Master Basic Poker Math Concepts and Start Making Better Decisions at Once

• Minimum Defense Frequency (MDF)
• Fold Equity
• Balanced River Betting Ranges
• Required Bluff Success Frequency
• Independent Chip Model (ICM) Math
• Risk Premium
• Managing Your Poker Finances

• Mastering Poker Math Introduction
• Preflop Sizes & Calculating a Pot-Sized Raise
• Counting Combinations
• Equity, Expected Value (EV), & Equity Realization (EQR)
• Pot Odds
• Stack to Pot Ratio (SPR)
• Facing a Preflop All-in

While poker may seem like a game of chance at first glance, everything that happens at a poker table can be explained by poker mathematics.

With that in mind, we have created a page to explain all the key poker math concepts, such as equity, expected value, pot odds, poker outs, and more. Keep on reading this page to master the basic concepts.

If you want to go even deeper and learn more, make sure to grab our free course that covers additional content.

Poker math can be used in almost every single scenario in the game. From the selection of starting hands to the bet sizing on the river, everything in poker is based on sheer math. At its heart, Texas Hold’em is a game of mathematics.

Even players who don’t actively use poker mathematics often end up applying its core ideas. Some of the key poker math concepts we will focus on in this article include:

• Pot Odds: Representing the ratio of the bet size and pot size, pot odds can be critical in deciding whether to call a bet or fold your cards in a given situation.
• Outs: Knowing how to count outs allows you to calculate your equity, which is essential in knowing whether or not you can profitably continue playing your hand.
• Expected Value: If you want to play poker right, you should not focus on the outcome but on the expectation. Expected value (EV) allows you to calculate the expected long-term results of your decisions.
• Counting Combinations: Counting poker combos makes it easier to break down your opponent’s range and figure out if they are likely to be bluffing or not.
• Fold Equity: Whenever you consider bluffing, understanding fold equity will allow you to make the right bets that will actually make your opponents fold their cards.
• Implied Odds: Whenever direct odds are not enough, implied odds might come in handy. Use this math concept to consider the equity of future bets.

On this page, you will learn all of the basics you need to know to make math-based decisions, so let’s dive deeper into these key concepts.

Pot odds are one of the most essential ideas in poker mathematics. They represent the ratio between the size of the bet you are facing and the pot size.

For example, if your opponent is betting $20 into a $40 pot, you can quickly deduct that you are getting pot odds of 3:1, as you need to call $20 to win the $60 that’s already in the pot.

In doing your pot odds calculations, make sure to remember to add the current bet to the overall pot size. This way, you will get the correct calculation and come up with the right ratio.

You can also quickly convert the ratio into a percentage. For example, the 3:1 odds you are getting in our previous example represent pot odds of 25%, which is the poker equity you need to profitably call the bet.

By calculating your pot odds, you can find out if you can profitably call a bet you are facing. Of course, to do this, you will also need to understand poker equity and know how to calculate it in relation to pot odds.

Here is a table that showcases the equity you need to make a call based on the bet size in relation to the pot, the main purpose of pot odds calculations:

Let us demonstrate how pot odds are calculated in-game. For this example, imagine playing a hand of $2/5 cash game in your local casino.

Holding 9s8s in the big blind, you face a raise to $15 from the cutoff. All players fold, and you make the call, going to the flop.

The flop brings Ks7s5c, giving you a flush draw and a gutshot straight draw. With $32 in the pot, you check, and your opponent proceeds to bet $16, a half-pot bet.

Here are the simple steps to take to calculate pot odds:

1. Calculate Pot Size: Pot size is $32 + $16 + $16 = $64
2. Divide the Bet by Pot Size: $16/$64 = 0.25
3. Multiply by 100: This gives you the number of 25%

The number 25% represents your pot odds in a percentage. This percentage is the equity you need to have in the pot to make calling the bet profitable.

In this case, you have more than enough equity with your flush and straight draws, but you will learn how to make those calculations in further chapters.

