This article was written by blackrain79.com contributor Fran Ferlan
A lot of beginner poker players struggle with the math concepts that are the
core part of the game of poker.
While some aspects of the game can be quite advanced, most of the basic math concepts are
actually really simple, and being familiar with them is the key for your poker
success.
One such concept is the pot odds.
This article will cover everything you need
to know about pot odds, as well as other poker math concepts, cover why they are important, and outline how you can use them to
make better decisions on the felt.
Your Poker Odds Cheat Sheet: Understanding Basic Poker Math
Let’s start with why some mathematical concepts like pot odds shouldn’t be
overlooked, and why it’s important to understand them.
Poker is a skill game pretending to be a luck game.
It’s essentially a big,
complex math problem, and it comes down to odds and probabilities. A lot of
players don’t pay much attention to the math part, though, claiming to be more
of a “feel” player.
That’s not really the best approach to take, however.
Granted, intuition is an important part of a winning poker strategy, but it’s mostly a
consequence of a sound theoretical knowledge that precedes it.
Just because you rely on your gut feelings, doesn’t mean you should disregard
the analytical part of the equation. One does not exclude the other, they
actually complement each other.
Still, a lot of players don’t feel like crunching numbers on the felt for one
reason or another. But doing so is a huge disservice to the quality of your
decision making.
What’s more, the basic poker math is fairly simple, and you don’t need a math
degree to understand it and apply it successfully. In fact, it’s no more
complicated than what you learn in grade school.
With that in mind, let’s get into the topic, starting with a basic definition.
1. What Are Pot Odds?
Pot odds are a ratio between the current size of the pot and the price of your
call. Put simply, it is the reward-to-risk ratio, and it’s what poker is all
about.
Minimizing the risk while maximizing the reward.
The first, bigger number in the ratio is always the pot size (i.e. the reward)
and the number 1 is always the call amount (i.e. the risk).
This makes sense,
because the reward is always bigger than the risk. That’s because when the
villain makes a bet, a raise, or a reraise, that amount becomes a part of the
pot.
Calculating pot odds is very simple, so you should get into the habit of
figuring out the pot odds in every spot you play.
All you have to do is divide the pot size with the amount of money you need to put in to continue playing.
All you have to do is divide the pot size with the amount of money you need to put in to continue playing.
Let’s use an example.
Suppose there is a $100 pot on the flop, and the villain
bets $50. The reward is $150, and the risk is $50. We divide the two numbers
and get a 3:1 ratio, so the pot odds are 3:1.
So the pot odds formula looks like this:
Pot odds = Reward / Risk
Or
Pot odds = Pot Size / Price of a call
The bigger the pot odds, the better the risk/reward ratio, and the more often
you can continue playing profitably.
If the pot odds are bigger than the odds of you winning the hand, your play
has a positive expected value (+EV), and if the pot odds are smaller than the
odds of you winning the hand, your play has a negative expected value (-EV).
For example, if you are getting 5:1 odds on a call, and you have a nut flush
draw on the flop, calling is +EV because the odds of improving to a flush by
the river are 1.86:1. (more on some common odds below).
However, just because a call is a +EV play, doesn’t mean it’s the most +EV
play. Raising could be more +EV, but other considerations need to be taken
into account.
The point is that pot odds tell you if your play is profitable “in a vacuum,"
or is it profitable RIGHT NOW, without other considerations.
It’s exact and
precise, unlike other poker concepts that require a bit of guesswork. And it is important that you understand this concept in order to beat small stakes poker games in particular.
Memorize These Basic Pot Odds
It might be worthwhile memorizing the pot odds for some common bet sizes, so
you don’t have to calculate them manually every single time:
¼ pot bet: 5:1
⅓ pot bet: 4:1
½ pot bet: 3:1
¾ pot bet: 2.5:1
Pot sized bet: 2:1
Most bet sizes will be somewhere between a half-pot bet and the full-pot bet,
so you will usually get between 3:1 and 2:1 pot odds.
You’d do well if you at
least memorize those two.
2. Why You Need to Know the Pot Odds
You can turn the pot odds ratio into a percentage, and then compare that
percentage to your hand equity in order to figure out the profitability of
every play.
This is something that will help you tremendously at the poker table, especially if achieving the best poker winrate (big blinds won per 100 hands), is your goal.
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Now, I prefer to turn the pot odds into a percentage because it gives me a better idea of the EV of my play, because I can easily compare it to how often I expect to win a hand.
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Now, I prefer to turn the pot odds into a percentage because it gives me a better idea of the EV of my play, because I can easily compare it to how often I expect to win a hand.
The way to turn the pot odds into a percentage is to divide the risk by the
risk and reward, then multiply it by a hundred.
