Flush Question

[iash]

What is the math behind figuring out the odds of making a Flush with a 4 Card flush after the flop?

Thanks.

[beerbandit]

approx. 30%

[Lost Wages]

The probability of making a flush from a four flush with two cards to come is 1 minus the probability of not making a flush.

To calculate the probability of not making a flush; there are 47 unseen cards on the flop, 9 of which are in your suit 38 of which are not. If you don't make your flush then on the turn there are 46 unseen cards, 9 of which are in your suit 37 of which are not. So the probability of not making a flush is 38/47 * 37/46 = .650 and the probability of making a flush is (1 - .650) = .350 or 1.86:1 against.

The reason that you cannot multiply the probabilities of making a flush on the turn and river is that you double count the times that you draw two of your flush suit.

Lost Wages