Hello everyone. I'm studying fundamentals and confused about about semi-bluff math. I know its all depends of the opponent and fold equity but I have a question about simple poker math.

Do you calculate pot odds or bluff breakeven% when you make semi bluffs (non-all-in)? Which is the right one?

For example bluff breakeven%, we need to win the hand 25% of the time when we bet 33% of the pot. And as a pot odds example, we need to win 20% of the time when we call 33% of the pot. Can we think like we can bet (instead of check-call as aggressor or making float bet on the flop etc) 33% of the pot and need to win 20% of the time? Like we're not facing bets but we're betting with amount of what pot odds says, instead of bluff breakeven%. If its like that, isn't it better to calculate it like pot odds instead of bluff breakeven%? Cause its not pure bluff and we have some equity.

Please define the term bluff breakeven%.

You probably need to think in EV terms. Your EV if you do not bet is simply the pot size multiplied by your card equity. If you do bet it is the pot size before you bet multiplied by your fold equity plus the pot size when called multiplied by your card equity. If the EV of betting is at least higher by the bet amount then betting is correct.

To make this more concrete, suppose you have a flush draw IP on the turn and your opponent checks to you. To make simple math, pot has $60 and your opponent will fold 1/3 of the time if you bet $30. If you check your EV is $11.74 (9/46 x $60 - I am assuming that you win if you hit your flush and lose otherwise). If you bet 30, your EV is 1/3 x 60 + 9/46 x 120 = $43.48. Betting $30 increases your EV $31.74 so it is a good strategy.

In general such calculations are likely going to be too complex to do at the table, but generally the more hand equity you have, the less fold equity you need to profit from your non-river bluffs.

Thank you for that detailed amazing reply!

But I didn't understand why do you say 9/46 for flush draw. There is our two hole cards and 3 cards on the flop, so there is 47 unseen cards but you wrote 46. Is that wroten by mistake or am I missing something about calculations?

Thanks again!

This is the mathematical way of saying “if X play works this amount it’s breakeven, or 0EV. If it works less then it is -EV and if it works more then it’s +EV.”

For example:

If you bet 1/2 Pot = You need to be success 33% of the time to be breakeven
If you bet 2/3 Pot = 40% You need to be success 40% of the time to be breakeven
If you bet Full-Pot = 50% You need to be success 50% of the time to be breakeven

In my example I was talking about a decision to bet a flush draw on the turn (mainly to make the situation simpler to analyze). At that point you know 6 cards, your hole cards plus the 4 cards on the board, so 46 is the appropriate denominator.

The example was on the turn.

Oh sorry you're right!

Thanks again!

EV can get tricky depending on how deep you want to get into the analysis. Typically you are never drawing dead in poker so even though you may think/know you are on a bluff there could be as much as 11-13% where you will win 'anyway'. That will help your return rate of the bluff a little bit.

You also have to 'create' a fold rate for your opponent based on the bet size. You would typically think that the larger the bet the less often an opponent may call. If you double your bet AND your opponent's call rate goes down more than 50%, then that's a better bet over the long haul.

The opposite may be true as well. Being where an all-in may get a higher call rate than a more reasonable 'value' bet sizing.

So it's not all math, but math may help you better understand when a bluff just shouldn't be tried based on your opponent profile. GL

"Typically you are never" - Half the time it's 100% accurate.