Here is our detailed guide for learning more about the pot odds in poker.

It is worth mentioning that the odds concept can also be utilized for figuring out how often you need to be successful with your bluffs to make it a profitable play.

You can determine this with a simple calculation of bet/(bet + pot).

For example, suppose you bet $400 into a $800 pot with a total bluff that will never improve. If your opponent will fold more than 400/(400 + 800) = 33% of the time, you immediately profit. Therefore should bet with all of your bluffs.

These numbers can be used in situations where you have no way to win the hand, so they are most accurate on the river since you will rarely have no chance of winning when called on the flop or the turn. In that case, you need fewer folds than the actual % suggests since you win the pot some of the time when you hit your hand.

Here are the numbers for the most popular bet sizes so you can always remember how often you need to succeed with your bluffs.

This concept closely relates to the fold equity you have in a specific hand, and here is our detailed guide for learning more about fold equity in poker.

Minimum defense frequency (MDF) is a GTO poker term that describes the percentage of your range that you should continue with depending on the bet you are facing.

Typically speaking, the bigger the bet, the less of your range you should be continuing with, and vice versa.

By adhering to MDF, you make yourself unexploitable by always continuing with a balanced range, thus denying your opponent the opportunity to exploit your tendencies.

MDF is a very important concept to use against strong players who would look to exploit your game if they notice you playing an unbalanced style of poker.

However, it is also important to remember that few players play balanced, which is why you may be able to get away with folding more than MDF dictates in many cases.

Here is a look at the percentage of your overall range you should be continuing with when facing different-sized bets in your games:

Note that MDF only tells you the percentage you should be continuing with and not the exact hands you should choose.

Once you know what percentage you want to continue with, your job is to consider your entire range and pick the best hands from it that have the highest equity and make the most sense to keep playing while folding the rest.

Here is our detailed guide for learning more about MDF in poker.

The concept of outs is one of the simplest pieces of poker mathematics. In order to figure out your outs, all you need to know is how to count.

An out in poker is simply any card that can improve your hand. For example, if you hold AdKd on a board of QdJd7h, you can improve your hand in several different ways.

The nine remaining diamonds in the deck would give you the best possible flush. Any of the other three tens in the deck would also give you the best possible straight.

In this case, you have 12 outs that we call “clean outs,” as they give you the best hand, guaranteed. Apart from them, you also have 6 “dirty outs” in the form of three aces and three kings.

While these cards don’t guarantee you have the best hand, they do improve your hand to the top pair, which can win depending on the situation.

Whenever you play a hand of poker and get to the flop, you should start counting the number of outs, or rather cards that can improve your hand.

Outs counting is used to quickly calculate your equity (your chance of winning) in a poker hand. Here is a table with a number of outs for the most common situations so you can instantly apply it in the game.

Whenever you reach a point in a hand where you can count your outs, you can also assess your equity with some confidence.

A simple rule known as the “rule of two and four” allows you to calculate your equity based on your outs in a matter of seconds.

To use the rule of two and four, you should first count your outs. In the example above, we estimated 12 clean outs, so let’s only use those for our example.

• When you find yourself facing a bet on the flop, you should multiply those outs by four to get a number that approximately determines your equity. In this case, the equity would be 48%, making it a virtual coin flip.
• On the turn, you can estimate your equity by multiplying the number of outs by two. In this case, the equity would be close to 24%.

While these percentages are not correct on the dot, they do come very close to the actual calculation and are much easier to do in-game.

The calculation can become a bit murkier when you factor in the dirty outs, as you have to assess what type of hand your opponent may be holding and whether those outs actually improve your hand or if they have the potential to get you into further trouble.

Here is our detailed guide for learning more about counting outs in poker.

There are many things in poker you can calculate on the spot. On the other hand, some things are best memorized so as to free up your mental capacity in-game.

Here is a look at a few basic poker tables you should learn to understand the basic probabilities of different outcomes.

