Poker Basics – The math of bluffing

New players think bluffing is the biggest part of the game and in particular they assume that all you need to be a profitable bluffer is to be braver than your opponent. The reality is that bluffing is probably not as important as value betting for your bottom line, but when you do want to bluff there is a mathematical strategy behind it.

The size of the pot and the size of your bet determine how often a bluff has to get through to be profitable. There is a simple formula you can follow when you make a bluff to determine the bluff’s breakeven percentage. That is how often it has to work to have a long term neutral outcome. If your opponent folds more often than the breakeven percentage, your bluff is profitable, if they do not, it is a losing bluff.

This is the simple formula:

Risk/(Risk+Reward) = Breakeven %

Let’s take a simple example. It is a \$1/\$2 game and you raise \$6 from the Cutoff preflop with 67, the Big Blind calls and the flop is AK9. You have completely missed but you think you can represent a big hand on this flop. The pot is now \$13 and you decide to bet \$7, how often does this bluff have to work to be breakeven?

We are risking \$7 to win a \$13 pot, using the formula above that would look like this:

\$7/(\$7+\$13) = 35%

You are risking \$7 to win \$13, a little over half pot, which means that you only have to get this bluff right 35% of the time to breakeven. Given your read that you can represent a big Ace or better, this seems like a really good bet. Of course, by betting small you make it more enticing for your opponent to call. So what about if you decide to bet big to make it look like you are value betting a monster? Let’s say you bet full pot, so you bet \$13 to win \$13.

\$13/(\$13+\$13) = 50%

Now you have to be right half the time to breakeven, so this is where it is important to have reads on your opponent. If they are a tight or weak player who folds a lot this might be a good bet, if they are a loose passive player it might be a losing bet.

That is the basic math of a bluff (we will cover semi bluffing later where you have a chance of making a very strong hand when called). Until then the table below is handy guide to how often you need to get your opponents to fold with common bet sizings. They are worth memorising but it is even more useful for you to play around with this formula before you start commiting the below to memory.

Bet size Breakeven %
25% Pot 20%
33% Pot 25%
Half Pot 33%
2/3rd Pot 40%
Pot 50%
x2 Pot 67%

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