Ray Lee

Bridge, probability and information

Bob MacKinnon of Victoria, BC is probably best know as the author of the remarkable bridge novel Samurai Bridge, which we published a few years back.  However, in real life he knows more about the application of mathematics to bridge than anyone I know, and his new book, Bridge, Probability and Information, will be appearing in the Spring.  I have been working on editing it for the last couple of months, trying to make sure that the ideas are presented in such a way that, as the author himself says, it won’t immediately provoke the average reader into closing the book for ever.  It’s not easy, but there are a host of practical bridge results contained in it.  I was reminded of one of them by the deal Paul Thurston discusses in today’s National Post column.


7 5 3
9 7
K Q J 9
A 9 8 2
A K 6
7 5 3
K J 10 5 3

After an unrevealing auction (1NT-3NT), West leads the 4; dummy’s king holds, East contributing the 10.   Ace and a club now brings South to a familiar problem: to finesse in clubs or not?  It seems that West led from a five-card suit, and so the odds have surely shifted in favour of the finesse compared to the situation before any cards are played — but how much have they shifted?  What is the right play?

This is a great example of one of the first points Bob makes: odds in a suit should almost never be considered in isolation; you have to look at the most probable situation regarding the entire layout, as the split in one suit affects the odds of the split in another.  Here we have information.  First, we can surmise that West started with five diamonds to his partner’s one.  And what of all those missing hearts?  It seems likely that West has no more than 4 of them, else he would probably have led one (his diamonds aren’t that good after all).  That gives us an imbalance of Vacant Spaces in favour of West by a margin of at least 5 — is that enough to make us finesse in clubs?  If West has a stiff club, what is his hand, given that he led a diamond from 5?  3-4-5-1 with very weak hearts, I guess.  Isn’t it more likely that he was 3-3-5-2?

Bob discusses the Qxxx situation at length, along with the underlying probability concepts, and comes to the conclusion that the tipping point is a Vacant Space imbalance of 1.  If West has the same or fewer Vacant Spaces than East, you should play for the drop; 2 or more (as it is here), and you should go for the finesse.  If the imbalance is 1, look for other indicators, or toss a mental coin.  By the way, this isn’t the same situation as when you are missing QJxx and an honour drops — Restricted Choice among other things makes a difference there, and now you need an imbalance of 4+ Vacant Spaces in favour of West over East NOT to finesse.

So you see what I mean?  No complex math involved, just simple and highly practical bridge ideas that you can use at the table.  Kind of reminds me of Larry Cohen’s bestseller on the Law of Total Tricks — which Bob discusses in his book, by the way, as well as the recent Lawrence/Wirgren book (I fought the LAW of Total Tricks) that attempts to refine or discredit (whichever you prefer) the Law.  One of my favorite ideas in Bob’s book is basically ‘Don’t sweat the small stuff’ — if a decision is close, say 51-49, don’t worry too much about it, because mathematically speaking there’s very little gain or loss involved in the long run.  It’s the 57-43 ones you need to get right, since over time they’ll affect your score much more.  More on that one in a future blog.

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