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Game Theory in Bridge

Here is an interesting problem I resurrected.  Dummy has QJ9x in a suit and you have Kx.  The suit is known, or guessed to be 4-4 eg after a Stayman sequence.  The queen is led and you assume that declarer has Axxx but without the ten (if he has the ten it's immaterial what you do).  The best play is to duck.  Now declarer has to guess whether to play you for Kx or Kxx.  Now suppose you have KT.  Should you cover or duck.  Well it seems obvious to cover in this case. So now think of it from Declarer's point of view.  Since with Kx, it's right to duck and give him a guess, doesn't it mean that when you cover, he should play you for KT and play to drop the ten?  If so, maybe you should  therefore SOMETIMES play the K from Kx to keep him honest.  This enters the realm of mathematical game playing theory where your strategy is to adopt a statistical approach ie do one thing a certain % of the time and the other the rest of the time.

For the purposes of this exercise, let's assume for simplicity that the defensive distribution is 3-2 and not 4-1, if you don't like that, say they told you so at the beginning.  This simplifies the analysis.  And also, you are playing the same player 100 times with the same basic card combination.  The question is, should you always play low with Kx or sometimes play the king to 'keep him honest, ie play you for KT?  I think i worked this out a while back and came to the conclusion that with Kx you should always play low, and you pay off when you play the king and declarer drops your ten from KT.  So maybe this isn't the example I am looking for.

 

Would be interested to hear from folk who have some knowledge of Game Theory (a la John von Neumann).

Firstly, could they confirm my hypothesis above?

Secondly, are there examples in bridge where a game theory statistical solution is in fact the best strategy?

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