How to Calculate Poker Odds
Every action you make, hand you play, or bet you face has odds, probability, and statistics attached to it. Here are the main poker numbers you will have to face and calculate during poker play online or live:
- Pot Odds
- Implied Odds
- Pot odds in relation to equity
What are Pot Odds?
Pot odds refers to the relationship between the size of the pot and the size of the bet. Pot odds are the odds you're "being offered by the pot" to make your call. This is the amount of money in the pot compared to the amount of money you must pay to stay in the hand.
For example: If there's $10 in the pot and you have to call a $2 bet. Then you are getting pot odds of 5-1. If you have to call a $5 bet in the same $10 pot, you're getting pot odds of 2-1. How big is the pot; how big is the bet?
Understanding and calculating the pot odds is an absolutely fundamental skill to playing your best online poker - or live for that matter.
The Size of the Pot
You should always be aware of pot size. If you're playing Limit poker, you count the number of bets in the pot instead of the amount of money. When the bets double, as in Hold'em, you count the big bets as two small bets. If you're playing Pot-Limit or No-Limit it's a little bit harder to count the pot and, as a result, the odds will not be as exact. Regardless, you still should do it.
How to Use Pot Odds
Once you know your pot odds you must use this information appropriately. You do this by connecting the pot odds to the value of your hand. This means you can put your opponents on likely hands and understand your chances of making a better hand.
For example, you have a flush draw on the flop in Hold'em and you are up against an opponent who you think has at least top pair. There are 9 cards (usually referred to as outs) that will give you a flush when you have flopped four cards to a flush. As you can see in the table (further below), 9 outs give you a 35% chance (2:1 against) of making the flush on the turn and river combined. This means that you need pot odds of at least 2-1 to make a call on the flop profitable.
Implied odds are defined as the relationship between the size of the current pot and the pot you are expected to win. This means that occasionally the pot does not lay the correct odds even when you decide to play. Because you expect to get further action and win more when you hit your hand.
For example, in Limit Hold'em your opponent bets $20 into an $80 pot and your call gives you pot odds of 5-1 (you're risking $20 to win $100). But, if you expect your opponent to call a bet or raise on the river if you make your hand, your implied odds are 6-1 or 7-1.
A Simple Rule of Thumb for Hold'em and Omaha
Every out gives you an approximate 4% chance of hitting on the turn and river combined. For example, five outs give you about a 20% chance of improving. Six outs = about 24%. You will learn this by practicing your poker game more.
|Specific Draws in Hold'em and Omaha||Outs|
|Flush draw with two overcards or a straight flush draw||15 outs|
|Flush draw with one overcard||12 outs|
|Flush draw||9 outs|
|Open-ended straight draw||8 outs|
|Two overcards||6 outs|
|Gut-shot straight draw||4 outs|
Do I Need a Pots Odds Calculator?
There are a few simple Pot Odds Calculator tools online. But honestly being able to calculate pot odds quickly in your head is a good skill to have - both in live and online poker. It will take time to pull out a pot odds calculator at the live table anyway. However, if you’re playing poker online, we can offer a poker odds calculator by Pokerlistings to speed up your calculations.
How to Count Your Outs
In order to calculate your equity (your odds of winning the pot), you need to first know how many outs you have to make your hand. An “out” is any card that can come which will give you the best hand.
Obviously, before you can begin to count outs, you have to know the poker hand rankings forward and backwards. So start there if you don't know them. After you know the poker hand rankings you need to be able to read the board. Are there possible straights or flushes? Is the board paired? All of these things may affect your outs. Here's a simple outs cheat sheet covering the most common situations you'll be in after the flop (definitions for the terms are below the list):
|Open-ended straight draw||8|
|Gut-shot straight draw||4|
|Open-ender & flush draw||15|
|Three of a kind to make a full house||6 (flop), 9 (turn)(+1 out for quads)|
|Pocket pair to hit a set after the flop||2|
Remember: Remove the outs you know (on the board and in your hand) and not count outs twice.
Open-ended straight draw - There are two different values of cards that will give you your hand: 2*4= 8 outs.
