Showing posts with label bridge. Show all posts
Showing posts with label bridge. Show all posts

Wednesday, 23 June 2010

Bridge Probability

I've been re-reading Victor Mollo's classic bridge book 'Card Play Technique: the art of being lucky'. I've come, once again, to the sections about probabilities that I just can't get my head round. Consider the following passage:
If the Ace of Clubs is right, all is well. If not, the contract will depend on guessing the diamonds. How then, should we set about it? The man in the street will draw trumps quickly, sway in his chair slowly and mutter something like: "Well, it's six of one and half a dozen of the other".
But is it?
To the expert there is a vital difference between the Club and the Diamond positions. The latter will be the subject of guesswork. The former lends itslef only to prayer. The Club must be played first, and the reason is that it will provide a clue to the Diamonds.
If East has the Ace of Clubs, West will be credited with the Ace of Diamonds.
There is similar reasoning throughout the book, just one hand later:
West has pleaded guilty to 7 points hearts and to the King of Diamonds: 10 in total. East has only 3. It is more likely that the defender's high-card strength will be divided between them 10-5 than 12-3. Therefore the best chance is to play East for the King of Clubs.
I just can't believe that this reasoning is valid. The deck doesn't know which cards we assign points to, so it is no more likely to put the Ace of Clubs in a different hand to the Ace of Diamonds than it is to put, say, the Three of Clubs in a different hand to the Ace of Diamonds. Similarly, while it is true that a 10-5 distribution is more likely, a priori, than a 12-3 distribution, surely this ceases to be the case when you've alread placed the remaining points 10-3 (assuming that the principle of Vacant Spaces doesn't come into play - ie, every player has followed with a small card to each of his partner's honours).

To repeat: the deck doesn't know which cards we assign points to!

Maybe this sort of reasoning is a useful shortcut to some valid reasoning, or maybe I'm missing something (I certainly hope so). Can anyone shed any light?

Wednesday, 16 June 2010

The wisdom to accept the things I cannot change

There are several 'life lessons' that I've picked up from playing bridge. Some of them are incredibly obvious in hindsight. Some of them less so. This is one of the more obvious in hindsight, but also one of the more important, so I think I'll start with it.

It is fairly common when playing bridge to reason thusly: in order to make this contract, I need West to hold the King of Diamonds. If West holds the King of Diamonds, then he can't hold the Ace of Spades. Therefore, I'll assume East holds the Ace of Spades and play accordingly (an example).