Hold'em: Odds on the flop

[Raza]

Hi, I've recently been reading and studying Small Stakes Hold'em and wanted to ask specifically about the necessary odds to call when you have a backdoor flush draw. On the flop, after a bet to you, you can call for .5BB. On the turn, if you miss your flush card you fold (-.5BB total, odds are 37/47). If you do catch your flush card, you will continue, but may have to call a bet in the process. On the river, if you miss you flush card you fold. (-1.5BB total, odds are 10/47 * 37/46). If you catch you flush, you will win the pot. (odds are 10/47 * 9/46).

So this is what I have:

37/47 = .787
10/47 * 37/46 = .171
10/47 * 9/46 = .0416

EV = (.787)*(-.5BB ) + (.171)*(-1.5BB) + (.0416)*(final pot size not including your bets since the flop)

Break-even pot size: 15.625BB. So in practice, on the flop, you would add the size of the pot plus any future bets by your opponents and go from there. Is this analysis correct?

Thanks.

[binions]

If all you have is a backdoor flush draw, then all you have is a 23:1 shot with 2 to come. This equates to 1 out. Maybe 1.5 if you are generous.

So, if that's all you have, you need pot odds of ~23:1 to call on the flop. Extemely rare that you will you ever call based solely on a backdoor flush draw.

Where it factors in is when you have other ways to win. If you have something more, like a gutshot, bottom or middle pair, backdoor straight draw, overcards, open ender, then you'll have to add all your outs (counting the backdoor flush draw as 1 to 1.5 outs) and see if it makes sense to continue.

[Raza]

Ok so let's say I have middle pair as well. That's 5 outs to 2 pair or trips in addition to the 1.5 outs for the backdoor draw. But that's 5 outs twice; how do I combine 1.5 outs by the river with 5 outs on both the turn and river in my decision to call on the flop?

[bobbyi]

[ QUOTE ]
So in practice, on the flop, you would add the size of the pot plus any future bets by your opponents and go from there. Is this analysis correct?

[/ QUOTE ]
This analysis is only correct if the assumptions you make hold true. The first assumption you make is that you will win the pot if and only if you have a flush. If there is a decent chance you can make a flush and still lose (perhaps you have reason to fear that someone is on a bigger flush draw), then this formula will make you call too often. If you there is a decent chance you can win without making a flush (maybe you have a backdoor straight draw or maybe you have the nut flush draw and may be able to win just by pairing your ace), then this formula will make you fold too often. The other assumption is that you are always going to have to pay one bet on the flop and one on the turn (if you help). If you aren't closing the action on the flop, this may lead you astray as you will often call and then have it get raised behind you, which hurts you a lot. Even if you are closing the action on the flop, your assumptions about the turn may be wrong. If you are in passive game where you will often get a free card on the turn, you can call a lot more on the flop since you are getting to see two cards for one small bet. If you you are in a wild game where there are often raises and reraises on the turn, you are probably less happy than this formula suggests (unless many people are going to be in for the turn bets, in which case you don't mind because you are going to win a fifth of the time that you are calling them). So, in general, I would say that the sort of analysis you are doing is good and will help your play, but you need to think about how the game you are playing may violate the assumptions of your formula and adjust accordingly. Trying to create formulas and then rigidly following them when the game doesn't match them can be dangerous.

[binions]

[ QUOTE ]
Ok so let's say I have middle pair as well. That's 5 outs to 2 pair or trips in addition to the 1.5 outs for the backdoor draw. But that's 5 outs twice; how do I combine 1.5 outs by the river with 5 outs on both the turn and river in my decision to call on the flop?

[/ QUOTE ]

No - just count it as 6 to 6.5 outs to decide whether to see the turn.

If you pick up a flush card on the turn, you now have 14 outs to see the river. If you don't you have 5.