Two People Flopping a Flush??

[QnA]

I think if you have suited cards, then your chances are 1 to 112 (don't quote me on this) to flop a flush. What is the probability that two people flop a flush? Three? Four? Five?

[Copernicus]

I believe it is 162/1 odds against any individual player holding two of suit flopping a flush.

The answer to your question depends on the total number of callers, not just the number you want to know(ie its more likely that 2 of 10 flop a flush than 2 of 5). I'm also not sure of the usefulnees of knowing the answer to the question as posed, since that would include the possibility of a flush in any of the 4 suits, by any n out of the total number of callers.

What is more relevant, I would think, is "If I flop a flush, what is the probability that someone else has also flopped a flush." or further specifying your top card and asking what is the probability someone flopped a bigger flush.

The answer to the simpler part, "If I flopped a flush what is the probability someone else flopped a flush", and saying there are 4 "random" callers (by "random" I mean that you dont assume anything from the fact that someone called, such as the fact that they are more likely to call with two of a suit), I think the answer is around 10%. If you have the K, about 1/4 of that 10%, or 2.5% is the probability that someone has the A high flush against you, so jam away!

[irchans]

Brian Alspach addresses this question in the Oct 20, 2000 poker digest article Losing Flushes (http://www.math.sfu.ca/~alspach/mag57/).

[M.B.E.]

[ QUOTE ]
What is more relevant, I would think, is "If I flop a flush, what is the probability that someone else has also flopped a flush." or further specifying your top card and asking what is the probability someone flopped a bigger flush.

[/ QUOTE ]

Most relevant of all: "if the flop has three suited cards and I have top pair, what is the probability somebody else has flopped a flush?"