200/400 Check TP HU?

[jogger08152]

Assume the river action will always be bet-call if villain improves. How often does villain need to bluff, in order for a check to be correct?

When he holds QJ, he will improve 10 and bet out 10 times. Of these, he will lose one bet 6 times when he catches a Q or J, and win 5 bets 4 times when he catches a T. Same thing in effect with QT. In order to break even with his 4 winners, you need him to bluff 14 times on the end each time he holds one of these two hands. With 44 possible rivers in each instance, his bluff rate needs to be 33% here.

When he holds 22, 44 or 55, he will improve 2 times each and win 5 bets each time. In order to check in this spot, you need him to bluff 10 times every 44 hands. This is about 23%.

If he is equally likely to hold each of the above hands, he needs to bluff more than 27% of rivers for your check to be correct. (If you use a Bayesian distribution of hands, he will hold QJ and QT combined 32 times for every 18 times he holds a small pair. In this case he would need to bluff at least 31% of the time for a check to be correct.)

All of the above assumes you will never win an extra bet on the end when villain checks (either he check-folds a loser or checkraises or check-calls a winner). If this assumption is incorrect, reduce the above bluffing frequencies by one for every time he will check-call with a loser on the end, and by two for every time he will checkraise a loser (assuming you will call the raise).

Best regards,
Jogger