- Hand: 8 9 | Board: 6 7 2
Gut-shot straight draw - You need one card in the middle of four.
- Hand: 8 9 | Board: 6 10 2
Flush draw - There are 13 cards of that suit. You hold two, and two are on the board (four total): 13 - 2 - 2 = 9 outs
- Hand: 8 9 | Board: 6 K 2
Open-ender & flush draw - You have both an open-ended straight draw and flush draw.
- Hand: 8 9 | Board: 6 7 2
Three of a kind to make a full house - You have three cards of the same rank.
- Hand: 8 8 | Board: 8 7 2
Pocket pair to hit a set after the flop - You have a pair in your hand.
- Hand: 8 8 | Board: 6 7 2
Antiouts and Blockers
When counting your outs you need to remember the idea of anti-outs (and blockers). If by making your straight you also complete your opponent’s flush, then those cards are not outs to your hand. And they can't be counted. The possibility of a flush draw on the board can turn a profitable eight-out straight draw into a six-out straight draw, rendering your odds insufficient.
Bets err on the side of caution and assume that they have the hand most dangerous to your own. If there's a flush draw, assume they have the draw; if the board is paired, assume they have a full house - or trips if you’re lucky. It's less expensive to wrongly fold a hand than to wrongly call off your whole stack.
Q Q J J
9 9 8 8 3 3
How many outs do you have? Depending on what you put your opponent on you can have as few as four outs or as many as 10. Your straight draw is to the nuts so unless you run into a full house or backdoor flush you have four rock-solid outs.
If you put your opponent on just a single pair, like A 9 , then you have 10 outs. Unfortunately, it's near to impossible to know what your opponent's kicker is. If they're holding J 9 , then you're down to only seven outs.
Q Q J J
8 8 6 6 6 6
In this hand, you span the gap from drawing dead all the way to 15 outs depending on your opponent's cards. If your opponent has a full house (or quads), you're drawing dead or practically dead (technically you could catch running JJ or QQ for a higher full house).
If your opponent has a higher flush draw you're drawing to 6 outs and you have to dodge 7 hearts as well as as many as 6 higher pair outs. If your opponent had just a pair you're sitting with as many as 15 outs (assuming a J or Q doesn't give your opponent a better two pair).
Stick to these golden rules:
- Only pay for a draw if it's a draw to the nuts.
- Never draw to a straight or flush on a paired board.
In the long run, you're going to lose a lot of money chasing flushes on paired boards or flushes without an ace in your hand. If you can take this draw to the river for cheap then it's still a decent hand but it's not one to get your whole stack in play with.
8 8 7 7
Q Q J J 10 10
In this hand you have a gutshot straight draw and a flush draw. But even if the board was rainbow (rather than all spades), you're drawing to a one-card sucker end of a straight.
If the 9 comes you have 8 9 10 J Q while anyone with a king in their hand has a better straight 9-K. If a spade comes you're sitting with an 8-high flush, the third nuts. Your outs are effectively zero so this hand is a must fold.
When counting your outs it's crucial to look past the outs your hand has to improve. If improving your hand will make a better hand for your opponent that out is actually an anti-out. To learn more about anti-outs head to Anti-Outs and Money Cards.
When in doubt it's always better to assume you have the least number of outs rather than the most. It's always a less expensive mistake to fold when you're good than to call when you're behind.
How to Calculate Poker Equity
The next step after figuring out your pot odds is figuring out your equity (your chances of winning the pot compared to your opponent's). This trick is indispensable when playing live. The easiest way to get your equity is to remember these rules:
- On the flop, multiply your outs x4
- On the turn, multiply your outs x2
This will give you your chance at winning the pot as a percentage %.
So for example, if you have a flush draw, you have 9 outs on the flop. 9x4 = 36% chance at making the best hand. And with an open-ended straight draw (eight outs) you have a 32% chance of making your straight on the flop - that is, with two cards left to come.
Since we have the pot odds as a ratio, we then need to make that percentage a ratio to compare the two. Your equity ratio is then 64-36 (64 times you don't make your hand; 36 times you do).
