# Game Theory Optimal - Poker Maths

• Bronze
Joined: 03.10.2007
The hypothetical situation is one where you (Hero) are an omniscient player. You know that your opponent (Villain) is playing game theory optimally and that he never has the nuts in this situation. In this spot lets assume that Villain always has a bluffcatcher. Hero's hand is either the nuts (aka better than his bluffcatching range) or air (aka worse than his bluffcatching range). Hero has the nuts less than half the time.

Is Hero's optimal betsizing always all-in?

Doublechecking these also:

Hero's optimal bluff frequency should be Bet/(Bet+Pot) * Value%
Villain's optimal call frequency should be Bet/(Bet+Pot)
• 3 replies
• Global
Joined: 23.02.2008
hi chenny,

Not sure if I understand.

If villain's bluffcatching calling range doesn't depend on the sizing, then when we have the nuts we get max value from bluffcatchers (we can overbet) but if we have air then we get called by bluffcatchers; knowing we have nuts less than half of the time, why would we bet?.

Still, in real life, the sizing matters very much. And one other thing is important - does our opponent think of what represent?

Cheers,
Michal
• Bronze
Joined: 03.10.2007
nvm Saphael. I decided this is a pretty interesting topic that I have more knowledge about now (modesty etc) so I'm going to make it all into a video or two.
• Bronze
Joined: 12.04.2010
Hi Chenny,

I think I understand your question (cause I thought of something similar a while ago). In your case and using game theory, Hero's optimal betsizing will be all-in, or at least overbet pot. If Hero bets less, for e.g. potsize, Villain's call will always be +EV (since you said the chances of Hero having nuts < 50% and assuming Villain may suspect that).

Hero's range is polarized between nuts and bluff and at any point if Villain thinks that Hero is having nuts there <66%, he has the pots odds to call a potsize bet (I am assuming you are talking about the river here).

Hence, an all-in will be a good move if Hero thinks the fold equity against Villain will dramatically increase. For instance, the Villain thinks that over bet all-in is rarely a bluff and he re-evaluate his analysis of Hero having the nuts, i.e. thinks that there is a higher frequency of Hero having the nuts now. Or Villain is not someone who will hero call overbet often and will be pressured to fold.

I will love to see your video on this topic