The formula looks like this:
Risk / Risk + Reward * 100
In the previous example, turning 3:1 pot odds into a percentage would look
like this:
Risk = 1
Reward = 3
When you plug the numbers in, you get:
1 / 1 + 3 * 100 = ¼ * 100 = 0.25 * 100 = 25%
You can compare the percentage with your hand equity to figure out if you can
continue playing profitably. Hand equity shows you how often you expect to win
the hand.
In the previous example, if your hand equity is bigger than 25%, you can
continue profitably, and if it is smaller than 25% you cannot continue
profitably.
Poker Odds Example Hand
So that was kind of a mouthful, so let’s try to break it down with a simple example hand.
Suppose you (Hero) are holding A♥9♥ and the flop is J♥6♥2♣
The pot is $100 and your opponent bets $50.
You are getting 3:1 on a call, or
25%. This means you need at least 25% hand equity (i.e. you need to win at
least 25% of the time) for your call to be profitable.
You have 9 outs to a nut flush, and your chances of improving to a flush by
the river are about 35%.
For the sake of example, let’s assume that your opponent (Villain) doesn’t have any sets in his range and can’t improve to a full house, and if
you improve to a flush, you will have the best hand.
You have more than enough equity to continue profitably. This is something that Daniel Negreanu actually discusses in his recent Masterclass poker training as well.
Hero calls.
Now let’s assume the villain shoves $200 into a $100 pot on the flop, and see
how it changes the pot odds and our EV.
Now you’re getting about 1.5:1 odds on a call, meaning you need more equity
to continue profitably. If we turn these odds into percentages, we get about 40% (1/1+1.5 * 100).
Since the chances of improving to a flush are 35%, and we need 40% equity to
continue, in this case our call has a slightly negative expected value.
Hero folds.
This is just an example, of course. In real time it’s quite difficult to
accurately assess your opponent’s range, and even a slight change in your
assumptions can change the required hand equity dramatically.
This is something that is discussed in much more detail in Modern Small Stakes.
Still, it’s important to at least be aware of some common situations and use
them as a rule of thumb to figure out the most +EV play.
In order to do that, you might want to memorize how often hands are expected
to improve, and how much hand equity you need to continue profitably.
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3. How to Calculate Your Hand Equity (Rule of Fours)
A quick hack for this is the so-called rule of fours, where you multiply the
number of outs you have by four.
This will tell you how often you can expect your hand to improve from flop to
river.
If you want to calculate the chance of improving on a single next street (like
from turn to river), just multiply your outs by two instead.
In the previous flush draw example, you have 9 clean outs, you multiply it by
4, and you can expect to improve about 36% of the time from flop to river.
In
reality it’s 35%, so it’s pretty close. This means the rule of fours is
accurate enough for most in-game situations.
Memorize These Poker Odds
Here are some percentages you should have memorized:
Chances of improvement from flop to river:
- FLUSH DRAW TO FLUSH: 35%
- OPEN-ENDED STRAIGHT DRAW TO STRAIGHT: 32%
- INSIDE STRAIGHT DRAW TO STRAIGHT: 17%
- TWO PAIR TO FULL HOUSE: 17%
If you prefer the pot odds, this equates to:
- FLUSH DRAW TO FLUSH: 1.86:1
- OPEN-ENDED STRAIGHT DRAW TO STRAIGHT: 2.13:1
- INSIDE STRAIGHT DRAW TO STRAIGHT: 4.88:1
- TWO PAIR TO FULL HOUSE: 4.88:1
Another quick hack to quickly turn odds into percentages: add up the numerator
and the denominator, then divide 100 with it to get a percentage.
(Quick reminder: in fractions, the upper number is the numerator, and the
lower number is the denominator).
For example, if you are getting 4:1 odds, just divide 100 with 4+1 to get 20.
So if you’re getting 4:1 odds, you need 20% hand equity for your call to be
(outright) profitable.
If you have an open-ended straight draw or a flush draw, you can theoretically
continue profitably even without the additional implied odds, because the
chances of improving are about 35% and 32%, respectively.
If you have an inside straight draw, your call is not outright profitable,
because you can expect to hit your draw only about 17% of the time.
For an even deeper dive into all the basic poker math, check out my free poker cheat sheet.
Common Pot Odds Table
Here’s a table with common pot odds and the corresponding hand equity
required:
1:1 = 50%
2:1 = 33%
3:1 = 25%
4:1 = 20%
5:1 = 17%
6:1 = 14%
7:1 = 12.5%
8:1 = 10%
Again, since you will most often get pot odds ranging from 3:1 to 2:1, you
should at least remember you will need to win the hand at least 25% or 33% of
the time respectively in order for your call to be profitable.
