How often do you flop 2 to a flush of the suit you hold?

[Rayek]

I was looking in my pokertracker database of 11k played hands, and was losing slightly on AKs and AJs. I was curious why, and was looking through the hands. Turns out, in being dealt AKs 40 times, I have not hit the flush once. In 41 hands of AJs, I have made my flush once. Now Im sure that there are other combinations of suited hands where I have made the flush more than my fair share of the time, but I was just curious when you have 2 of a suit, what the probability is that you will make a flush by the river? I have read that when you flop the 2 to a flush, you are 35% likely to complete it by the time the river comes, but what about before the flop? Thanks in advance.

[Poker60181]

If you have the A /images/graemlins/diamond.gif K /images/graemlins/diamond.gif, you have about a 20% chance of making a flush draw on the flop. Your welcome. /images/graemlins/smile.gif

[RiverDood]

20% is a pretty dubious answer.

I've seen 10%, 11% and 10.81% as the odds of catching two to your suit on the flop, if you've got suited cards to start. Some number around that range makes intuitive sense. That would then mean about a 40% (4 x 10%) chance that the flop has two to some suit. (Non-rainbow flop.) Squares with my general experience. The claimed 20% chance of hitting a flush draw to a particular suit would suggest that 80% of flops aren't rainbow -- and that just isn't so.

There's a more interesting second question imbedded in the original post, and that is, what are the odds of making a flush by the river, given suited cards to start. They should be about 4%.

So our original poster is running cold with only one made flush in 80 hands. But he's only "entitled" to 3 or 4 of them.

Suited is always a little better than unsuited. I'm coming to believe that "little" is the most important word in that sentence.

[srm80]

that extra 4% helps a ton in the long run when you get bailed out by the flush, and you take down that many more big pots.

[RiverDood]

in a loose limit game, sure.

in NL, where it's often heads up by the flop/turn, everything gets tougher. No one to pay you off if the flush hits. Big ugly bets coming at you until it does.

[elitegimp]

If you have two sooted cards, then there are 50 left in the deck to see a flop from, which means there are 50c3 = 19600 _unique_ flops (i.e. As Ah Ac is the same as Ah Ac As). Of those, 11c2*39 = 2145 have two of your suit, and 11c3 = 165 are a flopped flush. Therefore, (2145+165)/19600 = 2310/19600 = 11.79% of the time you will flop either a flush or a 4-flush.

Just the 4-flush is 2165/19600 = 10.94%.

edit: also, by my calculation, when you are dealt sooted cards you expect to have a flush by the river 6.4% of the time. This seems a little low, so here's my math for you all to pick nits with:

Total 5-card boards: 50c5 = 2118760
3-flush boards: 11c3*39c2 = 122265
4-flush boards: 11c4*39 = 12870
5-flush (of your suit) boards: 462

So you have a flush on 122265+12870+462 = 135597 boards, or 135597/2118760 = 0.0640 or 6.4%