Help / Breakeven Percentage For Bluffing The Turn

What is the purpose of this tool?

When looking at how often a bluff needs to work to be profitable, most people use risk / (risk + reward) as a starting point. Here's how that formula works for a 1/2 pot bluff. You are risking 1 to win 2, so 1 / (1 + 2) = 1/3 = 33.3%. Therefore, a half pot bluff needs to work more than 33.3% of the time to be immediately profitable.

Many people end their analysis there. They shouldn't. That math assumes a few things that often aren't true:

1. You don't have any outs.
2. There aren't any cards that can come on the river that will give you a +EV bluff.
3. Checking has an EV of 0.

This tool helps you account for those things in order to figure out how often a turn bluff really needs to work for it to be profitable.

How do I interpret the table?

The first row of the table shows the breakeven percentages for various turn bluff sizes - 1/3 pot, 1/2 pot, 2/3 pot, etc. - including the one that you selected in the "Basics" section.

The second row shows the dropoff amount from what the immediately profitable breakeven percentage is. For example, the immediately profitable breakeven percentage for a 2/3 pot bluff is 40%, so if the true breakeven percentage is 28%, the dropoff amount is 12%. This is useful to know because you can think to yourself things like, "I can decrease my breakeven percentage by about 10-15% when I have a flush draw."

How do I interpret the graph?

The horizontal axis is how often your opponent folds. The vertical axis is EV. The teal line shows the EV of bluffing, and the black line shows the EV of checking. So when the teal line is above the black line, bluffing is the better option, and the point where they intersect gives you the breakeven percentage.

Why are we comparing it to the EV of checking instead of to zero?

Because as poker players, we don't just want to make +EV decisions, we want to make the most +EV decisions. (This of course doesn't only apply to poker. It applies to life too!) If bluffing has an EV of +$10 but checking has an EV of +$20, checking is the better choice and we should pass up the opportunity to bluff.

How do I know how many outs I have? I could make top pair on the river, but I'm not sure if I'd be ahead with top pair.

In poker, we talk about how clean an out is. If you have the nut flush draw and make your flush, those outs are pretty clean, because you're almost certain that you're ahead. But for something like an out to top pair, you're right that you often aren't sure if you're ahead when you hit it.

To deal with this uncertainty, use a fraction. Eg. if you have six outs to top pair, maybe count each out as 3/4, and say that you have 6 * (3/4) = 4.5 outs instead of 6. That's sort of "back of the napkin-y", but it's fine for our purposes.

How do I know what percentage of the pot I'll win when I hit an out? Sometimes I'll bet half pot, sometimes full. And the chances of me getting paid off depend on what the river card is.

The answer to these questions is very similar to the answer to the question above about how many outs you have. Ultimately, you have to use your judgement and come up with some sort of average.

For example, let's suppose that you're always betting full pot on the river when you hit an out, and on half the river cards you're 75% sure you'll get called, and on the other half you're 25% sure you'll get called. In that case, you'll win (0.5)(0.75)(PSB) + (0.5)(0.25)(PSB) = (1/2)PSB = half of a pot sized bet = 50% of the pot. If you're going to bet different amounts on different cards, the math gets a bit more complicated, but the approach is the same.

This is so inexact.

There's a trade off between accuracy and effort. By adding more and more variables, you would get a more accurate number, but it takes more time and is harder to wrap your head around.

I believe that the compromise I have now is appropriate for most players, for most situations. Knowing that the true breakeven percentage is 31.5% instead of 33% is rarely a big deal. Perhaps I'll add the option to include more variables in the future though.

How do you calculate EV?

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