Four to a Flush, post-flop, push all-in

[Tom22]

I have seen a lot of plays where someone would have the nut flush draw post-flop and push all-in. I understand the reason is that you have fold equity and also if someone calls you can still win when your suit hits. But mathematically, when would it be correct to make this move?

For example, if there is T100 in the pot. How many chips do you need behind and/or how many chips does your opponent need to have and/or what the fold equity percentage need to be to make this the correct play? I have seen this move many times on tv and would like to incorporate it in my game. Thanks in advance for the help.

[Tom22]

All of you poker experts out there, please , pretty please reply to my post.....

[whiskeytown]

I'm not sure this is a pot equity, per se...

look at it this way. Are you prepared to go all in till the river if your opponents bets $400/800/800 - (assuming you have 2000 in chips)

If you ARE willing to do this, then why not make the bet first - yer looking to drive out hands, not draw and hit -

that's my logic anyways...I hit 4 to the nut flush and if I'm prepared to call to the river even for all my chips, then I'm better off just betting it all in to begin with.

RB

[Indiana]

You must understand the probabilities involved with a flush flop to know how to play this hand...Lets say you are up against 4 guys on the flop....Then the probability that one of them has the flush is only around 20% if you dont have one of the flush cards...and this probability goes down as the number of players goes down...Thus, you should generally feel comfortable playing through this flop (especially if you have one of the flush cards). Pushing or not is really dependent on how short-stacked you are...If you are desperate then its a reasonable move, otherwise you may want to put in a healthy raise and proceed with caution...

This is just my 2 cents,

Indiana

[Ghazban]

It depends on a lot of things. For example, AKs on a 972 board with 2 of your suit is better to push with than A2s on a QJ6 board with 2 of your suit because your ace and/or king outs might be good in the first hand but your 2 outs are probably worthless in the 2nd and a hand like AQ (who would likely call) makes your ace outs no good either. With 2 overcards and a flush draw with all 15 outs clean and 2 cards to come, you are actually a small favorite over a made pair. If you just call and hit one of your outs, the made hand will likely fold (as either the flush hit or their top pair is no longer top pair) so you'll get no extra chips but, if you get all the money in beforehand (as an unmade hand that is a favorite), you'll either get paid off (if they call and you hit) or you'll pick up the pot.

[donny5k]

I think you misread or didn't read the original post. He was asking for advice on when to push as a semibluff with the nut flush draw. (2 of his suit on the flop not a monotone flop)

[Ghazban]

I should also have said it depends on your opponents (as everything in poker does). This play is only worthwhile if your opponent is capable of laying down a a hand that's ahead of you (usually top pair). If the opponent won't fold, you're often better off calling (and then betting when you hit because he'll call) or just folding (often folding is better because you don't want to be bleeding chips on draws).

[SossMan]

It's simply a function of the % chance that your opponent will fold, your pot equity, the size of the pot, and your stack (or really, the smallest of the two stacks). I'm sure the math types out there can give you a nice eloquent calculus equation with these variables, but ballparking it isn't that hard.

here's a fairly common example:

Preflop MP raises to t1,000 (he has a t15,000 stack)
folded to you (with t20,000 after posting) in the BB and you call w/ 2 /images/graemlins/diamond.gif3 /images/graemlins/diamond.gif.

Preflop pot = 2050 (sb = 50).

Flop comes K /images/graemlins/diamond.gif 7 /images/graemlins/diamond.gif 9 /images/graemlins/club.gif.

If you push, how often does he need to fold in order for this move to be profitable?

If he folds 50% of the time here's the EV calc:

50% of the time you win the t2050 in the pot uncontested.
EV of t1025.

32.5% of the time, you are called and lose t14,000.
-EV of t4,550.

17.5% of the time you are called and you win t14,000 + t2,050 = t16,050
+EV of t2,808.

Total EV = 1025 + 2808 - 4550 = -EV of 717.

