![]() ![]() For the other eight hands, we are choosing 16 cards from 48 and partitioning the 16 cards in 15!! ways to form completions. Then set aside the remaining two aces to go into another hand. ![]() The total number of completions to player semideals is given by the product of and 17!! because we are choosing 18 cards from 50 to be dealt to the other nine players, and there are 17!! ways to partition the 18 cards into nine hands of two cards each. Even though the probability, as we just saw, for two people to be dealt pocket aces is small, the result may be quite different once the condition that someone has aces is given. What is the probability another player also has been dealt pocket aces? This is now a question involving conditional probability and you must be careful. ![]() Let's take another viewpoint now and ask the following: Suppose you are playing a 10-handed hold'em game and upon looking at your two hole cards, you find A-A. ![]()
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