You have probably heard of the concept of expected value (EV) in poker before, but what exactly does it represent?

In very simple terms, EV represents your theoretical gain in the hand of poker. When calculating EV, you should not care about the final result (which you cannot control) but rather the value of the play you are making.

Every play you make at the poker table has a certain EV, whether it is a positive or a negative one.

The trick to making money in poker and winning over the long run is to consistently make +EV plays and avoid making –EV ones whenever possible.

Whenever you wish to calculate the EV of a certain play, you can use this EV formula:

EV = (%W * $W) – (%L * $L)

In the formula:

• %W represents the percentage of the time you will win,
• $W represents the amount of money you stand to win,
• %L represents the percentage of the time you will lose,
• $L represents the amount of money you will lose.

To showcase the idea of expected value in the simplest of terms, let us use an example that you might encounter somewhat often.

Playing in a poker tournament with blinds at 500/1,000, you hold KdQd in the middle position. You raise to 2,200, and the big blind re-raises to 7,000, holding 12,000 chips behind.

You call the re-raise, and the flop brings JdTd7c. Your opponent goes all in for his remaining 12,000 chips into the pot of 15,500 (7,000 from each of you, 500 small blind, 1,000 ante).

Let us assume your opponent will always have a strong hand like AA or JJ here, in which case kings and queens won’t improve your hand (although they might some of the time).

The first step is to calculate your equity in the hand. With a total of 15 outs to a flush or a straight, you can calculate that you have about 60% equity in the hand.

So now, let us put the numbers into the formula and see how we do:

• EV = (%W * $W) – (%L * $L)
• EV = (60% * 27,500) – (40% * 12,000)
• EV = 16,200 – 4,800
• EV = 11,400

As you can see, this particular call has a very high expected value, as your equity is very high, and there is already so much money in the pot, making this a trivial call.

In other examples where the equities may not be as favorable or the bets are bigger in comparison to the pot, your EV calculations may not be as clear-cut as this one was.

Here is our detailed guide for learning more about EV in poker.

Poker equity is one of the most common examples of poker math you will see. If you have ever watched poker on TV, you have seen equity displayed next to players’ hands in the form of a percentage.

Poker equity represents the amount of the pot that belongs to a player based on their holdings in theoretical terms.

Of course, equity assumes the hand goes to showdown, and no one folds their hand, which means it is not an actual representation of who will win the hand.

However, if the hand does go to showdown, the equity will be correct. For example, pocket aces have about 82% equity against any other pocket pair, and if you were to run the hand 10,000 times from flop to river, aces would win about 8,200 times.

As explained earlier, you can easily calculate your equity by multiplying your outs by four and two on flop or river.

You can also do the opposite if you believe you have the best hand and your opponent is drawing, in this case, calculating the equity they might have with their different holdings.

The more advanced approach is to calculate equity against your opponent's entire range, where you can clearly evaluate the strength of your had in any particular situation to make the right decision.

For example, suppose you are sitting on the button with 25 BB in a tournament and face a shove from the SB after opening pocket nines. In that case, you need to know how much equity you have in a particular situation against your opponent’s range and compare it to the odds you are getting.

For this, you need to approximate his range, so let’s say he is showing here around 8% of hands with 99+, ATs+, KJs+, AJo+, and KQo.

Against that range, TT has around 49% equity, so this is a snap call. If you play around with different situations and ranges, you will quickly be able to identify your approximate equity and make math-based decisions instead of just guessing.

Poker combinations, also known as poker combos, are important when trying to pinpoint the exact hands in your opponent’s range.

Broadly speaking, each particular hand on the poker hands grid includes a certain number of possible poker combos.

For a shortcut, you can remember that there are:

• 6 combos of each pocket pair,
• 4 of each suited hand,
• 12 combos of each off-suit hand.

Your opponent’s ranges will start very wide, and counting combos won’t be that important preflop or on the flop.

