flush-draw strategy Q

[Guruman]

This has probably been covered before, but I haven't been able to find it, so I'll just ask:

Assume I started with a suited Ace pre-flop (like A2[img]/images/graemlins/heart.gif[/img]): what are the odds that I will hit my flush on the flop or turn?

...aand the application being - given the result, how many limpers must I have in the hand with me in order to make a call profitable if it's given that I'll call one bet to see another card on the flop?

Thx!

[AaronBrown]

There are C(50,3) = 19,600 flops. C(11,3) = 165 of them will make your flush. That's 0.8% or 1 in 119.

C(11,2)*39 = 2,145 of them give you a four flush, that's 10.9% or 1 in 9. The chance of the next card completing your flush is 9/47 = 19%. That makes the chance of making the flush on the turn 2.1% or 1 in 48.

The chance of having a flush by the turn, either on the flop or the turn, is 2.9% or 1 in 34.

[Guruman]

well, this is the most obvious thing in the history of the planet, but it looks like the flush draw by itself is an impossibly weak reason to enter a hand. I guess it just took looking at the math a little bit to really drive home the point that suited cards only add marginal value compared to the rank of the cards.

Just didn't have it in my brain exactly how marginal that value was.

Thanks!
[img]/images/graemlins/grin.gif[/img]

[diebitter]

[ QUOTE ]
well, this is the most obvious thing in the history of the planet, but it looks like the flush draw by itself is an impossibly weak reason to enter a hand. I guess it just took looking at the math a little bit to really drive home the point that suited cards only add marginal value compared to the rank of the cards.

Just didn't have it in my brain exactly how marginal that value was.

Thanks!
[img]/images/graemlins/grin.gif[/img]

[/ QUOTE ]

It's not as marginal as it might appear when combined with other card strength. I can't remember the exact numbers, but say you play JT offsuit, and the chance of hitting something is 8% (say). If it's suited, this adds something like 4% more (say). 4% sounds marginal, but in fact improves your hand by 50% (8%->12%)

so flushing does add value, but only worthwhile combined with big cards/straight unless the number of players is 5-6 seeing the flop. The real+implied odds you get for a single bet of A2s (or a 2-bet if there's enough going in) make it worthwhile, but you should be folding if you don't flop a 4-draw (and even here, something like 54o is a little risky, as you're at the ignorant end of the straight).