Can the PF worth of a starting hand be calculated?

[Ludanto]

Let's say you play heads up and both players have 1000 BB in front of them.
Your opponent has to act first and raises.
Is there a 'mathematical reason' why you should call a raise of X BB with KK or QQ (or whatever hand) but not more? How many of those 1000 BB would it be mathematically correct to pay to see the flop with KK?

KK are the second strongest starting hand in a heads up game, right?
There are 169 different starting hands.
With AA it would be correct to pay the full 1000 BB to see the flop.
So with KK it would be (100 BB / 169)*168 = 994 BB?

Does it even make sense to think about a certain (calculatable) value of certain starting hands?

[AaronBrown]

It makes sense, but it's more complicated than your first approach.

If you know the other player's strategy, you can compute the best counterstrategy. For example, suppose she bets the entire 1,000 with any pair of T's or better, plus one time in 100 with a random hand. You can figure which hands have positive EV against this range, and call with those.

In game theory, we assume you know what the other player will do, and that she knows you know and will select the best counterstrategy. No-limit poker, even heads up with one betting round, gets complicated quickly. It's relatively easy to solve limit a limit game with one betting round if players get random numbers from 0 to 1 instead of hands.

[erocplayer]

Ithink it's better to discuss these numbers as a percentage. The number you came up with for KK was 994, so I think that the best way to discuss KK HU would be to say that it's statistically ahead of youropponent .994 or 99.4% of the time, or that it's statistically 'ok' to call off your whole stack .994 or 99.4% of the time, rather than to discuss how often. But either way, whether what you suggest or I suggest is correct hypothetically, I don't think that either resolution is appropriate for HU play. After all, is it EVER ok to call a 994 raise preflop w/ 1,000 starting chips and not shove the rest? I'd say not..

-eroc

[Bang584]

Can you really call it a shove if it's only six more chips?

[mvdgaag]

[ QUOTE ]

So with KK it would be (100 BB / 169)*168 = 994 BB?


[/ QUOTE ]

All that this calculation will tell you is the chance that you have a hand with positive showdown value against a random hand. You are ahead in 168/169 deals so it's a good spot to want to get ALL your chips in ALL the time, not up to 994 of them or in 99,4% of the cases.

Also (to be precise) there are 52*51 ways to deal a hand and 4*3 ways to deal aces, so there is a 1:221 chance he has aces, not 1:169... There are fewer ways (12) to deal pocket pairs than there are ways to deal a hand of two different cards (16).

Is there is already a pot worth fighting for your range should be wider. What you are suggesting is realy the same as comparing (implied) pot odds to hand odds. In your example the odds you are giving yourself is his stack VS yours (1:1) So you need to be just ahead of his range to justify to want to play for all your chips.

If there is already money in the pot you will have better odds (pot+stack : stack) so you can call even if you are behind his range.

Sometimes if you win you win more, but if you don't you loose less... This is because you can fold easily if you don't hit. Suppose he is realy tight with his raises (only raises the big pairs). You pick up 22... You want to play, because without a set you will only lose a little, but with a set you might win everything. While the showdown value against his range is only 1:4. This explains why a mathematical approach like this will work for an allin decision, or a decision that will commit you, but won't if there is still room to win a lot of lose a little because of later decisions.

[imlosing]

I think thats when you gotta just go with it. Like they did in rounders... He's trying to bully you, Make your stand. If you believe him then muck, if not Throw down.