How to Calculate Poker Odds: Mastering the Most Important Skill in Poker

What are the Odds in Poker?

Poker odds tell you how likely hands are to win in certain scenarios, but that’s just the tip of a much larger iceberg. In reality, odds are the foundation of poker, and moreover, they inform almost every decision you make.

I’ll get into the specifics throughout this guide. What I’ll say right now, however, is that poker odds govern how you choose starting hands, how you size your bets, how you make reads, and when you call, fold, or raise.

The reality is that poker odds are the framework within which all decisions should be made. That’s why they’re so important, and it’s the reason why you have to know how to calculate odds in poker.

Understanding Poker Odds

You can only make informed decisions if you understand poker odds. As I’ve said, odds are the foundation on which virtually all poker strategy decisions are based. Within this foundation are four pillars you need to understand:

How Do I Calculate Odds in Poker?

There are various ways to calculate odds in poker, depending on the information you need. I’ve already shown you have to calculate equity, but you’ll need to know hand odds to do that. Similarly, if you want to calculate implied odds, you need to know how to calculate hand odds and pot odds.

You can use a poker calculator for pre-flop hand odds, as we’ll explain in the next section. However, if you’re in the middle of a hand, you can use a shortcut known as the rule of 4 and 2.

The Rule of 4 and 2 for Quick Odds Calculation

The quickest way to calculate your equity is the rule of 4 and 2. As the name suggests, you need to multiply your outs (i.e. cards you can hit to complete a draw) by 4 and 2. Here’s an example to illustrate how the rule of 4 and 2 works in poker:

• You have K♦ J♦
• The flop is 4♦ 6♦ 10♠

You have a flush draw to diamonds at this point. Based on what you know (i.e. the cards you’ve got), we can assume that there are 9 diamonds left in the deck. Why? Because there are 13 cards per suit.

We can multiply this number by 4 on the flop to work out how often you’ll hit a flush, i.e. how much equity you currently have in the hand. So, in this situation, you have approximately a 36% chance of hitting a flush (9 x 4 = 36).

Let’s say you call a bet, and the 2♣ lands on the turn. The board is now 4♦ 6♦ 10♠ 2♣, which means you’ve only got one chance to hit your flush. At this point, you can multiply your outs by 2. This means you’ve got an 18% chance of hitting your flush on the river (9 x 2 = 18).

Pot Odds

Once you’re able to count your outs and calculate equity in a hand, pot odds are the next concept you need to grasp. As we’ve said, pot odds give you the minimum amount of equity required to make profitable calls.

For clarity, pot odds can be used to make pre-flop and post-flop decisions. Let’s start with the basic formula for calculating pot odds:

• Step 1: Calculate the pot size if you were to call the current bet, e.g. £10 in the pot + £5 = a pot size of £15.
• Step 2: Divide the amount you need to call by the size of the pot. Using the above scenario, you need to divide £5 by £15 = 0.33.
• Step 3: Multiply the result from Step 2 by 100 to get a percentage. So, in this scenario, you have pot odds of 33%, i.e. 0.33 x 100.

Once you’ve calculated the pot odds, you can look at your assumed equity in the hand to decide whether or not a call is profitable. Here’s how you’d do this pre-flop and post-flop:

Pre-Flop

• You hold A-K
• Based on your reads, you think your opponent’s range consists of A-A to 7-7, A-K to A-10, K-Q, K-J, Q-J, and 8-9, 9-10, J-10.
• You can plug this range into a poker calculator, such as Equilab, to see what equity A-K has against this range. Using the calculator, we can see that A-K has 60% equity against the opponent’s range.

Based on this, we can say that you need pot odds of at least 60% to profitably call.

Post-Flop

• You hold A-K
• Based on your reads, you think your opponent’s range consists of A-A to 7-7, A-K to A-10, K-Q, K-J, Q-J, and 8-9, 9-10, J-10.
• The board: A 7 8 J 10

We can input your hand, the opponent’s assumed range, and the board to calculate the equity in this scenario. As shown in the image below, A-K has 34% equity with a pair of aces against the opponent’s range. That means the opponent’s range has almost 66% equity.

Therefore, based on this, you’d need pot odds of at least 34% to call.

Poker Odds Calculator

As you can see from our breakdown of equity and pot odds, there are a lot of variables to consider when you’re running simulations (aka calculations) in poker. With this in mind, let’s talk about the different types of poker calculators you can use and how they work.

How Does a Poker Odds Calculator Work?

A poker calculator tells you the equity hands have against each other in specific scenarios. A basic poker calculator looks at pre-flop situations and the probability of each hand winning by showdown. It does this by running thousands of showdowns to give you a percentage value.

For example, let’s say you put A vs. 2-2 in an all-in showdown. Based on all the possible combinations of community cards, A-A wins a showdown approximately 81% of the time. The exact figure can vary depending on the exact cards.

For example, Ad As has an 82% chance of winning against Ad 2s because they share suits. Ad As has 81% equity against 2c 2h because they don’t share suits. This gives 2c 2h some extra outs to a flush.

You can also look at the equity of hands after the flop, the turn, and on the river. Then, if you want to get more advanced, you can use a poker calculator such as Equilab to compare ranges. That means you don’t have to know what specific hand an opponent has. Instead, you can give them a range of hands and see how that compares to your holding.

Using a Poker Calculator

Now you know how poker calculators work, here are the 5 steps on how to use one:

1. Decide whether you want to analyse a pre-flop or post-flop situation.
2. Enter your hand.
3. Enter your opponent’s hand or the range of hands you believe an opponent has.
4. Run the calculation to see what your equity is.
5. Think about how this equity will influence your decision. For example, if the pot odds don’t give you enough equity to call, there are two possible options: fold or raise. You can fold if the opponent is likely to call a raise. However, if the odds of getting a bluff through are high, go for the raise.

