another theoretical question |
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Posted Mon Dec 04, 2006 1:03 pm GMT by suitedaces84
You're playing limit hold'em against a player who will never bluff on the river. That is, every time his bet is called he expects to win 50% of the time or more. You've played this opponent for a long time, you know his exact strategy and he knows yours.
For simplicity assume:
-the pot will always contain 5BBs on the river
-a maximum of 1 bet can go in on the river
-your hand strengh can be converted to a percentile. For example a good hand would be in the 98.8 percentile and a bad hand would be in the 20.1 percentile.
With what hands should you call on the river? With what hands should your opponent bet on the river (keep in mind, all of his bets must be for value)?
The above two questions relate to each other. For example, if you'll call a river bet with the top 50% of hands your opponent will bet the top 25% of hands (this is so the worst hand he bets will be called by a worse hand 50% of the time).
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Posted Mon Dec 04, 2006 8:08 pm GMT by snoogins47
If both players are adjusting optimally, after stretching the back-and-forth-landwar-in-asia nonsense far enough won't we end up with nobody betting anything?
If we don't allow for the nonsense and just assume that we're going to play optimally regardless of what our opponent chooses, the question is moot since nobody is ever making a mistake. Duh.
However I think the equilibrium ends up being at never betting, and that's probably what you're going for here. Extra fuzziness for the definition of 'value bet' makes it slightly more interesting, since based on the way the post is worded we could probably argue both FOR betting an unbeatable hand, and AGAINST betting an unbeatable hand. Does 50% equity when called count as "winning 50% of the time" when called? Heh. Equivocation ftw.
Posted Tue Dec 05, 2006 10:29 pm GMT by suitedaces84
I could have worded that better.
Anyway, yeah, you got what I was going for.
And what made me think of this is many of the short handed limit games I've switched over to recently. I realized one of my bigger mistakes was liberally calling aggressive players one the river in these games. I did this based on the flawed logic of "my bluff catcher stands a better chance against a player who bets frequently on the river than a player who bets infrequently".
Of course, that isn't true. And the idea behind it is simple: the more you value bet the more you can bluff (and vice versa). Playing against a player who doesn't use the correct mix of value bets and bluffs is similar to a playing a basketball player you can only shoot jumpers or drive. Anyone who's played basketball has probably seen this. If you're hitting your jumpers it gets easy to sell the pump-fake and drive. If you're driving and scoring a lot you'll get more room to shoot the jumper.
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