"Immediate Profit When Opponent Folds" Checkup

[Lucky]

Basic Question: In NL Cbet situation, there's 100 in pot, with 1 opponent. The following are how I understand the ev related to villain mucking.

Please correct me if wrong.

1. If you bet 100 and villain folds 50 percent of the time, you show immediate profit.

2. If you bet 50 and villain folds 33 percent of time, you show immediate profit.

3. If you bet 75 and villain folds 41 percent of time, you show immediate profit.

4. If you bet 66 and villain folds 38 percent of time, you show immediate profit.

[AaronBrown]

You have to be careful. In (1), for example, you bet $100 and villain folds 50% of the time. So 50% of the time you make $100 profit, the other 50% you have some interest in a $200 pot. Since you can fold your interest in the $200 pot without risk, this should not have a negative value, but in practice, for many people, it could have negative value.

Also, you are computing your profit given that $100 is already in the pot. That is the correct view for decision-making, who put the money in is irrelevant. But it is not the correct view for accounting, you may have contributed up to $50 of that $100. So although you have an immediate profit from the $100 bet, you may not have a profit for the hand as a whole.

Given those constraints, the general statement is:

If you bet X and villain folds more than X/(100 + X) of the time, you show an immediate profit. So (3) should be 43% and (4) should be 40%. In 100 + X hands, you win $100 X times and lose $X 100 times for break even.