Bluffing more than one Opponent

The odds against a bluff succeeding increase significantly as you add additional opponents to the equation. The more opponents, the more someone is likely to call to keep you from winning a sizeable pot by bluffing. “I had to call to keep you honest” is a frequent heard expression at any poker table.

Supposed you were facing a single opponent and thought that your bluff would succeed one-third of the time. Those aren’t bad odds, particularly when the money in the pot exceeds the odds against a successful bluff. Suppose the pot obtains $90 and the price of a bet is $30. If this situation were to repeat itself and your estimate of successfully bluffing was accurate, you would bet $30 twice and lose, but you’d win $90 the third time. In the long run, this is an opportunity with a positive expected value.

But what happens if you add a third player to the mix? Once again, you figure that your chances of successfully bluffing the additional player are one chance in three. The presence of a third player will, of course, increase the size of the pot. Let’s assume that the pot now contains $135.

Although the size of the pot has increased arithmetically, the chances against your bluff succeeding can be argued to have grown geometrically. While the size of the pot increased, it usually does not increase to a point where it offsets the very long odds against successfully bluffing through two opponents. Bluffs work best against a small number of opponents. The fewer the better. Three is almost always too many, and even running a bluff through two players is both daunting and difficult.

There is one exception, however. Assume that there are no more cards to come. If you are first to act and are facing two opponents, you can bluff if you think that the last player to act was on a draw and missed her hand. Suppose you are playing Hold’em and there are two suited cards on the flop. If Phyllis, the third opponent, simply calls on the flop and the turn, chances are she may have had a flush draw that never materialized. If that’s the case, she is very likely to release her hand against a bet on the river, even if she suspects that you’re bluffing. When all is said and done, she might not even be able to beat a bluff.

But Stan, the player in the middle, has a lot to worry about. If you bet, not only does he have to worry about whether you have a real hand, he also needs to concern himself with the player to his left. Even if the player in the middle has a marginal hand -the kind he’d call you with if the two of you were headsup – he might release it.

After all, Stan has two concerns: Your hand might be stronger than his, and the third player might also have a better hand. When your opponent in the middle is a good player – good enough to release a marginal hand rather than stubbornly call ” . . . to keep you honest” -you might use the implied threat of the third adversary to force the man in the middle to shed his holding.