These paramaters should be easy to put into excel to backsolve for your opponents folding percentage. In this case, my guess is that he would have to fold something like 75% of the time for it to be profitable (probably not likely given his preflop raise).

[Indiana]

My apologies...I misread your post...I was in a hurry when I posted...Now that I have more time I would like to try to answer this question (because it is a good question) using my stats background...I know that Dolly Brunson preaches this type of push, but is is correct? My feeling is that you wouldn't push for a small amount of chips in the pot...Why take such a risk for so small a gain? Now to the stats:

Let Y be the Random Variable representing the gain that you get when Pushing on the nut flush draw. We will assume that you have 1500 chips just for the sake of the argument, and that your single opponent has you covered. Then what is the fold equity needed to result in a positive EV? Well here is the prob. dist of Y:

Y={100 with prob p that he will fold
? with prob 1-p that he will call
}

Well, let's assume that he calls...Then you will win 1600 with approx. prob .34 and loose 1500 with approx .66 prob...So here we expect to gain .34*1600 -.66*1500= -446...

SO EY=p*100 -(1-p)*446. Now, what is the value of p when this EY is zero? Solve and p=.82. This is too high...Thus, we need to have more money in the pot to make such a move worthwhile...How much? Depends on what we think a reasonable fold probability is...what if p=.5? Then EY=.5x-.5*(.34(1500+x)-.66(1500)) So x would be = 1090. So as you can see, unless you know that there is a really good chance of a fold, there had better be a lot of money already in the pot.

Does this sound ok?

Indiana

[ddubois]

I made a spreadsheet available here (http://ddubois.bounceme.net/poker/OddsBets.xls) that does calculations along this line and some others. I encourage anyone interested to download it and offer any comments on its accuracy or suggestions for its improvement.

I've never actually used it during play as it would be a bit tedious to enter all the data in the moment, but I use it for post-analysis. I think one of those real-time window-scanning poker softwares should add something like this, that would be an awesome feature.

PS: Just because a push is +EV, doesn't mean it's a good play. There's nothing in the spreadsheet that indicates the value of survival equity, because I've never seen any mathematical way to value it (except maybe the ICM, which I don't yet understand?). If a play has +t20 EV but puts t2000 chips at risk, it's probably not a good play.

[Tom22]

I like to thank everyone who responded especiallly Sossman and Indiana. I think both of your methods are sound and equivalent to each other.

Ddubois, there may be some flaws in your spreadsheet. I don't quite have the time to figure it out. For my own spreadsheet I used:

Pot: 1100
Min Stack:: 845
Fold %: 50
Win % if called: 43

I get an EV = 431.7

For your speadsheet you have a column called action to me. I assumed that your opponent has bet this amount. For these calculation purposes, you can include that amount in the pot. Then again, maybe my math is flawed.

I will playing an online tournament tonight, hopefully, I get a chance to use this new found strategy.

[ddubois]

[ QUOTE ]
For your speadsheet you have a column called action to me. I assumed that your opponent has bet this amount. For these calculation purposes, you can include that amount in the pot. Then again, maybe my math is flawed.

[/ QUOTE ]
I generalized the formulas involved to handle both the case where there is a bet to me post-flop, and the case where I have to call some portion of the blind pre-flop. Thus action to me is a separate input from the pot. If you are talking about the post-flop case with a bet to you, what you enter for the pot amount should have included that bet amount (after all, it is in the pot). Similarly, his stack should be the size of his stack after his bet (or after his blind post).

[ddubois]

[ QUOTE ]
Pot: 1100
Min Stack:: 845
Fold %: 50
Win % if called: 43

I get an EV = 431.7

[/ QUOTE ]

Assuming you are first to act, thus 0 action to you:
.5*1100 + .5*.57*-845 + .5*.43*(1100+845) = 550 - 241 + 418 = +727 EV

[Tom22]

Thanks ddbubois. I double checked your math and it is correct. I stand corrected.