A three-bet, or 3-bet, describes the first re-raise before the flop in poker. If someone raises, you may call, fold,…

Read More# Poker Odds

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

## 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.

**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.

In this hand, I was on the turn with a flush draw and facing a bet from my opponent. I was considering a call, but I wanted to know how likely it was I would make my flush on the river. To work this out, this is the thought process I used.

There are thirteen cards of each suit a deck of cards, and if in this hand, I had two diamonds in my hand, with a further two on the flop. That means four cards of that suit have been accounted for, leaving nine in the deck. I know that the probability of an individual card appearing on the river is around 2%, and nine cards will give me the best hand on the river. Therefore, I multiplied the 2% chance by 9, which let me know that I had an 18% chance to make my hand on the river.

The first scenario looks at calculating the odds of me making my hand across one street, but I frequently need to know the likelihood of making my hand across two streets. Let’s take a look at an example where I made that calculation; this time I’m on the flop with an open-ended straight draw and my opponent has shoved all-in. Their bet isn’t very big, so I’m considering making the call with my hand, but I need to know how often I will make my hand by the river.

As my opponent is all-in, I know that I’m going to see the river card, so I can calculate the likelihood that I make my hand on both the turn and the river. With my open-ended straight draw, I have two outs to improve. Using our quick calculation, I multiply those 8 outs by 2 to get a 16% chance of making my straight on the turn.

We’ve already seen that this equation works from the turn to the river, so we can run the same calculation again to find that we have a 16% chance of making our hand from the turn to the river. Both the turn card and river card are individual events, which means I can add together the probability of those events occurring to find out my overall probability of making my hand, which is 32%.

However, do bear in mind that this is a rough calculation intended to make it easier to calculate probabilities at the table – the exact calculation is performed in a different way, but this way is good enough for what we need in-game.

## 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.

## 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 4♥3♥ 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.

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

### 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.

### 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%.

### 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.

## Poker Odds FAQs

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## Poker Odds & Probabilities

To calculate your pot odds, simply divide the amount you have to call by the total size of the pot (current pot + opponent’s bet + your call). For example, if you have to call $100 and the total pot is $400 ($200 current pot + $100 opponent bet + $100 call), you divide 100 by 400, which gives you 0.25, or 25%.

If you have a flush draw on the flop, you have two attempts to hit nine outs, which means that you’re going to hit your flush around a third of the time by the river. However, if you have a flush draw on the turn, you only have one card to improve, so you’ll only make your flush around 18% of the time.

Flushes are rarer than straights in poker, but if you have a flush draw, you are more likely to make it. This is because a flush draw has nine outs, whereas a straight draw only has eight or four outs.

While flushes are rarer than straights, it’s easier to hit a flush draw than a straight draw. This is because a flush draw has nine outs, whereas a straight draw only has eight or four outs.

## Poker Rules & Terminology

The 2/4 Rule in poker is a way of easily calculating the odds of you making the best hand. If you want to calculate your odds across one street, simply multiply the number of outs you have by two, and if you want to calculate your odds across two streets, simply multiply the number of outs you have by four.