[pzhon]

I would be surprised if someone could produce a clean example. Maybe it could be done with a board of AAAAQ, or where the board is a king-high straight-flush, but normally you can't narrow your opponent's range to a bluff-catcher alone. Normally, there is some chance your opponent has a hand that gives him information about your hand.

Far more important than finding a clean example with no blocking effect where you can compute a precise bluffing frequency, is to realize that the general idea is robust and applies to many messy examples. If you have position, and are considering betting all-in on the river, and you expect that your opponent has a mediocre hand the vast majority of the time, then since the ideal bluffing probability for a pot-sized push is 1/3, you want to try to bluff roughly that frequently against an optimal opponent. If you think it is 5 times as likely that you would end up in that situation, with that board and betting history, with a bluffing hand as with a value-betting hand, then to make the value bets outnumber the bluffs 2:1, you need to give up 90% of the time, and you should bluff with 10% of your bluffing hands. If you think it is less than half as likely that you end up with a bluffing hand, you can push with 100% of your bluffing hands.

If you have played your hand so that it is overwhelmingly likely that you have a draw, but it is not clear which draw you have made, you can't pick random river cards for bluffs. You should pick river cards that might have completed another draw. Again, this assumes that your opponent has a bluff-catcher; you may need to adjust this if you think your opponent was drawing to a strong hand, too.