Something for you little bastards to think about

It's folded to you in the small blind with K8s. The big blind has 19 bb in his stack after posting the big blind, and you have him covered. K8s is a hand that you'll want to raise here most of the time, but against a short stack things can become tricky to evaluate quickly if he pushes over you.

So what if you just push into him preflop? Do you think this is profitable?

Let 22+,A2s+,K8s+,A2o+,K8o+ be the big blind's calling range, which is 26.4% of hands. If you can't figure out why I picked this range, then keep reading but try to figure it out (there's a very specific reason).

We have 38.095% equity against this range (ty PokerStove).

73.6% of the time, we pick up the blinds. (1.104bb of equity)
10.06% of the time, villain calls and we win a profit of 20.5bb. (2.0623bb of equity)
16.34% of the time, villain calls and we lose 19.5bb. (-3.1863bb of equity)

As it turns out, we will on average lose 0.02bb each time we make this push as long as villain calls with an optimal range. If villain doesn't call with exactly the optimal range given above, then we'll come about break even or even profit.

Now, a few things to consider:
1. Villain won't know whether we're pushing with K8s or AKs, so how will he adjust his range correctly?
2. Using this same process, you can quickly figure out what range of hands you can always profitably push with in this spot against different sized stacks.
3. Have you figured out why I used the range that I did in this example?

is there a nash equilibrium strategy here for SB against 19BB stack in BB?

if you push k8+, then your opponent can't call with k8+. so then you want to push with a wider range, and then your opponent will want to call with a wider range.

with K8+ you can push profitably no matter what your opponent calls with.

This confuses me. I hate tournament play

This is like the fourth time you've posted this

I wrote an excel file that will answer questions like this for when I was 20bb'ng. Its on my laptop, and I'm not going to go get it just for that, but I'm pretty sure I've posted it before.

The following is NOT the same chart, but it will help.

http://spreadsheets.google.com/pub?k...J-Nm72KjFyqPWA

Good thought experiment.

Although this is +eV it's not even close to optimal.

Originally Posted by swiggidy

Good thought experiment.

Although this is +eV it's not even close to optimal.

Just trying to throw something out there that doesn't get talked about much so the newbies get exposed to it.

And I was referring to SB's optimal calling range vs. our hand.

The one thing I did notice is that his range (26.4%) added to the amount of times we pick up the blinds (73.6%) equals 100%. Now whether this is not important or I'm working at things backwards I'm not sure. I'm still very green on the math side of poker.

But from what I've seen played I'll answer your questions.

1 - Villain should eventually work out that we have a wideish range in which we're stealing the blinds. Depending on his skill level and patience I'd say villain is going to wait until he gets a monster or at min a coin flip against us so the one time he calls, we're in trouble. Incidentally this exact method is exactly what Phil Hellmuth talked about on Poker After Dark this week. I think his range is going to be more like:

55+, A6/7s+, A6/70+, K9s+, K9o+

Not sure why though but that's what I figure it would work out to be.

I could be completely wrong though.

A.

Originally Posted by Andrew

The one thing I did notice is that his range (26.4%) added to the amount of times we pick up the blinds (73.6%) equals 100%. Now whether this is not important or I'm working at things backwards I'm not sure. I'm still very green on the math side of poker.

But from what I've seen played I'll answer your questions.

1 - Villain should eventually work out that we have a wideish range in which we're stealing the blinds. Depending on his skill level and patience I'd say villain is going to wait until he gets a monster or at min a coin flip against us so the one time he calls, we're in trouble. Incidentally this exact method is exactly what Phil Hellmuth talked about on Poker After Dark this week. I think his range is going to be more like:

55+, A6/7s+, A6/70+, K9s+, K9o+

Not sure why though but that's what I figure it would work out to be.

I could be completely wrong though.

A.

It adds up to 100% of the time because if we don't pick up the blinds that means he called.

You're thinking way too hard about the rest of it. If you were villain and saw our hand face up, what hands would you call with?

Originally Posted by spoonitnow

It adds up to 100% of the time because if we don't pick up the blinds that means he called.

You're thinking way too hard about the rest of it. If you were villain and saw our hand face up, what hands would you call with?

Like I said, not too hot on what the numbers are and where they come from yet but your range makes sense now you've asked that. I might even throw in some SCs - T9+ - in there too considering that I could end up with two live cards. Or would that be too open a range?

A.

Originally Posted by Andrew

Originally Posted by spoonitnow

It adds up to 100% of the time because if we don't pick up the blinds that means he called.

You're thinking way too hard about the rest of it. If you were villain and saw our hand face up, what hands would you call with?

Like I said, not too hot on what the numbers are and where they come from yet but your range makes sense now you've asked that. I might even throw in some SCs - T9+ - in there too considering that I could end up with two live cards. Or would that be too open a range?

A.

The idea is to figure out what the optimal calling range is for villain, or rather what hands villain can call with with +EV. Here that range is the range I gave before. Then we figure out if against that exact range if we're still +EV on our push. If so, then we'll be +EV against any possible calling range.

The thing is this: there is only one optimal calling range for villain against any one of our hands.