4. How to Use Pot Odds to Make Your Opponent's Life Difficult
We’ve discussed the importance of pot odds for making better in-game
decisions.
But as with any concept, true understanding doesn’t come from just
being familiar with something, but applying it effectively.
So when you get comfortable with calculating pot odds during your session,
think one step further and try to figure out how you can use them to force
your opponents to make mistakes.
Denying pot odds is in fact an art that many strong poker pros have mastered these days.
In other words, you need to think not only about the pot odds you’re getting, but also about the pot odds you’re giving.
In other words, you need to think not only about the pot odds you’re getting, but also about the pot odds you’re giving.
This comes down to exploitative bet sizing, and it’s a topic in and of itself, discussed in huge detail in Crushing the Microstakes.
Nathan famously goes deep into exploitative over-betting strategies in this book, intended to deny pot odds to your opponent.
But within the context of "normal" bet sizing strategies, denying pot odds means figuring out how to best size
your bets according to your opponent's individual tendencies.
For example, if you are up against a recreational player who loves chasing
draws, why not charge them a premium for their drawing hands?
This way you can effectively deny them the correct mathematical odds to call, which over the long run, will lead to a large profit source for you.
Because the one thing you can't do in poker is fight the math and expect to win!
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How to Manipulate the Pot Odds To Create an "Irresistible Offer"
Lastly, if you have stone cold nuts, you might want to consider giving your opponent a better price to lure them in and give them an opportunity to catch up on consecutive streets.
You can think of this like creating an "irresistible offer" that they just can't say no to!
For example, as Nathan also discusses in his latest book, you might want to "downbet" considerably to 30% pot in river situations when value betting versus good players in particular.
Because this will often entice them to hero call you with middle pair or worse, whereas if you bet a big amount, they will just throw their hand away.
These are some of the basic tricks that you can use in small stakes games in particular, to both deny and manipulate the pot odds in your favour.
Large Success in Poker Requires More Than Math!
Now with all of that said, poker is a lot more than just math.
While it is good to know the basic poker odds and math discussed in this article, real success in poker requires a lot more.
Simply put, if you want to to get world class results in this game, then you need to approach it like a world class professional.
If you are curious to know more, in my latest video, I discussed the top 7 poker lessons that I learned throughout my 10+ year career as a professional poker player.
And specifically, how to approach this game like a professional does. I think that if you study a few of the tips in this video, it will help you tremendously at the poker tables.
Bottom line though, poker math and odds is just one piece of the puzzle to getting the results you deserve at the poker table.
It is important that you are always improving your poker game in all areas. Make no mistake, this is how the best poker players in the world continue to stay on top.
Summary
Poker math and odds can be daunting, but the fundamental poker math concepts are no
more complicated than what you learned in grade school.
And therefore, you don't need to spend years studying advanced poker strategy in order to understand it.
Understanding the math behind your plays will help you make more sound
decisions and will make you much less likely to make costly mistakes,
especially when under a lot of pressure.
Conversely, you’ll be the one to apply that pressure to your opponents and
make decent money while doing it.
The best place to start is mastering the pot odds. It is the most basic poker
math concept any decent player should be familiar with.
In a nutshell, pot odds are the ratio between the pot size and the size of the
contemplated call. It’s basically a reward-to-risk ratio, and that’s what
poker is all about.
To calculate the pot odds, simply divide the pot size by the price of the
call. The better the odds, the more often you can continue playing profitably,
and the worse odds, the more selective you should be with your continuing
range.
Since most bet sizes fall somewhere between a half pot and a full pot, pot
odds will be somewhere between 3:1 and 2:1 respectively.
If you remember only one thing from this article, remember that a half-pot bet
equals 3:1, and a pot-sized bet equals 2:1.
You can use the pot odds to calculate the expected value (EV) of your plays.
You can do so by turning the pot odds into a percentage and comparing it to
your hand equity (i.e. how often you expect to win the hand.
A quick hack to turn the pot odds into a percentage is simply adding the
numerator and the denominator, and dividing 100 with the result.
You can’t actually ever know your exact hand equity in-game, so it’s useful to
memorize how often certain draws are expected to complete as a guiding point.
When you get the hang of it, start considering not also what odds you are
getting, but also what odds you are giving with your bet sizes. Adapt them to
your opponent’s individual tendencies for maximum profitability.
One bonus tip: If you’re ever feeling stumped in the middle of the hand,
consider the pot odds and work from there.
This is especially useful in situations where you are forced to make a big
decision. It will make the analytical part of your brain take the wheel, and
you’ll be far less likely to make costly mistakes.
When in doubt, consider the math first.
Lastly, if you want to know the complete strategy to crush your poker games,
make sure you grab a copy of the
free BlackRain79 poker cheat sheet.
