calculating correct pot odds

[2Fast2Furious]

I think I'm making mistakes on my pot odds calculations for outs to making a flush. As I understand it, you can guess your percentage of making your flush by multiplying outs by 4 on the turn and 2 on the river, assuming you need one card to hit. So say you hold A [img]/images/graemlins/heart.gif[/img] 8 [img]/images/graemlins/heart.gif[/img] pre-flop and flop comes 4 [img]/images/graemlins/heart.gif[/img] 5 [img]/images/graemlins/heart.gif[/img] 3 [img]/images/graemlins/spade.gif[/img] You've essentially got 9 outs to your nut flush which equals ~ 36% or c. 2.75:1 (this excludes any other outs you think are good, but in this case and A might be bad since it gives a straight draw life, so I exclued any A as an "out"). So if I'm being offered anything better than 2.75-1 on my pot odds I should call (implied odds probably would lower that to 2-1 if I do hit flush correct?)

If a blank comes on the turn I still have those 9 outs, but now it's more like 1/2 the 36% chance so pot would have to be offering me 5-1 essentially to call a big bet.....

Is that right? thx!

[LetYouDown]

This is if your only outs are flush outs, and if you make the flush you'll be good.

Hitting flush with 2 cards to come: 1 - C(38,2)/C(47,2) = ~34.97%
With 1 card to come: 9/46 = 19.57%
Hitting flush on the turn card (for immediate odds): 9/47 = 19.15%

So, if you were faced with an all in bet you need to have better pot odds than the percentages listed. Immediate odds are more of a concern, as well as implied odds. Keep in mind that pot odds are much more applicable to limit...but certainly still useful.

[2Fast2Furious]

Thanks. Am forgetting my old math/combination skills, but am wondering what the underlying assumptions are in your first formula. You said it works like this:

Hitting flush with 2 cards to come: 1 - C(38,2)/C(47,2) = ~34.97%

Am not sure what numerator C(38,2) represents and a little unclear on denominator (47 is # of unknown cards, what is the "2" (reps # of cards on the come?).
With 1 card to come: 9/46 = 19.57% (that's easier; 9 outs as numerator; 46 unknown cards in the deck (52 - turn + my 2 = 46)

[LetYouDown]

When calculating things like whether you will hit a flush with two cards to come, it's often easier to calculate the odds that you WON'T hit and subtract from 1.

There are 47 cards remaining in the deck. For you to miss, both cards have to be non-hearts, in this case. There are 38 non-hearts left in the deck. So there are C(38,2) ways you can "miss" out of C(47,2) possible turns/rivers. So you've calculated the odds of missing. Subtracting from 1 gives you the odds of hitting the flush.

[VivaLaViking]

I would count the A, it's the 2 that would concern me because you are putting yourself in a position to hold the sucker straight and likely in a reverse impled odds position (2 - 5 on board). But to answer your question, you have 9 outs for the flush, 3 outs for the A and 4 outs for the 2. 16 outs, that's 57% probability after the flop. So if you would feel comfortable with those outcomes it would not be an error to call up half the pot after the flop. It does sound like you are referring to a limit game. So you should probably call (or raise) to the river.

LetYouDown's odds are dead on, of course, but he leaves out one aspect of your reasoning that needs revision: the "rule of four" to which you're referring calculates odds on hitting with the turn and the river to come . These odds are only directly applicable if you're going all-in, or you doubt very highly that you'll be facing a bet on the turn.

More often, if you're drawing then you'll need to call a bet on the flop and the turn. This can skew your calculations considerably if you're drawing using odds for the turn and river. For instance, if there's $6 in the pot to your flopped flush draw, and your opponent has bet $4, you'll conclude that you're getting 5:2 on your call. With a 35% chance of hitting a flush draw by the river, you would be correct to call if the $4 put you all-in.

But if you're not all-in, and you don't hit your flush on the turn, you'll almost certainly be faced with another bet. With $14 in the pot, if your opponent bet $14, calling for the flush draw could not be right given the 2:1 pot odds. Your call on the turn was incorrect because on the bet you were making - the $4 on the flop - you had a 19% chance of hitting one of your nine outs. The 5:2 pot odds render this a poor call.

That's why unless you're all-in, use the odds of hitting your hand on the turn if you're calling on the flop. The odds of hitting your outs on the turn are almost the same as hitting on the river, so the "rule of 2" is a decent starting point. Using the rule of 4 every time on the flop is a sure way to overvalue your draws.

[LetYouDown]

That's why I specifically mentioned immediate and implied odds. Pot odds are much more applicable to limit than no limit, in my opinion. Unless there's an all in (myself or someone else), I almost never calculate pot odds on the fly at NL. At limit, I do it constantly.

[2Fast2Furious]

Thanks - good advice all the way around. Levarkin stated sort of what I was thinking (i.e. I'm valuing my flush drawn outs too much on the turn)...but with the other outs mentioned I think I still put a decent sized-bet in there in this situation with 12+ outs - just want to make sure it's not too much (say 1/2 - 3/4 pot) so I don't scare out any drawing hands or bet too much against hands I'm almost drawing dead to (say if I had a lower flush possibility or boat on the turn)

[VivaLaViking]

When I started to post you hadn't posted yet. You know I would never disagree with you and always value you're input.

BTW: Is your B&M Foxwoods? And how often do you go there?

[LetYouDown]

Nope, never been to Foxwoods. My current B&Ms are Seneca Niagara, Casino Niagara and Fallsview. I live in the Western New York area. All are within 10 miles. I'm most likely moving back to Florida in the coming weeks...so I have no idea what my new B&M will be. I'm actually off to the B&M forum to find that out, oddly enough.