t bid the GS
G what one gains when one bids the making GS and the opponents don’t
L what one loses when one bids a failing GS and the others don’t

Here are the expected scores under the various conditions when you take an action different from the opposition.

When the GS makes
YBTD   G x PM x (1 – PB)
YDTB – G x  PM x PB

When the GS fails
YBTD -L x (1 – PM) x (1 – PB)
YDTB L x (1 – PM) x PB

The difference between expected scores when you bid and when you don’t gives the result: (G + L) x PM – L > 0,    when PM > L / (G + L).

Miraculously (or not) the condition for achieving a positive result by bidding the GS is independent of whether or not the opponents bid it. So one needn’t hold back just because the opponents are too conservative. If the scoring is the total scoring of a minor suit GS, nonvulnerable, G equals 500, the slam bonus, and the loss, L, for bidding a GS when it goes down is 970. On this basis one is justified in bidding a GS if PM> 66%.

If the scoring is IMPs, G equals 11 and L equals 14. On this basis one is justified in bidding a GS if PM>56% (14/25). The most important factor in estimating PM is the trump quality. With a 9-card fit, one may be able to tolerate a missing Queen, but with a 4-4 trump fit one needs to hold AKQ and the ability to tolerate a missing Jack.

If the trump Queen is missing, don’t tell the opposition, as an opponent helpfully may lead a trump. Bad bidders have the advantage there. There may be other requirements in the side suits, but often there is more than one way by which a loser can be averted, a squeeze being the most satisfying method, and a helpful opening lead perhaps the most common.

There may be further considerations during a match. If behind in a match one may wish to maximize the possible gain by bidding a making GS when the opponents don’t, or not bidding a failing GS when the opponents do.  This requires a guess at the probability they will bid it. Generally if the odds are N:1 that they won’t bid the GS, one gambles best by bidding the GS if  PM> L/ (N x G + L).

Maximum uncertainty with regard to what the opponents will do is expressed by a PB of ½, (N equals 1), in which case the maximum IMP gain on average is got by bidding the GS when PM>56%. In other words one ignores what the opponents are doing and just bids the GS according to the normal criterion. However, it makes sense that if the opponents are unlikely to bid the GS, you best chance of gaining on them is to bid it and hope it makes.

Suppose they are 2:1 against bidding the GS. The PM required to make such a gamble profitable on average at IMPs is 39%. One would have to be very desperate to bid a GS with less than a 50% chance of making, but it is a better gamble than backing the odds that they will get too high.

One final word of advice, and this comes via Margaret Atwood. Happiness comes from what you do, therefore, rather than seeking Happiness for its own sake, look for something to do that makes you happy and do it ….something like playing bridge.