## Poker Odds

Poker is a very math-heavy game, and one of the aspects of poker math that’s important to learn is poker odds. Not only does knowing your odds prevent you from making bad decisions, but it can also be the difference between winning and losing.

Calculating and understanding your odds when playing poker will let you know whether you are in a good or a bad position. Knowing your odds allows you to make informed decisions and hopefully secure a win. This guide breaks down what they are and how to use poker odds to improve your game.

## What are Poker Odds?

The term “poker odds” covers several aspects of poker math. One aspect is understanding the number of “outs” your hand has, particularly when drawing, and how you can determine the likelihood of the cards you need being dealt.

For example, you have two diamonds in your hand and two diamonds on the flop. Your odds here for making a flush are around 2 to 1, which means you can expect to hit a flush approximately every three hands. This information can help you make your move and potentially give you an advantage over other players.

We’ll also look at an aspect of poker odds called “pot odds,” which helps you decide whether or not a call is profitable. Pot odds are used in conjunction with other poker math like equity and hand odds, which lead us to more advanced topics such as hand ranges.

### Poker Probability

The first thing we’ll look at is poker probability, specifically the probability of any given card appearing on the flop, turn, or river.
A deck contains 52 cards, and we are dealt two cards preflop, meaning there are 50 unknown cards that could appear on the flop. Therefore, the odds of a specific card appearing in the flop is 1/50, or 2%. When we look at the probability of a card appearing on the turn, there are three more known cards (the flop), so our new odds are 1/47, or 2.12%. Similarly, if we want to work out the odds of a card appearing on the river, there are four known cards, so our odds are 1/46, or 2.17%
For most purposes, assigning each card a 2% chance of appearing on any street is an easy way to help do the math in your head.

## How to Calculate Poker Outs

Another key set of odds you’ll want to learn to calculate to be successful in poker is your ‘out’ odds. Outs are any cards in the deck that can help improve your hand. For example, if you have two hearts in your hand, and there are two hearts on the flop, then you have nine outs. There are 13 hearts in the deck, four are visible, so there are potentially nine left to be dealt.

In the table below, you will find some common draw scenarios that show the number of outs you have and the specific cards you will need to hit your draw.

### Important ‘Outs’ Terms

You have [A K]. Flop shows [T 2 5]. You need both a [J] and [Q] for a straight.

Overcard Draw: When you have a card above the flop.
You have [A 3]. Flop shows [K 5 2]. You need an [A] overcard to make top pair. 3 total outs.

Inside Straight Draw (aka ‘Gutshot’): When you have one way to complete a straight.
You have [J T]. Flop shows [A K 5]. You need a [Q] to complete your straight. 4 total outs.

Open Straight Draw: When you have two ways to complete a straight.
You have [5 6]. Flop shows [7 8 A]. You need a [4] or [9] to complete your straight. 8 total outs.

Flush Draw: Having two cards to a suit with two suits already on the flop.
You have [A K]. Flop shows [7 8 J]. You need any heart to make a flush. 9 total outs.

### Poker Outs Scenarios

So, now that we can determine the probability of any card coming on the flop, turn, or river, how can we use that information? Well, knowing this math is particularly useful when working out your likelihood of making a draw. For example, suppose you have a hand like a flush draw or a straight draw. In that case, you can work out how many cards will give you the best hand and calculate the odds of any of those cards appearing.

#### Scenario 1

For example, you’re on the turn with a flush draw facing a bet from your opponent. You’re considering calling, but you want to know how likely you’ll make your hand before you do. So, let’s look at the probability you’ll make your hand.

There are thirteen cards of each suit a deck of cards, and if you have a flush draw, you likely have two of those in your hand, with two on the flop. That means four cards of that suit have been accounted for, leaving nine in the deck. You know that the probability of an individual card appearing on the river is around 2%, and nine cards will give you the best hand. Therefore, multiplying the 2% chance by nine gives you the probability of you making your hand = 18%.

#### Scenario 2

But what if you’re on the flop with two cards to come? How does the math change? In this example, you have an open-ended straight draw on the flop, facing an all-in from your opponent. Your opponent’s stack isn’t huge, so you’re considering gambling, but first, you want to know how likely you are to win.

As your opponent is all in, you’re guaranteed to see both the turn and the river, so we can calculate the likelihood of each card appearing on both streets. You have an open-ended straight draw, so you have eight outs to improve. You can multiply those eight outs by the 2% probability to know that you have around a 16% chance of hitting your card on the turn. We also know that the same equation works for the river, so both the turn and the river have a 16% chance of being the card you need.

As the dealing of the turn and river are individual events, we can add the probability of these streets together, so 16% + 16% gives us a 32% chance that you’ll make your hand by the river.