If we use the same ratio shortcut from the pot odds section to get the right side equal to 1, the equity ratio is (64/36):1 or 1.7:1. Meaning for every one time you make your hand there will be 1.7 times that you don't.
On the flop and with a large number of outs (>8), the previous shortcut gives a slightly incorrect answer. There's a simple formula you can remember to get a slightly more accurate figure:
- (number of outs * 4) - (number of outs - 8) = Equity
This means the equity of an open-ended straight flush draw (15 outs) would be:
- (15 * 4) - (15 - 8) = 53%
Without this formula, the percentage would be higher by seven points, giving us an artificially large result. However, for fewer outs, you don’t need to be as precise in your pot-odds calculation, the simple shortcut is close enough to decide on a call.
Combining and Comparing Pot Odds and Equity
If your equity is higher than your pot odds, then it's a good call. If it's lower, then you're making a bad call. In its most basic form, odds are no more complicated than this.
Random Poker Odds and Ends to Keep Handy
|Being dealt a pair||17:1 (5.9% )||7 7|
|Being dealt Aces||221:1 (0.45%)||A A|
|Being dealt Ace-King Suited||331.5:1 (0.3%)||A K|
|Flopping a set with a pocket-pair||8.51:1 (11.76%)||8 8 |
| 2 8 A
|Flopping two pair (without a pocket-pair pre-flop)||48:1 (2.02%)||7 10 |
| 7 10 3
|Making a Flush by the river (flopped 4 to a suit)||1.9:1 (35%)||A Q |
| 9 4 A 10
|Making an open-ended straight by the river||2.2:1 (32%)||6 7 |
| 8 9 2 3 10
|A full house or better by the river (flopped three of a kind)||2:1 (33%)||4 4 |
| 4 K Q K
Jonathan Little on Basic Poker Math
Jonathan Little, two-time World Poker Tour (WPT) Champion & producer of poker training books.
“Quite often in NLHE with your good draws - like open-ended straight draws and flush draws - you're almost always getting the right price to draw to those on the flop. And sometimes on the turn -- especially when considering implied odds.”
“If you memorize the most common outs, such as six outs when you have overcards, or eight outs with most straight draws, nine outs if you have a flush draw, or more if you combine them.”
More Poker Tools:
- Poker Odds Calculator (odds of winning at each point in a hand)
- Which Hand Wins Calculator (determine which poker hand wins)
- Poker Starting Hands Cheat Sheet
- Poker HUDs and Trackers
More Beginner Tips:
- How to Get Started Playing Poker Online
- Proper Hand Selection in MTTs
- Expected Value (EV) in Poker, Explained
- Have a Proper Bankroll
More Intermediate Tips:
Poker Odds FAQs
What are poker odds?In Texas Hold'em, poker odds are THE probability tool you need as a poker player. In fact, you should always be thinking about poker odds - yours and your opponents' - when making decisions. In short, poker odds is the probability of you winning that hand, or the price it offers (pot odds).
How to learn poker odds?You can learn poker odds by studying our poker odds chart and trying hand situations in our poker odds calculator.
How to calculate poker odds quickly?To calculate your poker equity - or how often you should win a hand, you can use a simple formula. Count how many outs you have. For example, if you're drawing to a flush, you have 13 suited cards, two in your hand, two on the board - leaves 9 outs. The chance of you hitting on the turn is 9*4 (+4) = 40%. On the river it's half of that - 9*2 (+2) = 20%.
- For a half pot bet, you get 3:1, and so need 25% equity or more to call.
- With a 3/4 pot bet, you have 7:3 pot odds and need +30% equity to call. - With a pot sized bet, you get 2:1 pot odds and need +33% equity to call. - With a 2x pot bet, it's 3:2 pot odds and you need 40% equity to call. So, say your opponent has a hand lesser than a flush and you're drawing to a flush. They bet the pot size on the flop, you may elect to call. But if they bet the pot on the turn, your equity has decreased. Not to mention that if they have a hand like two pair, they also have equity to hit a full house and beat whatever cards you're drawing to.
What is the best poker odds calculator?We can offer a great, fast poker odds calculator right here on this page.
