[rufus]

[ QUOTE ]
With 2 players, there are 5 cards exposed at the river,
you see 2 additional cards in your hand, that leaves 52-7
=45 cards remaining. Your opponent could have one of
45*44/2=990 hands. If only 1 hand is the nuts, You can NEVER bet more than 989 times the pot, else you're guaranteed to be making a negative expectancy bet. 989 is an upper limit.

If you have Kxs with a flush, 3 of your suit on board and none is an Ace, there are 7 ways your opponent could have the nut flush- A and any of the 7 remaining cards. In that case, he'll have the nuts 7/990 of the time so you can't bet
more than 990/7 = 141 3/7 of the pot or you're guaranteed to be making a negative expectancy bet.

[/ QUOTE ]

But you can infer things from the opponent's behavior on prior rounds, so that the probability of the opponent having a particular holding could be less than 1 in 990.

For example, let's say you're holding two AsAh, raise, and get called pre-flop. When the turn comes up AdAcKs you check and your opponent raises. The turn and river are 3c and 4c both of which he also raises hard. Now the nuts is the skip-straight flush 2c5c, but a reasonable opponent, might never make that sort of play with that holding so the proposed limit could asymptotically approach infinity.

Making some similar assumptions about the players being familiar with each other, it's also easy to show that the appropriate bluff-raise is equal to the legitimate raise, so it too, can asymptotically approach infinity.

Edit: Altough, I guess with super-deep stacks, all kinds of strange plays will start making sense, so this is really a weak counter-example.