c-betting (and other bluffs) and number of opponents

[LawDude]

At the tables I play at, both limit and no-limit, online and live, most players that I see either c-bet in situations where they probably shouldn't or don't c-bet in situations where they probably should. Given we just had a really great thread about c-betting that explored most of the issues (dryness of board, tendencies of opponents, fold equity), I wanted to simply focus on one mistake that I see tons of players making with their c-bets (and other bluffs) in looser games where lots of players see the flop with marginal hands even after a pre-flop raise.

And that is this: even in a game with weak, passive players who fold a lot, a c-bet is mathematically much less likely to be effective in a multi-way pot. In other words, I'd rather c-bet against a single player who will call a fair percentage of my c-bets than against 5 players who tend to fold to aggression.

That seems counter-intuitive. But let's do some simple math to show it.

Let's give ourselves AQs on the button. 6 players limp in behind us, we put in a sizable pre-flop raise, and 4 players call it. Now the flop comes J73 rainbow. Now, let's say that each of the 4 players is 85 percent likely to fold to a c-bet. It checks around to us, and we put in our c-bet. What's the chances of all 4 players folding to the c-bet?

Well, it's .85 to the 4th power. About 52 percent. And that's in position! (Out of position, we're much more worried that someone after us actually has a hand, so the likely percentage of c-bets that called is higher.)

In other words, we'd be much better off c-betting against one player who calls 35 percent of the c-bets that come his way than against 4 players who call only 15 percent! And yet I see players with AK, AQ, AJ, even KQ reliably c-betting in multi-way pots.

(Additionally, the more players in the pot, the greater likelihood that perhaps one of our reads may be wrong. In other words, if one of those players happens to be a strong player who is willing to check-raise a suspicious c-bet, look out! And the chances of that are 4 times higher when there are 4 other players in the pot.)

This same principle, by the way, applies to any bluffs. Bluffs work best heads-up, because there's only one person you have to fool.

[AFchung]

cliff notes:

cbets work ideally against 1 player. with reads or a dry flop 2 players can still warrant a cbet. refrain from cbetting into 3+ people without the goods