Semi-Bluff Shove Poker Math

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. In this video I explain when and how to expand the math to make sure you are solving the spot correctly. If you’d rather read the script of this video, read on below. Otherwise, turn the video to 720p and enjoy easy-to-digest complicated poker math!

(Save time and download my free EV spreadsheet to make these calculations MUCH quicker!)

Hello, and welcome to today’s Quick Plays video on advanced EV in poker. We’ve done another video on basic EV, but there are many situations in poker when a basic EV formula just doesn’t quite cut it. So in this video ill show you a more complex EV formula and how to use it with an example.

The basic EV formula we worked with in the past was EV = (%W*$W)-(%L*$L). So essentially what we stand the win multiplied by how often we’ll win…minus what we stand to lose multiplied by how often we’ll lose. If this seems confusing at all, please first watch the basic EV poker video and then come back to this one.

But there are times when we need a more complex version of this formula. So 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 we can proof this using some simple poker math, so let’s pull out our EV equation.

You may notice that this basic formula doesn’t account for all possible outcomes. Once we shove there are 3 things that can happen:

1. He calls and we lose
2. He calls and we win
3. 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:

EV = F($Pot) + C(%W*$W) – C(%L*$L)

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%. 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 we 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, so that’s easy. 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 should avoid making it. 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 the 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!

Same as always, if you have any questions please don’t hesitate to let me know…otherwise…good luck and happy grinding!