As I was just busted out of a tournament on the button trying to steal the huge blinds of a turbo tournament, I screamed to myself "OF THE COURSE HE PICKS UP #$%$ING POCKET JACKS IN THE BB."

This isn't the first time i have been busted out of a tournament pushing all in from the button to steal the blinds. It seems to happen a lot.

I do feel i made a mistake in this hand (because i am out), but I am curious if anybody knows or is smart enough to calculate the odds that a blind picks up a hand worth calling a push from the button (chip stacks being close enough that a call would be a big chunk of a blinds chips .) I would say those hands would be pocket 6s-As, AK AQ KQ AJ maybe even KJ, QJ, and J10. I bet if somebody figured this out then I would be surprised by the likelihood and try to steal like this far less...

I am still steaming and shocked i didn't just fold and wait for at least an ace to put my chips in with. As you can see though the blinds were huge and i believe my M was at 2.5 - deep in the red zone - so is this the right play in the situation?

Let's calculate the odds for a player to have 66+,AJ+,KJ+,QJ,JT.

These hands constitute 12.5% of all possible hands. This can be calculated by direct count or, easier yet, by using pokerstove.

The probability a player behind you to have one of these hands is

**approximately** 12.5%. (It is a little more, but not by much.) So let's round it to 13% per player(easy to remember too

).

So if you are in the SB and push, there is 13% chance the BB will call you.

If you are on the button, you have 2 players behind you, and each one has about 13% chance to call you. So your total chance to get called by at least one of them is about 26%.

Your hand, K6o, is 38% dog against the above range. So on the button, you will win the blinds 74% of the time and get called 26% of the time but you will win 38% of the time you are called. The chance you will get called by both blinds is less than 2% and we will ignore it since even when you do get called, your

equity in the pot doesn't change much (you will lose more often, but triple up when you win).

If you get called by one of the players, your total cEV is:

**cEV= 74%*1.5BB + 26%(38%*(Stack+1.5BB)-62%*Stack)**
where

**Stack** is the smaller of the remaining chips of the caller or your stack.

We can solve that equation to find out the maximum stack when this play is +cEV by setting cEV = 0. This yields:

**cEV(max) = 20BB**
To understand this result, look at the attached image. I calculated the cEV for variouis stack sizes. The smaller the stack, the larger percentage your wins are. We can see that this non-linear trend slows down at around 10BB.

In addition, cEV is not the same as $EV. But when you are <10BB, unless you are near a bubble, increasing your stack is MORE important than losing it because if you don't increase your stack, it will become so small that you will have no chance to come back.

On the other hand, when you are >10BB, the risk of busting out with marginal hands becomes less desirable since you have time to wait for a better situation.

At 20BB, this play is a clear loser even in cEV, let alone $EV.

In your particular case, your stack was 6.5BB. So this move has a positive cEV of about 14% of your stack. Unless you were near a bubble, it is correct to do that. Note that the earlier your position is, the greater the chance people behind you will call you.

So don't feel bad about the outcome. You didn't do anything wrong.

Let's note that the tighter the players are, the better this move is. When called, you are a bigger dog, but only by a little bit. On the other hand, you pick up more blinds.

There is another benefit of making moves with your marginal hands in position. If later you get a premium hand in early position, and push again, some player may get tired of this and call with a marginal hand. There is of course a huge difference calling with a marginal hand and pushing with it

Finally, a note on why the max cEV of 20 seems so high. In particular, it implies that in cash games, moving all-in with a small stack from late position is a profitable strategy (but not optimal!).

This concept is a generalization of the so called Sklansky-Chubukov numbers. For those who don't know what they are, they represent the required

**maximum** stack of the SB to open-push and show their cards to the BB. The idea is that if the SB doesn't have a big enouigh stack(for their holding), the BB cannot call profitably often enough to make a profit. Since you don't usually show your cards to your opponent, you get the benefit of "bad" calls as well.

The calculations I did are only for one specific hand (K6o) against a specific range. A proper generalization of the Sklansky-Chubukov numbers to button play would involve all hands against any range for both players. It is doable but a lot of work. If I find time, I might do it one day.

But the practical conclusion here is that stealing from the button with marginal hands is profitable (though not always successful

).