Issues With a Poker Calculator

Poker odds calculators are great but don’t rely on them to give you answers for every situation. Indeed, mathematics is an important part of poker, but it’s not the only part of the game. We’re not robots, which means we’re prone to mistakes, illogical decisions, and emotional swings. Therefore, you can’t always play the numbers.

Some of the issues with using a poker calculator are:

Operating Without a Poker Hand Calculator

Poker hand calculators should be an integral part of your arsenal, but, as we’ve said, you can’t rely on them completely. The best way to use calculators is as a study aid. Run through hands away from the table so you have an internal database of odds you can draw from when you need to.

Once you’ve done that, combine poker odds with reads on players, psychology, and tactics. For example, let’s say the pot odds are 25%, and your hand has 20% based on the range you’ve given an opponent. Poker maths, in this situation, states that you should fold. However, this doesn’t take into account psychology, table image, and game dynamics.

How to Think Holistically About Poker Hands

Let’s take the above scenario and add in some additional variables:

• You’re on the bubble of the $10,000 (around £8,000) WSOP Main Event
• Your opponent is a tight amateur
• People have only seen you showdown strong hands

I’ve already established that calling is mathematically incorrect because you don’t have enough equity. Based on this variable alone, folding is the correct play. However, when you factor in the other variables, raising might actually be better than folding.

Why? Because it’s a high-pressure situation against a player who is likely trying to make it into the money. This gives you a lot of fold equity which, potentially, could make raising as a bluff more profitable than folding.

Variables to Consider

This example is exactly why I’ve described poker odds as the foundation for decisions. It gives you a base to work from, but poker maths can’t give you the full answer. So, to conclude this section, here’s a checklist of variables to consider when you’re making decisions:

1. What is your equity?
2. What are the pot odds?
3. How big is your stack and your opponent’s stack?
4. What are the table dynamics?
5. Are there any reads that might affect how your opponent has played/how you should play?

Maths and Poker

By now, you should realise that maths and poker are inseparable concepts. You can’t be successful in poker without an understanding of odds, probabilities, and equity. With this in mind, let’s delve deeper into the mathematics of poker.

What Kind of Maths is Used in Poker?

Other than the concepts I’ve already explained, you need to understand the following mathematical principles in poker:

• Hand combinations
• Bet sizing
• Expected Value (EV)

How to Use Maths to Win at Poker

Here’s how to use maths in poker to analyse ranges, size your bets, and make profitable long-term decisions:

Combinations: Analysing an Opponent’s Hand Strength

I’ve talked a lot about making decisions based on an opponent’s range, but how do you decide which hands someone could have? Having a read on the player matters. If they don’t play many hands, you can assume their range is fairly small. Conversely, if they play a lot of hands, you can assume they have a wide range.

In addition to reads, you can use combinatorics to get a general overview of what players could have. Basically, you can think about what someone is likely to have based on the odds of being dealt certain types of hands pre-flop.

You can be dealt 1,326 possible hand combinations ranging from pocket aces to 3-2 offsuit. These combinations break down in the following ways:

• 16 combinations of every unpaired hand i.e. you can be dealt 3-2 in 16 different ways.
• 12 combinations of unpaired offsuit hands, i.e. you can be dealt 5-6 offsuit in 12 different ways.
• 4 combinations of suited hands, i.e. 5h 6h, 5c 6c, 5s 6s, 5d 6d.
• 6 possible combinations of each pocket pair, e.g. Ah As, Ah Ad, Ah Ac, Ad As, Ad Ac, Ac As

As you can see, you’re much more likely to be dealt a random hand such as 6-8 than a pocket pair. Therefore, you can take this into account when you’re assigning ranges.

Bet Sizing: Pot Odds, Implied Odds, and Fold Equity

Pot odds and implied odds aren’t just for calling. You can use them to decide how much you’re betting. For example, if you think someone is drawing to a flush, you can deny them correct pot odds by making a large bet.

Another variable to consider is fold equity. This variable looks at how often someone will fold to bet rather than call or raise. For example, if you believe someone will fold 40% of the time and there’s £100 in the pot, you have 40% fold equity. You can use this number to size your bets accordingly, i.e. if there’s a small chance someone is going to fold and you want to bluff, make a big bet.

What is the Most Important Maths in Poker?

The most important mathematical concept in poker is Expected Value (EV). It’s the most important because it’s the result of every decision you make. Therefore, it’s the product of all the mathematical moves you make during a game.

💡The definition of Expected Value (EV) in poker is: “the total return of your decisions over time.”

The aim of poker is to make more positive Expected Value (+EV) decisions than negative ones. The caveat here is that +EV decisions don’t always result in positive results. You can correctly call an opponent’s bluff on the flop and lose when they hit a one-outer on the river. You need to ignore results like this.

The only thing we can do as poker players is make as many +EV decisions as possible and ignore the money you win or lose in a single hand. Why? Because variance (aka luck) swings in both directions. However, over time, results converge around the EV. Put simply, luck evens out, and if you’ve made more +EV decisions than -EV decisions, you’ll be ahead.

Most Common Odds in Poker

Here’s a quick overview of the most common drawing hands in poker and the odds of hitting on the turn or river. As I’ve discussed, the pot odds should justify a call. For example, if you’ve got 32% equity on the flop, you need pot odds of 32% or greater to call.