Re: simple game theory question
I didn't make myself clear earlier, but I was trying to get an idea of the optimum- game theoretic way to vary bet size in no limit. Say it's now the river, and your stake balance is, say, 100 times the pot. If you bet 1/2 the pot, your opponent will have to call with 2/3 of the hands he would play, to prevent you from stealing the pot by bluffing with anything. If you bet the pot, your opponent following game theory will have to call you half the time to prevent you stealing with anything.
If you bet 10 times the pot, your opponent will call with the top 1/11 of his hands to keep you from stealing. You'll win more money if he DOES call and loses, but he's much
less apt to be calling with a losing hand, so you're giving up all those 1 pot size calls where his hand ranged between the top 50% and top 9.09%. In addition, if you DON'T have the nuts, he's much more likely to have the nuts if he DOES call. Obviously you can't bet 10 units only with the strongest hands, else you're telegraphing the strength of your hand by bet size. My first guess was that the proportion you bet any amount should be roughly proportional to the strength of the hand you're representing;i.e., if you're
representing a top 1/11 hand, you bet 10 times the pot once for every 10 times you bet the pot. Of course you'll HAVE a top 1/11 hand only 2/11 of the time you'll have a top 50% hand, so you'll actually BET 10 units 1/11*2/11= 2/121 as often as you'll bet 1 unit. Any further inputs on general rules on optimum bet size in proportion to pot size?
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