When Manure Gets in the Way by Amit Chakrabarti

Source: When Manure Gets in the Way

An alien comes from outer space and wants to pick a human being randomly to take back to planet X and show what an advanced civilization they have. What is the chance that this alien randomly picks an Indian? Well, there are about 1 billion Indians and the Earth’s population is about 7 billion. If all the human beings are uniformly distributed over the globe, then the random chance of picking an Indian will be about 1/7 or 14%. Now consider that this alien lands in India. What is the chance of picking an Indian now? Almost 100%. This last case can be written as a condition: Given that the alien lands in India, what is the probability of picking an Indian? This is the basis of conditional probability, a very important concept. Understanding the basics of conditional probability will be extremely useful to you at the Bridge table. What does this conditional probability have to do when manure gets in the way i.e. when they preempt? Given that someone has 6 or 7 cards in a suit, all those a priori probabilities of suit breaking that we talked about in my 1st column are now irrelevant. For example, consider that they preempt 3D and you observe that the opponents have 9 diamonds among them split as 7-2. Your trump suit is spades with a 4-4- fit and thus and you have 5 trumps outstanding. Without a knowledge of the preempt, the priori probability of a 3-2 break is about 68%. But now conditional probability comes to rule. Given that diamonds break 7- 2, what is the probability that spades break 3-2? Not only the percentages change but now it is asymmetric — the breaking of 3-2 and 2-3 are not the same any longer. This is because of the simple fact that the preempter has less vacant places to hold the spades. Now the probability to break 3-2 is 18% and 2-3 is 40%. Not only that the probability for trumps breaking 5-0 is now increased from 4% to about 8%. (If you are mathematically inclined and want to know more about these conditional probabilities, lots of tables and discussions are given in this fine book: “Probabilities and Alternatives in Bridge” by Vivaldi and Barracho.) So we note that preempts not only take away space from your bidding, they also suggest that trump contracts may not be the best contract now as poor trump break is looming in the horizon. Thus, I follow a simple axiom: When they preempt 3N is the best contract to play in. Marshall Miles, an ACBL Hall of Fame member, stresses this point in the introduction of his excellent book “Inferences at Bridge” with the following example. What action do you take holding:  8 3 A 6 5 3 A K Q 9 7 5 4 and opponents are vulnerable and you are not. Here I quote from Marshall Miles’ book: “At least nine players out of ten would bid 4. They would do so either because they lack imagination or because they are unwilling to gamble, even when the odds are in their favor. Think about it. At favorable vulnerability would LHO open 3with a solid spde suit? No; he could miss a game since with a singleton or void in spades, his partner would pass holding 15 or 16 high card points (hcp). ….. Then what about RHO? Would he pass with Kxx or Axx ? No again. …… Do you see where I am going? I think the odds favor a 3NT bid.” The real reason I think most players would not bid 3NT with this hand is that they are afraid of the post-mortem. If the opponents take the first 7 tricks, everyone will hear about how you thought of your doubleton 8 as a stopper. Yes, there are some cruel bridge players in this world who, instead of protecting their partner’s emotional well-being, would rather tell everyone in the room how “dumb” their partner is. But as I said in my first column, post-mortems are not where battles are won.