Odds for a flush

[papa_georgio]

If i've been dealt two suited cards, and then two more of my suit come on the flop, what are the odds of completing my flush? I'm only asking because I've been told that it's something like 1.86 to 1 that it will come by the river, but it sure doesn't seem to hit that often. Any replys, or links to accurate odds charts are very appreciated.

[Paxosmotic]

1.86 to 1, and it does come in that often. 35% is 35% is 35%

[carsten]

This is a classic example for an "outs" calculation: Of the 47 unseen cards, 9 are outs that will make your flush. A good rule of thumb for the probabilty of hitting at least one out is the 2/4 rule: With one card to come, multiply the number of outs times 2. With two cards to come, multiply the number of outs times 4. The result is the approximate probability of hitting at least one of your outs.

So, if you flop a flush draw, your chance of making the flush by the river is approximately 36%.

The exact probability for hitting at least one of n outs with two cards to come is 1 - (47-n choose 2)/(47 choose 2), which can be simplified to 1 - (47-n)*(46-n)/(47*46). Plug in n=9 and you get a probability of 34.96%, which is equivalent to odds of 1.86 to 1. Your source is correct.

-Carsten

[LetYouDown]

Part of the confusion may stem from the fact that 2-to-1 means the same as 1/3.