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In Spades, I wish to know the probability a certain suit is distributed in a particular way. For example I wish to know what is the probability that the diamonds are distributed either 4-4-4-1 or 5-4-4-0 among the 4 players.

Is this question equal to the probability a hand is distributed 4-4-4-1 or 5-4-4-0 among the four suits? If this is true, then I can use the Hand pattern probabilities

EDIT: This question came up because I wanted to know what is the probability that my partner will not be able to cover my nil bid on the forth trick of a suit. Only on those two hand distributions (4-4-4-1 or 5-4-4-0) is it possible for an opponent to lead that suit, me having that suit, and my partner to not be able to cut with a spade.

I guess I need the conditional probabilities, conditioned on the number of cards I have from that suit. Do you know to find the distribution when I have either 4 or 5 diamonds?

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Yes, and the tables are used in exactly this way by Contract Bridge analysts and experts.

However, be careful when extrapolating from these tables to perform analysis based on your own holding in any suit, not just the suit under examination. The formulas for properly calculating conditional probabilities are non-intuitive.

A good first test that you are understanding conditional probability is a clear grasp of the Principle of Restricted Choice.

  • You are right, I need the conditional probabilities, conditioned on the number of cards I have from that suit. Do you know to find the distribution when I have either 4 or 5 diamonds? – Cohensius Sep 10 at 13:18
  • @Cohensius: That would make a great follow up question to this one. I don't have a formula memorized, but do know how to go about determining one. – Forget I was ever here Sep 10 at 13:20
  • Some of that analysis is here in the sub section Single Suit Analysis. – Forget I was ever here Sep 10 at 13:27
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    see follow up question here boardgames.stackexchange.com/questions/48591/… – Cohensius Sep 10 at 13:32

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