[AaronBrown]

It is often correct in tournaments to bet into a dry sidepot. It rarely makes sense to run a complete bluff, but you don't always need a really strong hand to go all-in.

Let's take a simple example. There are three players left in the tournament with remaining prizes of $10,000 for first, $7,000 for second and $4,000 for third. Players A and B had 40,000 chips left at the start of the hand, player C had 10,000. Everyone is in for 10,000.

If A and B check and C wins the hand, all three players will be left with 30,000 in chips and $7,000 in expected tournament winnings. If A and B check and one of them wins, the winner will have 60,000 chips and $9,000 in expected tournament winnings while the loser will have 30,000 in chips and $8,000 in expected tournament winnings.

Suppose instead A goes all-in. If B calls and A wins the pot, she gets $10,000 instead of $9,000. If B calls and beats both A and C, A gets $7,000, the same EV as if she checked. If B calls and beats A but not C, A gets $4,000 instead of $7,000. Therefore, A gains from betting if B calls, as long as her chance of beating B and C is more than three times her chance of losing to B who then loses to C.

If B folds, and A beats C, she now gets $9,000. This is the best she could have done if she had checked in this circumstance, and it makes her an extra $1,000 if B's hand would have beaten hers. If B folds and A loses to C, she has $7,000. This is the same as she would have hand if C's hand were also better than B's, but it costs her $1,000 if C's hand were worse than B's. So if B folds, A profits from betting if she has better than a 50/50 chance of beating C, given that B beats them both.

Thus the key to betting in either case hinges on A's confidence of beating C. That's counterintuitive, because the bet is only with B, C's hand seems to be irrelevant. But if A has better than an even chance to beat C, a bet is often to her advantage. She should not run a pure bluff, but she only has to be a little better than C to act as if she has the nuts.