### Calculating Poker Odds and Hand Odds

To calculate your hand odds, you first need to know how many outs your hand has. An out is defined as a card in the deck that helps you make your hand. If you hold [A K] and there are two spades on the flop, there are 9 more spades in the deck (since there are 13 cards of each suit). This means you have 9 outs to complete your flush – but not necessarily the best hand! Usually, you want your outs to count toward a nut (best hand) draw, but this is not always possible.

The quick amongst you might be wondering “But what if someone else is holding a spade, doesn’t that decrease my number of outs?”. The answer is yes (and no!). If you know for sure that someone else is holding a spade, then you will have to count that against your total number of outs.

However, in most situations you do not know what your opponents hold, so you can only calculate odds with the knowledge that is available to you. That knowledge is your pocket cards and the cards on the table. So, in essence, you are doing the calculations as if you were the only person at the table – in that case, there are 9 spades left in the deck.

When calculating outs, it’s also crucial not to overcount your odds. An example would be a flush draw in addition to an open straight draw.

Example: You hold [J T] and the board shows [8 Q K]. A Nine or Ace gives you a straight (8 outs), while any diamond gives you the flush (9 outs). However, there is an [A] and a [9], so you don’t want to count these twice toward your straight draw and flush draw. The true number of outs is actually 15 (8 outs + 9 outs – 2 outs) instead of 17 (8 outs + 9 outs).

In addition, sometimes an out for you isn’t really a true out. For example, let’s say you’re chasing an open-ended straight draw with two of one suit on the table. In this situation, you would typically have eight total outs to hit your straight, but two of those outs will result in three-to-a-suit on the table. This makes a possible flush for your opponents. As a result, you only have six outs for a nut straight draw. Another more complex situation follows:

Example: You hold [J 8]o (off-suit, or not of the same suit) and the flop comes [9 T J] rainbow (all of different suits). To make a straight, you need a [Q] or [7] to drop, giving you four outs each or a total of eight outs. But, you have to look at what will happen if a [Q] drops, because the board will then show [9 T J Q]. This means that anyone holding a [K] will have made a King-high straight, while you hold the second-best Queen-high straight.

So, the only card that can really help you is the [7], which gives you four outs, or the equivalent of a gut-shot draw. While it’s true that someone might not be holding the [K] (especially in a short or heads-up game), in a big game, it’s a very scary position to be in.

### Poker Odds Chart

 Outs One Card % Two Card % One Card Odds Two Card Odds Draw Type 1 2% 4% 46 23 Backdoor Straight or Flush (Requires two cards) 2 4% 8% 22 12 Pocket Pair to Set 3 7% 13% 14 7 One Overcard 4 9% 17% 10 5 Inside Straight / Two Pair to Full House 5 11% 20% 8 4 One Pair to Two Pair or Set 6 13% 24% 6.7 3.2 No Pair to Pair / Two Overcards 7 15% 28% 5.6 2.6 Set to Full House or Quads 8 17% 32% 4.7 2.2 Open Straight 9 19% 35% 4.1 1.9 Flush 10 22% 38% 3.6 1.6 Inside Straight & Two Overcards 11 24% 42% 3.2 1.4 Open Straight & One Overcard 12 26% 45% 2.8 1.2 Flush & Inside Straight / Flush & One Overcard 13 28% 48% 2.5 1.1 14 30% 51% 2.3 0.95 15 33% 54% 2.1 0.85 Flush & Open Straight / Flush & Two Overcards 16 34% 57% 1.9 0.75 17 37% 60% 1.7 0.66

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## What are Pot Odds?

### Examples of Correct and Incorrect Pot Odds

#### Profitable Pot Odds

In our first example, we’re on the flop with 43 and a board of 2♣5♠9♦. Our opponent bets \$20 into a \$30 pot. Do we have the right odds to call? Let’s take a look.

First, we need to figure out our pot odds. We’re calling \$20 into a \$30 pot, so let’s see how that looks in our equation:

Pot odds = (\$20 / (\$20 + \$50)) x 100

Pot odds = (\$20 / 70) x 100

Pot odds = 0.285 x 100 = 28.5%

So we know we need to win at least 28.5% of the time to break even with our call. Now we need to figure out the likelihood of making our hand by the turn. We have eight outs with our open-ended straight draw, meaning we’ll make our hand on the turn 16% of the time, making it an unprofitable call. However, if we think our opponent won’t bet the turn very often, we could have a profitable call, as we’re 32% to make our hand by the river.

In spots like these, you need to make a judgment call about what your opponent is likely to do on future streets. Consider your opponent’s playing/betting style, likely hand strength, and stack size.

