Quad Aces losing to Royal Flush in Holdem
January 31st, 2010 at 10:27:46 PM
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I've heard a way range of estimates on the probability of this occurring, but would like some verification.
http://www.youtube.com/watch?v=XunAlp2azhA
http://www.youtube.com/watch?v=XunAlp2azhA
February 1st, 2010 at 1:22:41 AM
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The correct answer is that it depends -- it depends on how specific the question is or isn't. Must Player A have two pocket aces and Player B have two to the royal? Or can Player A have one Ace and the board have the other three? Or can Player B have one to the royal and the board have the other four?
If the question is, "What are the chances of any Royal Flush beating quad Aces, any which way it could possibly happen, in heads-up Texas Hold'em where both players stay in to the end?", then the answer would be "approximately 1 in 164,617,720" assuming my rough calculations are correct.
If they are, then that is the highest probability possible for any variation of this question, because it includes all of the possible ways it could happen. There are many ways to make the question more specific to yield a different, smaller, yet valid, probability.
If the question is, "What are the chances of any Royal Flush beating quad Aces, any which way it could possibly happen, in heads-up Texas Hold'em where both players stay in to the end?", then the answer would be "approximately 1 in 164,617,720" assuming my rough calculations are correct.
If they are, then that is the highest probability possible for any variation of this question, because it includes all of the possible ways it could happen. There are many ways to make the question more specific to yield a different, smaller, yet valid, probability.
