Re: What are the odds of 2 people flopping a flushin Hold\'em?
The probability of a monotone flop is 22/425 ~ 5.1764%.
Given that there is a monotone flop, the following is the distribution of the number of people with flushes (or straight-flushes, henceforth counted as flushes):
0 66.017%
1 29.877%
2 3.932%
3 0.172%
4 0.002%
5 0.000003%
Given that you flop a flush (~ 1/505) the following is the distribution of the number of people with flushes, including you:
1 78.079% (no other flopped flushes)
2 20.552%
3 1.347%
4 0.022%
5 0.00004%
The probability that you flop a flush is about 1/505. The probability at least one person flops a flush is about 1/56.8, so the probability that you flop a flush that is high is about 1/568. 1/505-1/568 ~ 1/4511 of the time, you flop a flush that is not high.
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