Give your opponent the opportunity to make the mistake.
Pop Quiz Hotshot (you're Snoopy)
Situation. You, Snoopy, are first to act on the river in a $1-2 limit holdem game headsup with the Red Baron and $8 in the pot. Betting patterns and the board make you think that old Manfred might well have missed the board. Unfortunately, so have you and Manfred might just have made a pair or something. Your Ace high should beat a stone cold bluff, but nothing else.
Check or bet? You could check, and then call if bet / pot > chance of opponent is bluffing. But can you really tell if the Red Baron is 33% likely to bluff at the river, or just 25%?
Game Theory attempt (excuse the lack of text art, I've evolved to pseudo Basic commands)
If Snoopy bets. Then the Red Baron can fold, call or re-raise.
If the Baron folds, Snoopy wins $10
If the Baron calls, it's a tossup (EV = 0 old manfred might have bottom pair, or king high)
If the Baron raises then Snoopy has to decide again
If the Baron raises and Snoopy folds, Snoopy loses his bet and his half chance at the pot so the EV is -$7
If the Baron raises and Snoopy calls, it's a tossup $0
If the Baron raises and Snoopy comes right back at him, then things are getting a little crazy, and Snoopy has balls of steel or had just finished reading Phill Hellmuth's book. So we'll ignore this.
If Snoopy checks and the Baron checks, then it's a tossup $0
If Snoopy checks and the Baron bets, then Snoopy has to decide between folding and calling (unless he wants to check-raise bluff). Folding costs him his expected half of the pot (in the absence of knowledge of the Baron's hand, we'll assume it is a tossup). - $5
If Snoopy calls, it's a tossup. $0 (although more variance than check-check)
You see how complicated things get. However, the point I was trying to make is that Snoopy seems to do best when he forces the Baron to make the decision. So, in the absence of tells, my advice would be to bet it out on the river. Unless the Baron is very good, or very aggressive, a re-raise will means Snoopy can be fairly certain he's lost. However, the potential is there to win the pot for sure.
Betting puts the Baron in the worse half of the decision tree (the mirror image of Snoopy checking and the Baron betting, only with the extra knowlehge that Snoopy chose to expose himself to a re-raise.
Give your opponent the opportunity to make the mistakes.
