#11
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your intuition has gotten the best of you!
Dynasty,
Another angle to consider: Consider this as a pass/fail test with 18 trials (for the 18 cards dealt to everyone but you). A success is an ace or king, a failure is anything else. Here's how the probabilities would break out: P(zero): .057 P(one): .228 P(two): .346 P(three): .255 P(four): .096 P(five): .017 P(six): .001 So yes, the most likely result is two ace/kings being dealt out when you hold AK against 9 opponents. But notice that when you take the weighted average of the 7 possible results, the expected value is actually 2.16 successes. If exactly two opponents hold ace and/or king, that's actually LESS than you should expect. There are actually an extra 0.16 ace/kings left in the deck for the flop. |
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