Quote:
Originally Posted by Portencross
This is maybe a dumb question, but as a pot-sized bet is offering odds of 2-1 to call, isn't the orthodox defence 2/3rds not 50%?
First, its not a dumb question. Second, the answer is no.
In a perfectly polarized situation such that there are no blocker effects and all of Hero's calls beat the opponents bluffs, but do not beat any value, you would not fold at a frequency greater than (bet/(bet+pot)). (bet/(bet+pot)) is often referred to as alpha and Minimum Defense Frequency (MDF) is referred to as 1 - alpha.
For a pot sized bet, this is equal to: 1/(1+1) or 1/2. If you fold more than this frequency, then villain can profitably bluff any and all combos of bluffs.
In the situation where the bluff from villain has EV of check > 0, then the equilibrium would be such that the folding frequency equates to the EV of bet = EV of check... this frequency would be greater than bet/(bet+pot) in order to have EV > 0.
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Also, from the other perspective, the bluffing frequency of the better will be equal to the pot odds given to his opponent in order to achieve indifference/equilibrium. In the pot sized bet situation, you need equity equal to or greater than pot odds to have neutral EV. Pot odds would be equal to 1/(1+1+1) = 1/3 = 33%, so the overall bluffing frequency of the villain should be equal to this value. If he exceeds it, then you would have equity > pot odds and would always call. If he bluffed less than this frequency, then you would always fold. It is only in the perfectly polarized situation and when the bluffing frequency is equal to pot odds that you would be indifferent, and the EV of all calls would be 0, but you would only fold at a frequency equal to alpha in order to make opponent indifferent to bluffing all combos.