The honest truth is that poker bluffs are simple with a small amount of math. But in saying that, I also realize that many players are scared of poker math. It can look overwhelming at first, but with some basic knowledge it becomes very easy to do. And with a just little bit of extra practice, you can memorize a few things and correctly estimate the value of certain bluff plays at the table.
In this video my goal is to show you some simple poker math for bluffing, so you can understand how often your opponent needs to fold given your bluff size. We will even go a step further and give you some simple numbers to memorize so you can eye-ball things easier in real-time! Press play and let’s start putting some mathematical backing behind your bluffs…
Poker math can seem very complex, but with some basic knowledge and practice it can become very easy. And better yet, if you use this math correctly, you can find easy ways to improve your winrate and become a tougher opponent. In this guide I’ll show you how to figure out the breakeven percentage of certain plays…and of course, how that number will help you at the tables.
The Simple Bluff Formula
What exactly is a breakeven percentage? 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.”
Once we know the breakeven % necessary to run a bluff, we can use our hand reading skills to estimate if the bluff will actually work often enough to make it profitable.
The good news, if you are a math nerd like me, is that the formula is incredibly simple:
Even if you aren’t a math nerd, that’s a pretty easy formula to remember. In poker, we are constantly focusing on risk and reward, even if you’ve never visualized it like this before. Every bet you make risks money, and you are making those bets in order to win the reward…or rather, the money in the pot. Let’s look at an example to make this more tangible:
In this hand we raise from EP with 6♠ 6♥, the BB calls, and we see a HU flop of K♦ 9♠ 7♥. The BB checks and we bet for $4. Even though we have a pair in this hand, it’s doubtful to be ahead of the BB’s range if he calls or raises. So we can rightfully assume that our bet here is closer to a bluff than a pure value bet. It would be worth discussing the value of balancing our betting range in poker here if our opponent were a strong player, but let’s assume they are a less competent opponent for now.
If we pull out our fancy breakeven formula, we only need to fill in two numbers. The risk is our bet size of $4, since that is what we are risking in this spot. And the reward is the pot, or $6.5. So:
This means if villain will fold 38% of the time, this bet is breakeven. If he folds less than 38% of the time, the bet is outright -EV. If he folds more than 38% of the time, this bet is outright +EV.
We purposefully use the word “outright” since there are plenty of times in poker where a single bet may be outright +EV or -EV, but in the context of an entire play, it can swing the other way. For instance, a spot where a flop cbet is outright -EV because your opponent doesn’t fold enough given the breakeven %, but he’ll fold a ton on Turns and Rivers – thus making the overall play +EV.
You may be wondering how you can estimate if villain will actually fold more than the breakeven %. I personally use the tool Flopzilla to work that out, and you can watch out full-length video on the software if you are interested. With enough off table practice with a tool like this you can more correctly visualize how common ranges hit or miss common flop textures.
One last thing that I want to say here is that you should memorize some of these breakeven percentages. Whether you are playing 1 cent/2 cent online or $10/$20 live, the breakeven percentage math never changes. If you are betting half pot the breakeven % will always be the same, whether you are betting 15 cents into 30 cents, or $300 into $600. So here are the most common breakeven %s that you should memorize:
- 1/2 Pot = 33% Breakeven
- 2/3 Pot = 40% Breakeven
- Full-Pot = 50% Breakeven
Know these percentages like the back of your hand because these are common bet sizes we use postflop. If you decide to use a less standard size when bluffing, like 1/4th pot or an overbet, just pull out the formula and do a quick calculation. It should also be noted that your own equity will influence things. If you have a big draw you don’t require as many folds compared to a pure bluff since your draw can improve and win sometimes. But the 66 on K97 example from above has very few outs, and thus we’ll treat it closer to pure bluff to simplify things.
Bluff Raising Math
We can also use this concept on other streets and for other actions. Say in this 66 example that villain calls our cbet. The turn is a 4♥ and he bets into us for $12. For giggles, let’s say we are considering a bluff raise up to $32. We can still use the same breakeven % to figure out how often we need villain to fold in order for this bluff raise to be profitable.
By raising to $32 our risk is $32, and the reward is the pot size before we make our raise…or $26.5. So using the formula again we see:
Meaning that if we can expect him to fold more than 55% of the time we should bluff…if not…we should likely fold unless we really think our measly pair of sixes is ahead enough of the time.
If the only thing you take from this lesson is the breakeven % formula, you’ve won. If you also take the breakeven %s to memorize, then you’ve crushed. Understanding the breakeven % will help you put mathematical backing to all of your bluffs. Of course, figuring out if villain will actually fold enough is another skill set all together…but strengthening the math part of your game is never a bad thing.
Semi-Bluffing Poker Math
Once you have the breakeven % of a bluff understood, you can go a step further and prove the actual EV of your bluff. Things are simple when you have a pure bluff that has no chance of winning (like 98 on AT4-2-K) – but more often than not we have at least some glimmer of hope to improve and win the pot.
