In this episode I dive into poker math with hot and cold equity. I also take a little stroll down math memory lane with mathematical excerpts from prior episodes.
In episode 137 I concluded the Cbet MED when I discussed the shenanigans your opponents could attempt when you cbet: check-raises, cbet raises, floats and slow playing… oh, my.
Percentage Form (2:25)
Understanding the math behind percentage form and how to use it to assign and analyze ranges is key in all the hand analysis you do off and on the felt. You need to understand this stuff before we talk about combo counting then ultimately hot and cold equity. Here's a snippet from episode #66 called The HAND Reading Lab Part 2: HAND Reading and Percentage Form (starts at 13:38)
Combo Counting (5:10)
Percentage form and understanding the hands that make up various %’s are closely related to Combo Counting. Here’s a snippet from episode #68 called The Hand Reading Lab Part 3: Flopzilla and Hand Reading (starts at 9:49)
Combo counting is important for understanding just how many of a specific or group of hands your opponent might have. Some combo counting basics:
- Every pp has 6 combos
- There are 4 combos of all suited hands (like KJs)
- There are 12 combos of all non-suited hands (like KJo)
- And 4 combos of KJs and 12 combos of KJo means there’s a total of 16 combos for all non-paired hands
Combo Counting Example
You’re on the river, there are 4 to the straight on the board, and your opponent bet full pot. You need to be right 33% of the time vs his full psb. If your opponent has a King for the King high straight, then he’ll beat your lower end Q-high straight. How many Kings does he have here?
We think he could’ve started the hand pre-flop with KK, AK and KQs only. All other Kings would’ve folded pre-flop. So, there are 6 combos of KK, 16 combos of AK and only 4 combos of KQs. You don’t block any of these with your 98, so he has a total of 26 combos that beat you. You need to compare this to all the other combos of hands he could’ve reached the river with. If the 26 combos is more than 33% of his range, you shouldn’t call his river bet. 33% is the magic number because that's the break-even % for you calling a pot-sized bet here.
PokerNerve.com wrote an incredible poker combinatorics article that's worth checking out called “Poker Hand Combinations: The Critical Skill Required For Hand Reading”.
Before discussing hot and cold equity, we’ve got to talk about equity in general.
- Equity Definition – this is the % of the pot that belongs to you
- Example: If you have 50% equity, then you can expect to win half the pot
- You can also think of equity as how often you can expect to win the hand right now
- Example: Pre-flop, AA, which is a tight 6 combos, has 85% equity vs a range made up of entirely of broadway cards and TT+ (which is 153 combos). But, on a flop of KQJr, the Ace’s equity drops down to 55%. Now it can expect to win only 55% of the time. The Aces are still a favorite, but there are still two cards to come.
- This means that equities change with every card dealt.
Hot and Cold Equity (10:40)
- Hot and Cold Equity Definition – this is the equity of your hand or range right now, given no more action and you’re all-in. It’s the equity you consider when you’re short-stacked and somebody shoves and you have a decision whether or not to call all-in. Once you call, there’s no further action and you’re getting to SD no matter what.
- If you don’t know how to calculate equities, all you need is a little time spent playing with an equity calculator like Flopzilla or Equilab.
Hot and cold equity is great for tourney situations. “I have KQs, he’s shoving 13bb’s with a 20% range, so my hand has 52% equity vs him. I must call!”
The Problem with Using Hot and Cold Equity
The problem here is when we use hot and cold equity at the wrong time.
The First Problem
We’re in the BB w/J8o. Our aggressive opponent opens to 2.5bb’s w/ a 15% range. We have to call 1.5bb’s which means we only need 28% equity. There are full 100bb stacks behind us both, so we can expect lots of post-flop action. Our hot and cold equity vs this range is 35%, so, since we only need 28%, we decide to call.
- This is a bad call. Sure, you’ve got the requisite equity now, but how likely are you going to make money in this spot? You’re the pre-flop caller w/J8o, OOP and up against an aggressive opponent. You won’t necessarily like a Jack or an 8 on the flop, you might flop an oesd but now you’ll have to pay more to catch that, and you can’t even flop a flush draw. Your opponent prolly won’t let you see a free turn, so you’re calling now with a very weak hand and you can expect to fork even more money over post-flop. This is not a bread and butter situation.