However, as you reach the turn and river, the number of possible hand combinations in your opponent’s range will be significantly reduced, allowing you to count them and get an even clearer picture of how likely they are to be value betting or bluffing.

Let’s look at a real in-game example of counting poker combos. We will use a simple preflop situation for this example, but it will show you how you can count combos in any spot.

Playing in a $1/2 cash game, you look down at KK in the middle position. You raise it to $6, and the opponent on the dealer button re-raises to $22. You make another raise to $60, and your opponent moves all-in for $300.

At this point, you must consider your opponent and their tendencies. Assuming they are fairly tight, you can give them a range of QQ+ and AKs.

With this range, they would have the following poker combos in their range:

• 6 combos of AA
• 1 combo of KK
• 6 combos of QQ
• 2 combos of AKs

Against this particular opponent’s range, your KK is a favorite. You are an underdog against the AA and a favorite against QQ, and the two cancel each other out. However, you are also a favorite against the two combos of AKs, making you a favorite against the entire range.

If you assume your opponent can also have hands like JJ, AKo, or even A5s at some frequency, your hand becomes even stronger against such a range with way over 60% equity.

On the other hand, if you find yourself playing against an opponent who would only do this with AA or KK, you may be able to fold your KK. Likewise, if you held QQ against an equally tight opponent, the hand would become a fairly trivial fold.

Here is our detailed guide for learning more about poker combinations.

Implied odds represent the amount of money or chips you stand to win on future betting streets if your hand improves.

Whenever you find yourself facing a bet, your first move is to calculate your pot odds. If the pot odds are not high enough, you can proceed to think about implied odds.

In practice, it is impossible to calculate how much money exactly you will win on different turn and river cards.

This would require you to do a separate calculation for every possible card and know exactly how your opponent will respond to different bet sizes you may use.

However, you can calculate the minimum amount of money you need to win on future streets to make the call you are considering now profitable.

Implied odds come into play whenever you find yourself facing a flop or turn bet, and you don’t quite have enough equity to make a profitable call.

For example, imagine you are facing a half-pot bet on the flop, and all you have is a gutshot straight draw.

Your four outs give you about 16% equity to win the hand, while you should have about 25% equity to make the call profitable, as per our earlier pot odds and equity calculations.

However, if the bet is small enough and there is a lot of money behind it, the implied odds may be working in your favor.

If your opponent has a strong hand, they may pay you off big the times your hand does improve into a straight. In other cases, you can easily fold your hand, and you will not have a difficult decision to make.

Here is our detailed guide for learning more about implied odds.

Not only is poker math worth learning, but it is an essential tool to have in your arsenal if you want to take poker seriously.

A strong understanding of poker mathematics is the first step to becoming a successful poker player, although it is not the only skill needed.

Once you have mastered poker math, you will need to learn when and how to apply it, as well as when to deviate from it.

When facing highly exploitable players, you may be able to make plays that go against the poker math and still be very profitable, but you should not be going into a game with this assumption.

In fact, until you reach a very high level of poker skill, you should usually never deviate from poker math and should make the plays indicated by concepts like pot odds, equity, implied odds, and others explained on this page.

If you are new to poker, you should start by learning all about poker odds and outs, pot odds, implied odds, and equity. These terms will give you the basis to learn more advanced strategies. 

Poker equity is a concept that represents your theoretical share of the pot. For example, if you have AA against KK, you have about 82% equity in the hand, meaning your hand will win about 82% of the time. 

Pot odds represent the ratio between the bet size and the pot size and indicate if you can make a profitable call. Implied odds consider the future value of your hand and money you could win on future streets when you don’t have enough equity to make a profitable call. 

Counting poker outs is easy. Consider all the cards that improve your hand and count them. Over time, this will become second nature.

Poker combos are the different combinations of poker hands. For example, there are six combinations of every pocket pair such as AA (AsAh, AsAd, AsAc, AhAd, AhAc, AdAc).