#### Unprofitable Pot Odds

In our next example, you’re playing a \$1/\$2 cash game and facing a \$100 bet into a \$200 pot on the river, and you have a flush draw. The first thing you need to do is calculate what the pot size would be if you were to call. In this case, it would be \$300 + \$100 (the pot size includes your opponent’s bet), making a total pot of \$400. Next, divide the amount of your call by the total pot size. In this case, it would be \$100 / \$400, which gives you 0.25. Finally, multiply this number by 100 to get your percentage, which in this case will be 25%. Let’s see how our equation looks when we’ve put some numbers in it:

Pot odds = (\$100 / (\$100 + \$300)) x 100

Pot odds = (100 / 400) x 100

Pot odds = 0.25 x 100 = 25%

In our scenario, you need to win more than 25% of the time to make a profit. However, we worked out earlier that a flush draw has an 18% chance of hitting on the river, so this would not be a profitable call.

## How to Use Pot Odds

Once you’ve calculated your pot odds, you should be left with a percentage. This percentage is your breakeven point. You need to win the hand more often than this percentage to make money; if you don’t, you’ll lose money. Of course, this is just the first step; you need to combine pot odds with other aspects of poker strategy to decide whether or not your call is profitable.
Some hands are easy to figure out. For example, if you have a drawing hand, you know your odds of winning, so you can compare those to the pot odds to see if you have a profitable call. Similarly, if you have a very strong hand, you know your chances of winning are extremely high; therefore, you have the odds to call.
However, things get trickier when you have a marginal hand, such as second pair. In these situations, you need to analyze your opponent’s likely range of hands, work out how much equity you have against that range, and compare that to the pot odds you’re getting. This complicated process is more art than science, as you’ll never know exactly what hands will be in your opponent’s range!

## Equity

A term you’ll hear a lot when talking about poker odds and expected value is “equity.” Let’s take a closer look at what that is.

### What is Equity?

Equity is the percentage of the pot that is “yours” based on the likelihood of you winning the hand. The term is often used interchangeably with the likelihood of winning, so if someone says they have 20% equity in the pot, it means they have a 20% chance of winning the hand.

There are three possible ways of calculating equity: hand vs hand, hand vs range, and range vs range. Working out equity for one hand against another is easy, but we often don’t have the luxury of knowing what our opponent has, so we need to look at equity in terms of hand vs range.

To do this, we compare our hand to all the hands in our opponent’s range to calculate our total equity. Followers of poker legend Phil Galfond may be familiar with this concept, as it’s the basis for his “GBucks” theory.

This theory advances the concept of Sklansky dollars and applies it to a range vs hand scenario. It’s quite complicated, so I’ll do my best to cut it down to bullet points.

• Take the equity of your hand against each part of your opponent’s range.
• Multiply your equity by the number of hand combos in each part of your opponent’s range.
• Add up the total of the results from each section.
• Divide by the number of total hand combos in your opponent’s range.

This will give you the average amount of equity your hand has against your opponent’s range.

Given how complicated this is at the table and the fact that most casinos won’t provide you with a pen and paper or wait the half an hour it would take to work it out, most people don’t use this at the tables. Instead, they use a rough version where you try to work out equity against different parts of their opponent’s range and average them together. But, of course, even that takes time if you’re not used to it!

### How to calculate your equity

While we can use pot odds to work out whether or not a call will be profitable, we can’t use it to put an exact number on how profitable or unprofitable it will be. If we want to do this, we need to calculate the expected value of a decision (EV), which is the average result of our play if we were to repeat it hundreds or thousands of times.

This is the equation for working out your expected value:

EV = (Win % * \$ Won) – (Lose % * \$ Lost)

Simply put, if the EV is a positive number, you’re making a profitable play, and if it’s a negative number, you’re making a losing play.

For example, we have a flush draw on the turn, and our opponent has bet \$10 into a \$50 pot. The pot odds calculation says we need 16.66% equity to call, and we know from the poker outs calculation that we will make our flush 18% of the time, but exactly how profitable is our play?

EV = (18% * \$60) – (82% * \$10)

EV = (\$10.80) – (\$8.20) = \$2.60

We can see that the expected value of our \$10 call on the turn is \$2.60, and we confirm that our call is profitable.

## The Four and Two Rule

The “Four and Two” rule, sometimes referred to as the 2/4 rule, is one of the most reliable and easy methods of working out the odds of hitting your desired draw on the turn and river. First, after the dealer has drawn the flop, calculate the number of outs left in the deck. Then, once you have done this, multiply the number of outs by four to get the percentage chances of you being dealt a winning card on the turn or river.
For example, if there are 8 outs, then the percentage of you drawing one is 8×4 – 32%. After the turn, you can multiply the number of outs by two to give you your percentage odds. So if there are still 8 outs, your odds are 16%.
Now that you have the percentage odds, you can work out the ratio odds. This is done by dividing the 100 by the percentage and subtracting 1. For example, 100/32 = around 3, so -1, and you have odds of 2/1.