KK vs all in

[AlphaWice]

Suppose you and your opp. have stack sizes of x, and you have 1 chip committed to the pot.

You opponent goes all in. What is the maximum x for which you call? Obviously, if he had a trillion chips behind, it is incorrect to call. So what is the maximum size x?

I remember there is a chart for this but DAFS turned nothing for me.

[mosdef]

why is it incorrect to call a bet of 1 trillion with KK, if you think you're ahead that's still a call. I'm confused.

[AlphaWice]

But does anyone know anything about that chart? It was related to this problem.

ps. about the "incorrect" KK, if your ahead of his range, its okay to call. But for isntance if a player only plays AA, then its incorrect (because your not ahead of his range)

[KJL]

If he only plays AA then it is always incorrect, isn't it? unless x is smaller than 1. I think I am misunderstnading this.

[mosdef]

[ QUOTE ]
If he only plays AA then it is always incorrect, isn't it? unless x is smaller than 1. I think I am misunderstnading this.

[/ QUOTE ]

i THINK that what he's getting at is that you could build a chart with the cutoff values for x for all of your opponents possible holdings, not just AA. and apparently someone HAS done this, and he is looking for these mystery charts.

[danq]

Per Pokerstove, here is the EV of KK versus a few hand ranges:

AA only .181
AA/KK .226
AA/KK/AKs .322
AA/KK/AKs/AKo .473
AA/KK/QQ .500
AA/KK/QQ/AKs .521
AA/KK/QQ/AKs/AKo .572

So basically, you can call whenever you think he'll do this with QQ.

The next question is, if he's a rational player, when can he push with QQ? Assume there's $1 in the pot, and stack sizes are X.

If he thinks you'll only call with AA, then there's about a 0.49% chance he gets called, in which case he'll win X with probability .181 and lose X with probability .819, for an EV of -.638X. The rest of the time, with probability 99.51%, he'll win the 1 in the pot. So his EV is

.0049 (-.638 X) + .9951 = .9951 - .0031X

which is negative when X > 318. So if stacks are more than 318 times what's in the pot, it's -EV for him to push with QQ if he thinks you'll fold anything but aces; so if he's a rational player, you have to fold KK.

Now, if he thinks you'll call with AA or KK, his EV from pushing with QQ is .990 - .0062 X, which is negative when X > 160. So if stacks are 160 times what's in the pot, he can't push with QQ if he thinks you'll call with AA and KK.

(The latter is the relevant question from a game theory perspective; with stacks over 160 times the pot, calling with KK can't be your equilibrium strategy. The former is a more "robust" answer: no matter what villain thinks of your play, he must expect you to call with AA, so with stacks over 318 times the pot, he can't push with QQ if you'll never call with worse hands, so you must fold KK.)

Of course, all of this assumes a rational opponent who's playing to maximize his EV this hand. If you're playing with someone who might push 92o his first hand to show his bluff and get action later, that changes everything. Also, this all assumed a heads-up game; if he's pushing into more than one player who hasn't acted, the chance he's against AA is higher, so stacks need to be smaller for him to do it.

Dan