The Second Problem
Same hand as the previous, J8o. Flop comes AT9r. Our opponent is a double-barreler by looking at his stats with a Flop Cbet at 70% and a Turn Cbet at 65%. We flopped an oesd for 16% h&c equity right now to hit our straight on the turn, and our opponent only bets only 40% pot. Looking at the equity of our call, calling a 40% psb means we need to have 22% equity to profitably call. We’re so close that we decide to make the call even though we’re not getting exactly the right price.
- Once again, this is a mistake. We’re playing passively and just hoping to hit. If we had check-raised at least we’d have some fold-equity on our side. We’re not getting the right price, and we can expect a double-barrel on this Ace high flop. We’re paying now and we can expect to pay even more on the turn. We’ve gone from bad to worse in this hand, again, not a bread and butter situation.
Because there’s more action expected, we can’t just base our decisions on hot and cold equity. We need to consider more than just this.
The 3 Advantages (14:50)
The two situations above are not bread and butter situations. Bread and butter means this is the best spot to be in, that we’re most likely to realize some profit in this hand.
So, what makes a bread and butter situation? It’s having the 3 Advantages in poker. Here's a snippet from episode #25 called “Plug Your Leaks #1: Playing Weak Hands OOP” (starts at 4:40)
If we had thought about the three advantages pre-flop before we called in the BB with our J8o, we would’ve realized the following:
- We do not have card advantage. Guaranteed, every card in the opener’s pre-flop range is 100% stronger than our J8o.
- We likely don’t have skill advantage. It’s possible we do, but he’s aggressive and it’s tough to out-aggress a double-barreling player post-flop. If we’re going to rely on this, then we need to realize that it might take our full 100bb stack to push him off at some point, and that risk shouldn’t be taken with J8o.
- We definitely don’t have positional advantage. That's too bad because being IP makes bluffing easy, pot controlling easier, and it’s easier to get value when we flop the miracle trips or miracle straight.
Pot Odds (19:10)
In that prior example of flopping the oesd, we needed 22% equity to make a profitable call. How is that calculated on the spot during a hand? I discuss just that in this snippet from Q&A episode #106 about Pot Odds (starts at 5:06)
You “drill the math in your head” off the felt during hand history review sessions. I recommend that you look at a series of 25 hands every day for a week. Your goal in these 25 hands is to practice your pot odds understanding. It doesn’t matter if you’re involved in the hand or not.
Here are some questions to ask yourself with each hand that will drill the numbers in:
- Nobody’s called yet, so what are the pot odds for limping?
- A player opened to 3bb’s, what are the pot odds for calling?
- I opened, he 3bet me to 9bb’s, what are the pot odds for calling his 3bet?
I recommend you write all these down to help you memorize these pot odds calculations.
In that prior J8o hand, we had 8 outs to the straight and I said that we’ve got a 16% chance of hitting on the turn. But how do we know this is the case? We follow the x2 rule. We can multiply our outs by 2 to estimate our chances of hitting one of those outs on the next street.
The math behind the x2 Rule with 8 outs:
- The deck contains 52 cards.
- We’ve seen our two cards and 3 cards on the board for a total of 5 cards.
- That leaves 47 cards in the deck. Of those, 8 cards make our hand.
- On the next street our odds of being dealt one of those 8 cards is 8/47, or 17%, which is very close to our estimated 16% using the x2 rule.
Once you know the rule, you don’t actually have to run this exact math because the x2 rule is always close enough to base your decision on. For some people, though, the tough part is counting their outs. It can take practice, and in episode #334 called “Poker Development Plan, Outs & Odds Practice, Overboard HUD Use | Q&A”, I gave you a simple way to do so.
Outs & Odds Practice (23:55)
We’ve covered practicing your odds understanding… we’ve covered practicing your outs understanding… now it's time to combine them. In this snippet from Q&A episode #130 called “Going Pro and Outs & Odds Practice” (starts at 5:26)
Here’s my challenge to you for this episode: Practice your math. As you run your 25 hand reviews this week, have a calculator and an equity program open and calculate the following things with every hand, every bet made and every card turned over:
- The pre-flop ranges in %-form for you and your opponent
- The number of combos in your ranges
- The pre-flop hot and cold equities
- The pot odds the current bet is offering the caller
- The number of outs on the flop and the odds of hitting
Your goal with these exercises is to up your poker math familiarity to improve your in-game decision making.
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- Poker Q&A: Tournament Statistics Analysis, Defense Frequency, Adjusting to Players and Going Pro - February 14, 2024
- The 8 Poker Lifestyle Habits LOSING You Money – and How to Turn Things Around - February 6, 2024
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