Poker odds are a fundamental concept that every poker player needs to understand to elevate their game and become successful. Knowing the odds of hitting certain hands, making draws, and calculating pot odds can help players make better decisions and improve their chances of winning.

Learning the Odds

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.

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 Your 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.

Draw Hand Flop Specific Outs
Pocket Pair to Set 4♠4❤️ 6♣7♦️T♠ 4♦️4♣
One Overcard A♠4❤️ 6❤️2♦️J♣ A♦️A❤️A♣
Inside Straight 6♣7♦️ 5♠9❤️A♦️ 8♣8♦️8❤️8♠
Two Pair to Full House A♦️J❤️ 5♠A♠J♦️ A❤️A♣J♠J♣
One Pair to Two Pair or Set J♣Q♦️ J♦️3♣4♠ J❤️J♠Q♠Q♦️Q♣
No Pair to Pair 3♦️6♣ 8❤️J♦️A♣ 3♣3♠3❤️6❤️6♠6♦️
Two Overcards to Over Pair A♣K♦️ 3♦️2❤️8❤️ A❤️A♠A♦️K❤️K♣K♠
Set to Full House or Quads 5❤️5♦️ 5♣Q❤️2♠ 5♠Q♠Q♦️Q♣2❤️2♦️
Open Straight 9❤️T♣ 3♣8♦️J❤️ Any 7, Any Q
Flush A❤️K❤️ 3❤️5♠7❤️ Any❤️(2❤️to Q❤️)
Inside Straight or Two Overcards A❤️K♣ Q♠J♣6♦️ Any Ten,A♠A♦️A♣K♠K❤️K♦️
Flush & Inside Straight K♣J♣ A♣2♣T❤️ Any Q, Any ♣
Flush & Open Straight J❤️T❤️ 9♣Q❤️3❤️ Any ❤️ 8♦️8♠8♣K♦️K♠K♣

IMPORTANT ‘OUTS’ TERMS

Backdoor: A straight or flush draw where you need two cards to help your hand out.
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.

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.

When I’m playing in my regular poker games, I frequently use these calculations to get a better understanding of my odds of making my hand. Let’s take a look at two recent scenarios where this happened.

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.

Dont Overcount Your Odds

Counting your odds seems easy, but beginners often make the mistake of overcounting their odds in situations where they have multiple draws. It’s easy to think you have 9 outs for a flush draw and 4 for a straight and therefore you have 13 outs, but two of those outs are the same card, meaning you really only have 12 outs.

Let’s look at a couple of examples of situations where players may overcount their odds and how it can be avoided.

Poker Odds Chart

We’ are going to 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.

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

EXAMPLES OF CORRECT AND INCORRECT POT ODDS

When calculating your pot odds, it’s important to remember that not every situation will be profitable. Sometimes you won’t have the odds to call, and you should throw your hand away. You must calculate your pot odds every time you’re faced with a new decision, as your odds can change across multiple streets; it’s common for a profitable flop situation to turn into an unprofitable turn situation.

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 $7 into a $30 pot, so let’s see how that looks in our equation:

Pot odds = ($7 / ($7 + $37)) x 100

Pot odds = ($7 / $44) x 100

Pot odds = 0.159 x 100 = 15.9%

So we know we need to win at least 15.9% 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 this a profitable 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

Following on from our previous example, we made the call and the turn brought the J – we missed our straight. Our opponent bets again, this time betting $44 into a $44 pot. As we’re facing a new bet, we need to recalculate our pot odds to see if this call is profitable.

To do this, we follow the same process as before; starting by calculating our pot odds. We’re calling a $44 bet into a $44 pot, so let’s look at our equation.

Pot odds = ($44 / ($44 + $88)) x 100

Pot odds = ($44 / $132) x 100

Pot odds = 0.333 x 100 = 33.3%

This means that we need to win the hand 33.3% of the time for our call to be profitable. We know from our previous example that the chances of us making our straight on the next card is 16%, so we do not have a profitable call.

Examples like this are why we need to calculate our odds on every street. Profitable situations quickly become unprofitable, and if you don’t recalculate your odds when facing a new bet, you’ll make a lot of unprofitable calls.

Pot Odds Application

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!

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 EV

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

1

Calculate the Outs

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.

2

Multiply Outs by Four and Two

Then, multiply the number of outs by four to get the percentage chances of you being dealt a winning card on the turn. After the turn, you can multiply the number of outs by two to give you your percentage odds.

For example, if there are 8 outs, then the percentage of you drawing one is 8×4 – 32%. Then multiply the number of outs by two to give you your odds. So if there are still 8 outs, your odds are 16%.

3

Calculate the Ratio Odds

Now that you have the 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.

Putting It All Together

We’ve covered a lot of different topics in this article, so let’s put them together and see how much we’ve learned with one final example from a hand I played in a live $1/$2 cash game. We’re on the turn with Th9h and the board reads Jh6c3hKs. The pot is $100, and our opponent has shoved for $75. What are the chances I improve to the best hand, what pot odds am I getting, and what is the EV of a call in this scenario?

Let’s start with working out how often I make the best hand. Assuming that both my flush and straight outs are good, I have nine outs to make the flush, and another three outs to make my straight (the Qh is already taken by the flush outs), giving me a total of 12 outs. As we’ve learned, the quickest way to find the probability of making my hand across one street is to multiply my outs by two, so 12 x 2 = 24, meaning that I will make my hand 24% of the time.

Now that we’ve established that, we can look at the pot odds I’m getting in this hand. I have to call $75 into a $100 pot, so including our opponent’s bet, I’m calling $75 to win $175 total. $75 divided by $175 is around 0.42, which means we need to have 42% equity to profitably make this call.

So, given that we have the probability that we improve on the river and our pot odds, we can run an EV calculation to see the profitability of a call in this spot. 24% of the time we will win $175 and 76% of the time we will lose $75. Let’s see how these numbers look in our EV equation.

EV = ($175 * 0.24) – ($75 * 0.76)

EV = $42 – $57 = -$17

So, we can see that a call in this spot would have an EV of -$17. In-game, I ran rough versions of these calculations, and realized that I would be losing money if I called, despite having a straight draw and a flush draw, so I made the fold.

Conclusion

Understanding poker odds is a crucial skill for any serious poker player. By grasping the concept of probabilities and calculating odds, you can make more informed decisions at the poker table and improve your overall game. However, theory alone is not enough; practical application is key to solidifying your understanding.

That’s why we encourage you to visit our poker odds calculator page, where you can put your newfound knowledge to the test. By practicing with real-life scenarios and calculating odds in various situations, you’ll sharpen your skills and become a more confident and successful poker player. So, don’t hesitate! Take the next step on your poker journey and visit our poker odds calculator page today.

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Jordan conroy

Author
Jordan Conroy, a respected name in the online poker arena, has cultivated his authority through years of dedicated play and content creation. Since 2020, he has earned a stellar reputation for his in-depth analysis of poker theory and his ability to keep a finger on the pulse of the latest developments in the poker world. Jordan's dedication to staying at the forefront of poker knowledge allows him to consistently deliver top-quality content that resonates with both novice players and seasoned professionals. Beyond his poker expertise, he brings a diverse perspective, closely following other competitive domains like soccer, snooker, and Formula 1, enriching his insights and providing a comprehensive understanding of the gaming landscape.
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