Esoteric odds question

[keikiwai]

Here is a question about overlays.

The general question is how do you decide on the overlay you'll accept, a hypothetical example follows.

Let's say the flop comes in LHE and you have a 2 to 3 chance of completing a flush by the river. You feel confident that your real pot odds will be 1 to 3 at the end of the hand. So if you would win every time you made the flush you should clearly go for it.... however.....

In this situation if you do not have A suited, you may make the flush and lose. Second even if you make the flush there is a 45% (9/47 + 12/46) chance that there will be a pair on the board. So there is a chance then that one of your opponents will have a four of a kind or full house.

So clearly if you cut your overlays too thin you may lose money eventhough the quick and dirty calculation would indicate that you shouldn't.

Is there a practical way of dealing with this in a live game, where it is rather difficult to first calculate your outs then subtract the chance of a higher hand showing at the end, then subtract the chance of a higher card showing in the same hand you have.

I try to make as good a guess I can whehter I'm drawing dead or will be outdrawn, but it's nothing quantitative. Can anyone do this quanitatively during a game?

thanks,
Peter.

[Kaz The Original]

Figure out roughly the % of the time you will be drawing dead and adjust your outs. I am not sure about this, but you probably have to adjust double. If you are 20% drawing dead, you have 40% less outs. This is a rough guess.

[highland]

[ QUOTE ]

Second even if you make the flush there is a 45% (9/47 + 12/46) chance that there will be a pair on the board. So there is a chance then that one of your opponents will have a four of a kind or full house.


[/ QUOTE ]
45% is not quite right. The math is much harder. First, you have forgotten Bayes' thereom, and double-counted when both the turn and river pair. But, really it's even worse than that, since all the events are not independent. Since what you're computing is the likelihood of two things happening in the course of 2 events, there's 4 ways it could go:

1) You make the flush and the pair on the turn
1/47

2) You make the pair on the turn and flush on the river
8/47 (don't count (1) again) * 9/46

3) turn is a blank, and the flush/pair come on the river
30/47 * 2/46

4) You make the flush on the turn and pair the river
8/47 * 12/46

add these up for the probability that you'll see a flush and a pair by the river: 12.67%

The chance that you'll make the flush, more precisely, is 9/47 + 38/47 * 9/46 = 34.95%

So, there's a 12.67/34.95 = 36.25% chance that the board will be paired if you've made your flush. Your estimate wasn't great, but you're in the ballpark at least. As far as how to compute these at the table, some studying of common situations could help (which you are doing right now). Also, you can use common sense estimates for a lot of situations, since you really don't have to be all that accurate. The probability of a no pair board pairing is 9/47 + (38/47)*(12/46) = 40%. This is an upper bound on how likely the pair is if you happen to make your flush, since it's harder to make the flush and the pair than just the pair...

[AlwaysWrong]

Step 1) Buy Small Stakes Hold'em
Step 2) Read Pages 98-107 on counting outs

Pretty much the less solid your outs the less you should value them. King-high flush versus Ace-high flush you shouldn't discount very much at all, it's rare enough that I don't think you'll enter situations where it matters when deciding on your flop play. But you might want to discount your 7-high flush draw from 9 outs to 6-7 outs, say. You can discount your overcards from 6 outs to something like 3 outs. Then you just pretend you're drawing rock-solid to however many outs you've given yourself and make a decision.

[keikiwai]

I like your suggestion. What highlander wrote makes sense too.

Discounting your outs seems like something that can be done during actual play. It's a shortcut, but it's definitely seems one step better than trying to figure out exact percentages.

I actually have the book, but I haven't gotten around to reading it yet, I'm still working on some others.

It'll definitely take some practice to do it fast enough.

thanks,
Peter.

[keikiwai]

PS I read the section in the book about outs. And I think it helped me turn a horrible session into an almost break even one. I got no good cards, and playing what I thought was OK I was down 20BB after half the session. Then I really tried to concentrate on counting outs at the flop like it's described in the book. Discounting ones that aren't sure wins and looking for the hidden ones, and eventhough I was down by the end of the session, I was down less than 1BB. Catastrophe averted! thanks,

Peter.

[steveyz]

In most limit games, you will be correct to draw to a flush whenever you flop a flush draw. Even in smaller pots where it is heads up on the flop, the lower odds you are receiving are balanced by the fact that your hand may be best already and by the fact that any pair outs are likely to be good.

Only in very rarely situations will it be correct to fold a flush draw on the flop.

[stoxtrader]

[ QUOTE ]
In most limit games, you will be correct to draw to a flush whenever you flop a flush draw. Even in smaller pots where it is heads up on the flop, the lower odds you are receiving are balanced by the fact that your hand may be best already and by the fact that any pair outs are likely to be good.

Only in very rarely situations will it be correct to fold a flush draw on the flop.

[/ QUOTE ]

agreed.