Odds that someone flopped a flush

Does anyone know what the odds are that soemone has flopped a flush in a loose hold 'em game when there are 3 flush cards on the flop?

It would depend upon how many players took the flop. According to Mike Petriv, from the "Hold'em Odds Book", if you start with two suited cards, the probability of flopping a flush is less than 1%. Suppose you start with two clubs in your hand. What is the probability of all three flop cards being clubs? The probability is (11/50)*(10/49)*(9/48) which is about 0.008. This doesn't answer your question but it is the part of your question I know how to answer.

If your opponents were playing random hands, the odds would be (10/49)*(9/48) for each opponent. If your opponents will only play hands which are part of the Sklansky hand groupings chart, there are 200 suited hands out of the 542 total. If you figure that the chance of somone hand being suited the same as the flop have dropped to around 10/52 (instead of 1/4) because you've seen 3 cards of the suit, you are left with a 7% chance per opponent. If you also believe your opponents will play any Q or J suited, that adds 11 more suited hands, and brings the chances per opponent up to 7.3%


Once you've decided the chances of a single opponent having the flush, you can calculate the chances of at least one opponent having it with the following formula, where X is the chance per opponent and N is the number of opponents:


1 - (1-X)^N


So for the 7% above and 5 opponents, you would get 1 - (93%)^5, which is 30.4%


Hope this helps...

Of course this doesn't take into account an unraised pot where the blind might have started with ANY 2 suited and the sb might have kicked in 1/2 bet with any two suited.

Based on your analysis coupled with mine, it appears our joint answer to Amanda's question would be "well under 1%".

I think the question should be rephrased viz: if 3 suited cards flop what is the probability someone has flopped a flush?


To make things easier lets ask this: if 3 suited cards flop, what is the probability someone was dealt 2 cards of this suit?


There are 3 cases (I assume we are playing and have 2 cards!) a) we flopped a flush b) we have 1 flush card and c) we have no flush cards.


MOre later...