Re: How do you calculate this?
Your intuition is correct. The chance of a single player getting a pair is 1/17 (the first card can be anything, the second must be one of 3 cards out of 51). Once a player does that, the chance of a second player getting the same pair is 2/50 * 1/49 = 1/1,225. The chance of a second player getting a different pair is 48/50 * 3/49, which is 72 times as big.
Therefore, it's approximately true that the same scenario (3 pairs out of 6 players) is 72 times as likely if all the pairs are different than if two of the pairs are the same. If three of the pairs are the same, shoot the dealer.
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