Proof that going all in with 37s has bad expectation.

[Enrique]

I noticed in the $150 Monday night tournament how in the final two tables a person with a not so bad stack went all in with 3s 7s from the button and I had a discussion with a friend whether it was a good play or a bad play.

The blinds and antes summed up T7000. He had a stack of T32000. The LB had about T95000 and the BB had about T40000.
Let's calculate in terms of thousands, so T7000 will be considered as 7, T95000 as 95, etc.

So here is the analysis:
Let's say that both players fold with probability p. Let's find how big p has to be to make the play good.
The expected payoff of the player is as follows:
7p when both fold
(0.342)*(1-p)(36) + (0.658)(1-p)(-32) when he is called (assuming only one caller)

The 0.342 comes from playing 37s against AX, KX suited, broadway hands and pairs. The .658 is the rest. 36 comes from the expected win, -32 because he'll lose.

(1-p) * (12.312 - 21.056) = (1-p)(-8.744) = 8.744p - 8.744

Hence the payoff is 7p + 8.744p - 8.744 = 15.744p - 8.744

To break even he would need p >= 8.744/15.744, p >= .555

Hence both players have to fold 55.5% of the time to be a break even play (which is in itself probably bad, since folding is almost break even, because of the antes, and risking your like for a gain of your ante sounds dumb).

So he needs to be able to get the pot at least 55.5% of the time without calls.
Now that means that 44.5% of the both the blinds are folding. Now if we assume both blinds have the same probability of calling, say x. Then one of them calls
1 - (1-x)^2 = 1 - (1+x^2 - 2x) = 2x - x^2 = x(2-x). Note x(2-x) = .445.
Solving the equation we get:
x = 0.255
So if the players have only 25.5% chance of calling. They are making the play bad for the 37s.
Note that 27.6% of the hands are any A, any pair, any broadway, certainly calling hands on this situation.

So, you can see the play is of negative expected value, and assuming the two blinds are tight (which they hadn't shown that in the game, LB making reraises with ATo in the past), then the play would still have very small expected value and patience would be a better advice.

Stealing is a good play, but not with 3s7s.

[CardSharpCook]

I'm going to state this a different way.

34% of the time you get called you now have ~67k
66% of the time you get called and now have 0K

.34 * 67 + 0 = 22800 = 23K

23 * (1-X) + 39X = 32 (where X = the successful steal% needed to break even)

23 - 23x + 39X = 32
16X = 9
X = 56%

you need to sucessfully steal 56% of the time. Which is exactly what you got. It has been so long since I've done any math. Nice work, Enrique. However, I think your calling range is too wide. He is pushing for some 10BBs. Fewer hands are going to call that the ones you listed. Also note that the SB has a tighter calling range than the BB. In limit Hold em, I can play 15% of my hands profitably. These are also the same hands I'd call a 10BB AI from the button with. I'm certainly not calling with any ace, and QT, and JT are folds as well. Debatable are KJ, QJ, KT, 22-55.

Intuitively, this 10BB steal works 60-70% of the time. If you assume a top 20% calling range for BOTH players, you are stealing 64% of the time. Say, top 10% for SB, top 20% for BB, you steal 72% of the time. Hate to say it, but I think that in a vacuum (that is, you haven't been maniacal pushing every time it has folded to you on the button) this is a +EV play.

[RDWallace]

funny, i was the protagonist in this hand. Doesnt seem +EV right now, but I subscribe to CSC's logic.

[Exitonly]

calling range isn't as wide as you say...i'd say like 10-15% of hands call that push.(i.e. 55+,A6s+,KQs,A9o+ which is 12%)

so it would be +EV.

[Enrique]

I think the call happens more than 20% of the time. You have to take into account that the BB will have good odds to call.
And even if the call is only 15% of the time. The +EV is so tiny, that it is not a good play. I am certain that waiting for two or three more hands gets you a better expected payoff.
So the play might be +EV, but I don't think it is a good play.

[locutus2002]

I've said this before and everyone ignored me then, so I don't know why I'm repeating myself.

SB should move all in with any two here. 100% of the time.

villain's range is any two. There is an overlay in the pot so its EV++.

In the event that SB does not make the correct move. BB should move all in with any two. BB is 1.4:1 in the pot and 1:1 in the hand.

Having said this, I don't mind the play even if I know I will get called by good players because survival has less value than acquiring a workable stack. (for me).

[Exitonly]

alright you said this last time it came up, and i argued then too, don't know why we stopped.. but

[ QUOTE ]

villain's range is any two. There is an overlay in the pot so its EV++.

[/ QUOTE ]


Ok, as far as we know now, villain just has a random two cards, but that's NOT what his CALLING range is. and that's what's important. Like the OP showed, if his calling range is wide enough (like 20%) then it's NOT +EV.

Just because you're ahead of a random hand, doesn't mean it's always going to be +EV. The risk/reward has to be right.

[Lloyd]

I agree that the calling range suggested is too wide. If you think the hero should pass up a small possible edge, don't you think the blinds should do the same. Yeah, it MIGHT be slightly +EV for them to call with A2, but do they want to risk all those chips with that hand for at best a 60/40 favorite? I think not.

Also:

[ QUOTE ]
So the play might be +EV, but I don't think it is a good play.

[/ QUOTE ]

is contradictory.

And in addition, there is so much more information that is needed to make a good decision here. Like CSC said, the hero's reputation is huge - if he's been tight then it's more +EV then if he's been a maniac in which case it certainly could be -EV. And how tight have the blinds been? How many players are left and who are the shortstacks? This is a bubble situation and people play differently. Thus, $EV also comes into play.

[AtticusFinch]

[ QUOTE ]
I am certain that waiting for two or three more hands gets you a better expected payoff.
So the play might be +EV, but I don't think it is a good play.

[/ QUOTE ]

This of course depends on the situation. If you are short-handed, or there are antes, then you may not have the luxury of waiting 2-3 more hands.

Furthermore, you need a much better hand later to have the same $EV, as there will be more opponents behind you.

At a full table with no ante, or a negligible ante, you're right to be a little tighter. And you're not deperate yet with a 10 bb stack. But if you're sitting on, say, 6 bb, and there's a decent ante, and you're 7-handed, you have to take your spots when you can get them. Because too often someone will raise in front of you, and you'll have to fold that pretty KT you would have pushed from the CO.

[AtticusFinch]

[ QUOTE ]
[ QUOTE ]
So the play might be +EV, but I don't think it is a good play.

[/ QUOTE ]
is contradictory.


[/ QUOTE ]

Not necessarily true. Remember those "small edges" you should sometimes pass up?

I think Enrique is saying it's +cEV, but not necessarily +$EV.