One of the first questions an outsider to the poker world tends to ask me when I tell them what I do is: “So is it all maths and odds and stuff?”
The answer to this question is of course an overwhelming no, and thank god it’s a no. I’m not a massive fan of mathematics. I’ve always preferred language and words to sums and equations. That said, one of the biggest mistakes my students make when they come to me for coaching is that they’ve made absolutely no effort to study any poker maths at all, ever.
This is a problem for the following reason: while there is a massive breadth of mathematics in poker ranging from the mind-numbingly simple to the mind-bogglingly complex; it’s the simple stuff that takes a few minutes to learn and a few hours to practice and develop true competency with. it’s also this same simple stuff that’s utterly essential and will make you a good several big blinds per hour just for nailing it down in the early stages of your poker learning.
This isn’t the fault of my students. Poker maths is the kind of thing you either embrace with thirst or shy away from completely and noone has helped to bridge this divide. The culprit, I think, is that most math orientated poker players and instructors have an all or nothing kind of approach to the maths of the game. In their GTO based “let’s actually delve so deep into poker math that we leave the consequentially bound world behind and drift into some other plane of abstract existence” math seres, they fail to broadcast one very crucial point that simply must be understood before you have any hope of getting anywhere in online poker.
There are many mathematical things you really don’t need to know at all at this stage of your poker career, but there are two mathematical tricks you absolutely do need to know.
Please now take a few minutes to read what these are below and then spend a few hours over the next week or so practising them over and over when you review hand histories until they’re automatic.
Trick 1 – Action Closing Decisions – How to Calculate Required Equity out of Game
We never have the luxury of being able to perform our off the table calculations in game, there’s just no time. However, the more you do this off the tables the better the feel you’ll have on them, and as we’ll see with the second trick, there’s always a shortcut for when that time bank is flashing in your face.
An action closing decision is one where there can be no more decisions to be made that hand after hero has made his choice regardless of what that choice is. Common examples include: facing river bets where we’re either going to call or fold; facing all in raises or bets post-flop, and someone shoving for their whole stack vs us pre-flop. The following calculation makes the assumption that all equity we have will be realised and that the pot will remain what it is after we call. Therefore, it can never be used in instances where there can be future action of any kind.
So time for an example. We’re on the river and the pot is 45bb. Villain has shoved his remaining 36bb into the pot having bet the flop and turn. There are two buttons lit up on our screen: [call 36bb] and [fold]. These two numbers alone are all we need to calculate how much equity we need vs villain’s range to call here. The second part will be working out if we have this amount of equity and that’s a whole different story, but for now let’s see how the maths works.
There are only three values here that matter and they are:
(A) Amount to call – this amount is simply the number that villain has bet or our full stack depending which is largest and is the amount that pops up on our call button like above. We’ll call this amount AC.
(B) Total pot after bet – this is the sum of what was in the pot before villain bet and his bet. It’s the new pot including money from previous streets and the river bet. We’ll call this TP
© Required Equity is the amount of the time we need to have the best hand in order for calling to be as good as folding. If we have any more equity than this then it becomes better (or +EV) We’ll call this RE. It’s what we need to know in order to determine what to do.
The sum: RE = AC / (AC + TP)
And there we have it. A simple sum using nothing but good old fashioned division and addition. As always in math, we perform sums in the brackets first followed by multiplication and division and only then may we add and subtract.
Let’s go back to our example.
AC = 36 (the bet we’re facing)
TP = 45 + 36 = 81 (be careful here we need the total pot AFTER villain bets not before)
So RE = 36 / (36 + 81) = 30.8%
We need to be good at least 30.8% of the time in order to call. This is the very first thing you do when you assess this spot out of game. Now you have this number, you can estimate if your equity is sufficient or whether your cards should hit the muck.
WARNING: People often make a mistake with this calculation. They sometimes take total pot to be what’s in there before villain bet and simply add villains bet to it to get the number on the right hand side of the /. This is wrong. You need to add villain’s bet to the pot as it was and then add on AC again to get this side of the sum. I like my students, but I will hit a point where I start killing them for this error. It’s only a matter of time…
Trick 2 – Action Closing Decisions. How to Estimate Required Equity In Game
There is no time amidst the heat of battle for TPs, Acs or REs. There is barely enough time to remember your own name while also making a decision as to how to decrease your chances of losing lots of money. This is why we always need shortcuts; ways of simplifying poker maths into a format digestible by the frantic rushed mind. This method involves something I’m going to call the waypoint scale of RE.
Here are your 4 mantras. You shall repeat and memorise these mantras until they are so deeply ingrained in your unconscious competence that you say them in your sleep to the cat perched on the end of your bed.
1. If the pot before villain bet was empty then I need 50% equity to call
2. I need 33% equity to call a pot sized bet.
3. I need 25% equity to call a half pot sized bet.
4. I need 17% equity to call a quarter pot sized bet.
Memorise those, seriously!
So these mantras are the waypoints on our scale of required equity. Some villain’s make it nice and easy for us by mashing the pot button like bet-sizing zombies. Others bet more random amounts that we need to stick in roughly the right place of the scale. The waypoints allow us to do this.
EG. If villain bets 7 into a pot of 30, we know that’s just less than a quarter (4×7=28) so we need just less than 17% equity to call by mantra 4.
If we do the first calculation one more time for good measure, we see that..
RE = AC / (AC + TP)
RE = 7/ (37 + 7) Again it’s not (30 + 7) because TP means after he’s bet.
RE = 15.9%
Like I said, just less than our way point of 17%.
How painless was that mathaphobes?
So there we have it. By reading this you’ve just learned 100% of the poker math that it’s essential to learn in the early stags of your poker career. Next time you analyse a hand where you’re faced with one of those pesky action closing decisions, you’ll know what to do. Both in game and out of game. Now go apply it!