FWIW, you can certainly use a concept and calculator for implied odds when FACING bets with drawing hands. But when betting or raising yourself, utilizing a complex EV formula is powerful.
And let’s be honest, there are very few things in poker that are more fun than shoving. And if you are considering doing more 5bet bluff shoving preflop or semi-bluff jamming postflop, then understanding the math behind it is crucial. Push play and I’ll walk you through the formula and methodology for proofing semi-bluffs with poker math…
All of this work rests upon already knowing the basic EV formula.
To refresh your memory, that formula is:
So essentially what we stand to win multiplied by how often we’ll win…minus what we stand to lose multiplied by how often we’ll lose. But there are times when we need a more complex version of this.
Let’s look at an example to get us started…
In this hand it folds to the cutoff who opens, we semi-bluff 3bet to $10 with 8♥ 6♥, the cutoff 4bets to $23 and we decide to 5bet shove.
Like most plays in poker, we can proof this using some simple poker math, But you may notice that the basic EV equation from earlier does not account for ALL possible outcomes. Once we shove there are 3 things that can happen:
- He calls and we lose
- He calls and we win
- He folds and we win
So at this point, the basic EV formula needs to be expanded to account for each outcome. The expanded formula would then look like this:
Where “F” stands for “times villain folds” and “C” stands for “times villain calls”. And if you only know one of them, you can always figure out the other since their sum is always 100%. E.g., if you know F is 20%, then you take 100% – 20%, and get 80% for C.
Now we can just start plugging numbers in. Since most of these numbers are related (F+C=100% and %W+%L=100%), it makes life even easier. Let’s review how to get each number quickly:
%F/%C = These are estimations based upon how often you think villain will call your shove. If you think he was bluff 4betting a ton and thus wouldn’t be able to call your shove often…then F would be a very large percentage. Conversely, if you think villain were 4betting a strong range and would call your shove often, then F would be a small percentage and C would be quite large.
%W/%L = These are based upon equity, which we can calculate using a program like Equilab. The W% is your equity vs. the range villain would open, 4bet, & call your shove with
$Pot = the size of the pot BEFORE you shove
$W = what you would win the times you get called and win
$L = what you would lose the times you get called and villain wins
Now we just have to make some assumptions on his range and frequencies, plug in some numbers, and proof the validity of this shove. Let’s assume villain would call our shove with TT+/AK. In that case, our 8♥6♥ would have 27% equity…so %W is .27 and %L is .73
Let’s also assume that villain does bluff 4bet sometimes, so we assume he will 4bet/fold 25% of the time. This means F is 25% and C is 75%.
Now for the dollar amounts and we can solve! The pot before we shove is $34.50. If we shove and villain wins we lose $96. Because villain has the shortest stack we can only lose $83 plus the $13 to match his 4bet. Our $10 3bet no longer belongs to us, and thus we cannot lose it once we shove.
If we shove and villain calls we can win $117.5. Because we have the largest stack the shortcut is just current pot + villain’s stack. Now we have all of the necessary inputs!
We see that at this point our shove has a -$20.14 expected value. Given the parameters and assumptions we’ve used, this is a bad shove and we would do better by folding correctly. But since we are analyzing this hand away from the table, and have this extra time, let’s do some experimenting…
Assume for a moment that villain 4bet bluffs a LOT more often, and thus we can expect a fold from him 60% of the time. That changes F to 60% and C to 40%. Let’s also change his calling range from TT+/AK to TT+/AQ+. This increases our equity up to 30%, and thus changes both %W and %L. Now if we plug everything in we notice our EV jumps up to +$7.92.
All of a sudden our shove is looking pretty good!
With this formula, the money won and lost will remain constant, but changes in ranges and frequencies can alter the outcome a ton. Essentially, the more villain folds and we pick up the pot outright the better for us. The more equity we have when called the better since we’ll pick up the all-in pot more often and lose less often. And if we can ever increase both our equity when called AND the times villain folds preflop…the better and better our semi-bluff will be.
Knowing how and when to expand the basic EV formula can greatly benefit you on and off the table. Now in real-time you won’t be able to plug-n-play with the formula…but with enough off-table practice things will get ingrained and you will be able to more correctly estimate the math at the tables. And to be honest, there are times when you could expand the formula even further…but just knowing how to do this gives you a nice mathematical leg-up on your opponents!
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An Advanced Example
If everything you’ve just read and watched made sense, the next step is to begin analyzing poker hands and comparing lines. It’s not uncommon to find that multiple lines are profitable – so knowing how to compare them and choose appropriately is incredibly valuable.
Watch this extended video to see how to apply this kind of work to your off-table study. In this video, I compare the EV of semi-bluff shoving overcards and a gutshot to just calling a bet on the turn. The process is crucial for advancing your exploration between sessions.
If you want to follow along and use the same All-In EV spreadsheet I used in this video, you can download it (along with many others) right here (and yes, you can enter 0 and get them for free).
Same as always, if you have any questions please don’t hesitate to let me know…otherwise good luck and happy grinding!