Poker is a game of math. The math can range from simple things like figuring out the size of the pot to very complex things like calculating the EV of multi-street plays. But poker is also a social/psychological game where tells, psychology, and dynamics come into play. Players that approach the game solely through the social lens are just as much missing a crucial element as players that solely approach the game mathematically. Like most things, balance is required to be a well-rounded player who can thrive at any table.
While most math-based players understand the value in the social side of the game (albeit, usually not giving it the credence it deserves – myself included years ago), social-focused players tend to ignore much of math side of the game. This is normally due to the fear that the math will be too complex, too cumbersome, and maybe even too nerdy.
Remember, we need both the social skills and the math skills to become the best possible version of our poker playing selves. If you’ve put off the math-side of the game, for any reason, I want you to HEAVILY consider giving it another chance. If you can do basic addition and multiplication, you can handle poker math. If you sucked at math in high school, it does NOT mean that you will fail at poker math. I was terrible at math in high school and ended up taking stats twice in college – and even I manage the math behind this game.
You need both the math and psychological skills…
The true reason why the math is so important is because it gives us an objective answer to many poker questions. “What was the EV of our shove on the turn?” “Did I have enough equity to draw facing a half-pot bet?” “How often does my opponent need to fold here to make my bluff profitable?” Answers to these questions are mathematical, and while your spidey-sense may lead you to the correct answer sometimes, the math will lead you to the correct answer every time.
These are the 4 most important things that poker math can help you with:
EV (Expected Value)
The EV of your line lets you know if your play is expected to make you profit in the longrun, or lose you money. EV is the heartbeat of poker and ensuring your lines are profitable is your first goal, with your second goal being to take the optimal line at all times (the optimal line is the MOST profitable line). If you’ve never worked with EV before, start with the basic EV video and then watch the advanced poker EV video after for a comprehensive look at this concept.
EV = (%W * $W) – (%L * $L)
If this is the first time you’ve worked with EV, this may seem a bit complex. But overall you just want to make sure you win enough money the times you win the pot to offset how much you lose the times you don’t win the pot. Remember, your hands are going to lose some percentage of the time and it’s impossible to win every hand you play (heck, even if you only ever played AA you’d still lose sometimes!) – so focus on maximizing value with your winning hands and minimizing loss with your losing hands.
Every bet you make has a breakeven percentage which tells you how often your opponent needs to fold in order for your bluff to make profit. This percentage can also be used when exploring GTO lines and building a proper ratio of value to bluff hands in your betting range – but that’s another topic for another day.
BE% = Risk / (Risk + Reward)
Say the pot is $40 and you are going to bet $30 into it. Your bet size is the risk and the reward is the $40 pot you are fighting for. So the BE% is 30/(30+40) is 43%. If you were bluffing and you expected your opponent would fold more than 43% of the time, you are making a profitable bet. Easy enough, right?
You can actually memorize some of these (and should). If you are betting into a pot, these are the most common BE%
- ½ pot = 33% BE
- ⅔ pot = 40% BE
- Full pot = 50% BE
- 2x pot = 67% BE
When raising and re-raising things get a tad trickier since your opponent’s bet size influences the ‘reward’ drastically – but with this powerful formula you can always quickly calculate the BE% in a few seconds at the table. And remember, you can round and be close enough to be profitable in real-time.
When bluffing, it’s vital to know how often you can expect your opponent to fold. If they fold more often than the BE%, you have a profitable bluff. But how do you know how often a player will actually fold to your bluff?
This is where software comes into play. Now in real-time you won’t have the time to use this software (and most places won’t even allow you to legally use tools like this during hands) – but getting an innate feel for this stuff through time and practice pays off in a big way. My tool of choice is Flopzilla and if you’ve never heard of it before you can learn how to use Flopzilla with my free video.
Take a situation where you 3bet preflop with A♦ 4♦ and your opponent calls. The flop is K♠ 8♠ 3♦ and you are trying to figure out if you should bluff. Without understanding this situation mathematically you are left to random guessing or hoping to find some hint of a tell – but with math we can have a more clear idea.
Say you think villain would call your 3bet with a range of 77-QQ (you think he would 4bet KK+), AQ, AJ, KQ, KJs. And you think if you bet he’s only going to continue with top pair+ and flush draws.
Then you can expect folds 72% of the time. And since we already know the BE% of our bet (you did remember the ones from above…right?), we can simply choose the size that works best and go from there. Always ask yourself if villain is likely going to fold the same % regardless of the size you choose. If the answer is ‘yes’ just bet as small as you can get away with.
A frequency is the likelihood that something happens. In poker there are frequencies pertaining to how often the turn is an overcard, how often villain raises preflop, how often multiple players will fold if you steal, and everything in between. At the end of the day, poker is a game of frequencies and improvements in our strategic frequencies while having an understanding of other frequencies is how you generate a huge edge.
You may be wondering how the heck do you estimate frequencies and, even if you could, how would you put them to use? Well you can use the information from above (EV, BE%, and fold%) to deduce the best lines to take. As for estimating frequencies…that takes a lot of practice and a good amount of awareness at the table. You will miss frequencies if you play while distracted, but you’ll catch a ton of them if your eyes are glued to the table.
These are some of the frequencies I’m always looking for:
- How often a player plays a hand from vaious positions preflop
- How often a player 3bets preflop
- How often a player continuation bets on the flop
- How often a player double/triple barrels postflop
- How often a player checks top pair postflop
- How often a player slowplays vs fastplays
- How often a player bluffs on turns/rivers
By paying attention to these frequencies in a player’s strategy I am able to get a well-rounded view on how they play and how I can profitably react to them. If a player has a low (or even non-existent) bluffing frequency on the river – I know that I shouldn’t call them down with second-pair. If a player 3bets a ton preflop, I won’t consider folding JJ vs their 3bet. And if they slowplay made flushes I shouldn’t discount flushes on the river after they check the turn.
Everyone has frequencies in their game. You do, I do, and anyone who has ever played a hand of poker does too. Our goal is to find their frequencies and exploit the shortcomings in their strategy – while making sure our frequencies don’t make us even easier to exploit. A combination of awareness and the ability to use basic poker math to exploit their leaks makes you a tough opponent in most games.
Since this is such an important piece of being a strong poker player, I created this free poker webinar for you. In it I teach you 5 frequency exploits you can start using in your next session. You’ll learn how to put all of these skills together to spot leaks and apply pressure with ease. And since catching big hands is such a rare thing, this will guide you through bluffing more often and ore profitably. A win/win!
To sign up for this webinar, go here and enjoy. And remember, poker math isn’t complicated. With some practice and a clear gameplan, you’ll be on your way towards playing more profitably. Just spend a little time with it, sign up for the webinar, and you’re on your way!
This post was shared on the Alec Torelli’s Best of Poker Series