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Most of the published mathematical tables for bridge are a priori probabilities. They are chances when the cards are dealt. But as the bidding started the probabilities changes. When play starts probabilities changes some more. This is where the newest computer technology come in. A very smart bridge program can uses all the information and recalculate the real probabilities of anything as the bidding and play is in progress. The program GIB uses this concept. It calculates the probability on the fly and simulate hands to test the playing of cards to see which one is better.

One common situation I want to mention is the combining of two or three types of probabilities in locating a key card.  One is the high card point distribution and the other is the length of the suit.  The two could be opposite of each other or could be in favor of one hand.

e.g. Base on the bidding and the cards play east is most likely to have 2 HCP left and west 6 HCP left. If you are looking for a Q it is about 3 to 1 chance that it is in the west's hand.  If base on the suit length, it is 2 to 1 chance it is in east's hand then the real probability for the Q to be in the west hand is reduced to 3 to 2. On top of this sometimes the fact one side did not lead the suit also may affect the probability.  When three or four things all having a different probability that may affect the location of a key card, it is very difficult for a human player to sort it out.  Here is where the computer can excel.  In the future that is where the computer can beat the human player.