Posted Jun 20, 2021
Owner and Lead Pro
Professional Cash game trainer Bart Hanson has been producing strategy content for over fifteen years. He first started on Live at the Bike! back in 2005, then moved on to host "Cash Plays" on Poker Road, then "Deuce Plays" on Deuces Cracked and then to CrushLivePoker in 2012.
In his career as a professional poker player, Bart Hanson has:
-6 WSOP Final Tables
-Over 15 years of experience at the table
-Over $1,000,000 in tournament earnings
-Multiple appearances on ESPN and Poker Night in America
-4th place finish in 2019 WSOP Monster Stack
Poker math is almost never fun for most players, but it can be extremely helpful in close situations where the default play isn’t obvious. Being able to calculate simple odds and equity in game will give you a massive edge over your opponents. @CrushLivePoker
Poker math is almost never fun for most players, but it can be extremely helpful in close situations where the default play isn’t obvious. Being able to calculate simple odds and equity in game will give you a massive edge over your opponents. In today’s article we’ll break down a simple math equation that will tell you roughly how much equity you have against your opponent’s range, and we’ll look at some practical ways to simplify calculation in game.
First let’s look at a hand example, then we’ll break down the math:
Hero has K ♠ Q ♠ in the Small Blind, is the preflop raiser, and is heads up versus the Big Blind.
The flop is Q ♥ 6 ♥ 6 ♦ ($85).
Hero bets $25, Villain jams all in for $150.
Should our Hero make the call?
There are a few steps we’ll have to take to break down this situation. First, we have to assign a range of hands for Villain before we can calculate our hand’s equity against it and compare it to the pot odds offered.
Given the preflop action in this hand we can basically assume that Villain can’t have AA, KK or AQ, because he probably would have 3-bet with them preflop. If you think that Villain can make this play with a worse hand like QJ this becomes a pretty obvious call, but in this example let's assume that Villain either has a hand that beats us or a bluff. This leaves us with basically two possibilities, either Villain has a 6 for trips or he has a flush draw.
Obviously it’s going to be near impossible to figure out exactly how often our exact Villain can be bluffing or value betting. In order to have any hope of calculating this problem in real time you’ll have to make some broad assumptions. Let’s say for the sake of simplicity that Villain can have 10 combos of trips and 10 combos of flush draws here. Now that we have made our approximation, we have to figure out our equity versus both Villain’s trips combos and his flush draws.
Now that we’ve decided Villain can have 10 combos of trip sixes and 10 combos of flush draws, we need to find our hand’s equity versus each of these possibilities. Let’s start with the value combos.
Our hand is K ♠ Q ♠ which gives us two pair, kings and sixes on a board of Q ♥ 6 ♥ 6 ♦ . If Villain has trip sixes we basically have just two outs to improve, since a queen on the turn or river would give us the better full house. We can quickly calculate our approximate equity by multiplying our outs by 2 for each street, then adding them together.
(Outs) x (2) x (Streets remaining) = Approx. Equity
(2) x (2) x (2) = ~8%
We could still hit running kings of course, so we’ll throw in an extra 2% or so to make things simple. This gives us approximately 10% equity against Villain’s trips.
Now for the combos of bluffs, let’s say that Villain has the nut flush draw. We can use the same simple formula that we just used to calculate how much equity his flush draw + overcard has. There are 9 remaining flush cards that will give him a flush, and three remaining aces that will give him a better two pair. This means there are 12 total outs for Villain. Let’s do the same simple calculation.
(Outs) x (2) x (Streets remaining) = Approx. Equity
(12) x (2) x (2) = ~48%
We can probably assume that Villain won’t always have the nut flush draw, so let's subtract a couple percent for the times that he doesn’t have an additional 3 outs to an ace. If we say Villain has around 45%, that means we have around 55% equity when Villain has a flush draw. To make our math a bit more simple, let's just round up and say we have 60% equity against Villain’s bluffs.
The rest is pretty simple. We average our equity against value and bluffs first, then we convert it to pot odds. If Villain has 10 combos of value and 10 combos of bluffs, that means that half the time we have 10% equity and half the time we have 60%. This averages out to about 35% equity against Villain’s range. Now that we have our equity, we just have to calculate the pot odds to see if we’re being offered the right price to call.
Going back to the hand history at the beginning, we can see that we’re being offered a price of $125 to win a total pot of $385 ($260 pot + Hero’s $125 call). To calculate your pot odds, simply divide the size of the call by the size of the pot, then multiply by 100.
(Size of Call) / (Total Pot) x 100 = Equity required to call
($125) / ($385) x 100 = 32%
We have 35% equity and we only need 32%, so… Should our Hero make the call?
Summary and Final Thoughts:
Being able to make these calculations quickly in game will take some time and practice. Hopefully this break down helped you to simplify and organize your process so that you’ll be ready the next time you’re facing a big all in. Remember that you should first assign your opponent a range then find your equity versus his value and bluffs, before comparing it to the pot odds being offered.
It’s important to remember that you can make your decision a lot quicker and easier if you know that your opponent can be value betting with worse. In this example we didn’t allow our opponent to have any value combos that we beat, but if you think they could have a hand like QJ or JT and shove, our decision becomes extremely easy and we can snap call. If we are still priced in when we’re beat by all of his value, we are obviously crushing him if he is value betting worse.
If you enjoyed this breakdown and would like to listen to Bart go over this process with a Crush Live Poker caller you can check out the video on the Crush Live Poker YouTube Channel by clicking on the link here.
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