A situation I struggle with...

[Six_of_One]

Another question that came up last night at the Bike. NL tournament, started with 481, down to 30 (top 36 in the money). Blinds are 800-1600, 200 ante. I'm the SB...after posting, I have 7300 left.

Folds all the way around to me. My basic question is, how often does the BB need to fold to make it correct for me to go all-in with any 2 cards?

I had 92s. I hated to pass up the chance to raise first in, and my stack was getting awfully short...we were 8-handed, so there was 4000 already in the pot. The BB had been playing tighter than most at the table, and he had about 12000 in chips. I decided to go for the steal and raised all-in, but unfortunately he called me. He had AJo, and I got no help.

Was this really stupid?

[dmk]

While you need to push soon, I'd probably wait. You have 6 free hands coming up that you can just muck or push with. Odds are you'll get something better than 92s to steal with, or a legit hand to play with.

[CrisBrown]

Hi Six_of_One,

I agree that short-stacked, you had to make a move soon, but I don't really like making it with 92o from the SB, an obvious steal position. The BB would be correct to call with almost any decent hand -- getting ~3:2 from the pot, with little -$EV if he loses, and substantial +$EV if he wins -- and almost any two cards are likely to be a favorite vs. what you have.

Cris

[Che]

[ QUOTE ]
My basic question is, how often does the BB need to fold to make it correct for me to go all-in with any 2 cards?

[/ QUOTE ]

21.6% is your breakeven point if you assume (as I did) that you will be a 2:1 dog on average when called.

If called you will have T18600 when you win (1/3 of the time) and zero when you lose. On average, this is T6200 when called.

When BB folds, you have T11300 every time.

If x=%fold, breakeven is:

6200(1-x) + 11300x = 7300
x=21.57%

If he folds 40%, you have:

6200(.6) + 11300(.4) = 8240 which is a 13% increase in your stack on average

If he folds 60%, you have:

6200(.4) + 11300(.6) = 9260 which is a 27% increase in your stack on average

If I'm shortstacked (and less than 5xBB probably qualifies), I push in since I figure BB will fold 50% or more since losing leaves him with less than T5000.

If his stack was huge such that losing wouldn't hurt much, I'd fold because the odds of a call would quickly increase.

Hope this helps,
Che

[Six_of_One]

Just to make sure I understand...your numbers are saying that as long as the BB will fold at least 21.6% of the time I raise all-in, that it's a +EV play to do it even with a bad hand?

That's interesting. My instinct at the table was telling me something similar, minus the exact numbers of course...but when I made the play I was thinking that he'll definitely fold well over half his possible hands, which is why I felt it was worthwhile. Afterwards I started having second thoughts, which is what led me to make this post. But now your numbers are making me think I made the right choice after all.

[Che]

[ QUOTE ]
Just to make sure I understand...your numbers are saying that as long as the BB will fold at least 21.6% of the time I raise all-in, that it's a +EV play to do it even with a bad hand?

[/ QUOTE ]

That is what my numbers are saying for this particular "bad hand" if I didn't make a mistake in either of two areas:

1. My math. If no one corrects me within 24 hours we can assume my math is correct since people like pointing out my math errors. And I'm glad they do [img]/images/graemlins/grin.gif[/img] - I'm not trying to disseminate misinformation here...

2. My assumption that you will be a 2:1 dog if called. After further consideration, I think 7:3 dog would have been better, but that shouldn't change the numbers by much.

Two other things to consider:

1. Regarding "bad hands"- I think this is a good play with 92s, but I probably wouldn't make it with 92o. Being suited makes a big difference when you're the underdog so don't extrapolate the results of this hand to be the results for any two cards.

2. Variance. Although any fold%>22% is +EV if my assumptions are correct, I wouldn't make the play unless I was confident that the fold% would be much much greater than 22%. Reasoning: As the folding % increases, your EV/stack size increases very slowly. No reason to push in knowing that you'll bust a large percentage of the time for a slightly +EV situation IMHO. Obviously, how much +EV is required per unit of variance is something that each player has to decide for himself (and a given player's decision will vary depending on other variables as well).

[ QUOTE ]
But now your numbers are making me think I made the right choice after all.

[/ QUOTE ]

I tend to agree, but I'd wait for confirmation from some of the better players before I took that to the bank (and some have already disagreed so confirmation may never come [img]/images/graemlins/crazy.gif[/img]).

Later,
Che

[Che]

...but not too bad.

I didn't factor in that the BB only has to call 6500 of your 7300 allin so winning when called only gets you T17800.

I'm too lazy to do the corrections right now, but this does bump the breakeven up a little. Sorry!

Also, BB will have around T6000 instead of T5000 if he calls and loses so this may increase his chances of calling a little.

Both changes move the correct play away from allin, but probably not by enough to change my decision if I thought he would fold over half the time (per your read).

Later,
Che

[Eric P]

Pushing in is fine, it is clearly a steal but he cannot outplay and cannot very well call with anything less than ace high, which he won't have very often (less than 50%). he is risking slightly more than half his stack to try and bust you out and he doesn't really need to bust you out that bad. You have no free hands becuase there is an ante, and while pushing is a fine play, and very possilbe the right one considering that it is more than 50% his chips to call, folding is also fine. Folding is fine because you can afford 200 a hand for a while and you are good position the next three hands. I would have folded but don't critize you for pushing at all, especially in live play as opposed to online.