In Poker, what are implied odds?Implied odds is the relationship between the size of the current pot and the pot you're expected to win. Because sometimes the pot doesn't lay the correct odds, even when you decide to play. Because you're expecting to get more action and win more when you hit your hand.
Implied odds changes things. For example, in Limit Hold'em your opponent bets $20 into an $80 pot and your call gives you pot odds of 5-1 (you're risking $20 to win $100). But, if you expect your opponent to call a bet or raise on the river if you make your hand, your implied odds are 6-1 or 7-1.
Poker odds: When to call?You'll often be asking this question if you're drawing to a straight or a flush. So you'll need to calculate if you're getting good enough odds to call a bet or raise on the flop or turn. First, you need to calculate how often you'll hit your draw - by first counting your outs.
If you're drawing to a flush, you have two suited cards in your hand and two on the board, that means 9 cards of that suit left in the deck. On the flop, it's 9*4 (+4) = roughly 40% of hitting. Meanwhile, on the turn (so the odds of hitting on the river) is 9*2 (=2) = roughly 20% of hitting.
With pot odds, think of the number of cards again. 52 in the deck, two in your hand and three on the board (flop). That means 47 unseen cards (including your opponents' hole cards). Nine cards can save you but 38 cards don't complete your draw. So that's a 38:9 ratio - or 4:1 (or 25%). So if you're not getting 4:1 / 25% pot odds, you shouldn't call. This ratio changes again when you consider implied odds.
What are GOOD poker odds?Say you're drawing to a flush and have 9 outs - you have roughly 40% equity on the flop and 20% on the turn.
- For a half pot bet, you get 3:1, and so need 25% equity or more to call.
- With a 3/4 pot bet, you have 7:3 pot odds and need +30% equity to call. - With a pot sized bet, you get 2:1 pot odds and need +33% equity to call. - With a 2x pot bet, it's 3:2 pot odds and you need 40% equity to call. So, say your opponent has a hand lesser than a flush, like two pair. They bet the pot size on the flop, you may elect to call. But if they bet the pot on the turn, your equity has decreased. Not to mention that if they have a hand like two pair, they also have equity to hit a full house and beat whatever cards you're drawing to.
In poker, what are pot odds?Pot odds refers to the relationship between the size of the pot and the size of the bet. For example: If there's $10 in the pot and you have to call a $2 bet. Then you are getting pot odds of 5-1. If you have to call a $5 bet in the same $10 pot, you're getting pot odds of 2-1. How big is the pot; how big is the bet?
Do poker odds change with more players?Absolutely. The more players involved in a pot, the less your chances of winning it. That's why it may make sense to shove pre-flop with certain hands instead of just calling, hoping to narrow the field to just one, or perhaps zero!
“If your pot odds number is higher than your equity number, then it’s a good call.”
This is wrong. it should be the other way around.
For the sake of this example lets use big number. Lets say you need to bet 100 to win 1000. Then your pot odds are 10%. But lets say you have 50% of getting a card to winning. Obviously, you would get in, in this case, but your pot odds are LOWER than your equity.
@BD: You’re right. It was worded incorrectly. Fixed now, thanks :).
My brain going to blow up
I want to point out that the formula for determining odds for making a hand by the river,
post-flop, with 8 or more outs can be simplified to 3x + 8, where x in the number of outs. In Sean’s example, a 15 outer has 53% equity. 3(15) + 8 = 53.
Furthermore, making a hand by the river, post-turn, with 8 or more outs can be simplified to x + 8.
You can’t consider things you don’t know, ever. For example, you are actually 0% if all your outs are folded but the flip side of that coin is you are 100% if every card left makes you winner. On average over the long run you will win as if you had 15 outs because you are that much more likely to have every card make you win than none, or some where between.
The 32% equity with two cards to come on an open end straight, and the 53% in the hand with 15 outs implies you’re getting two cards. But you’ll most likely have to bet twice. Shoving would avoid this, or being last to act and checking the turn, if possible, then these equity calculations are accurate. For example, if the pot is $100 and you have 15 outs, or 53% as he suggests, a pot sized bet of $100, if called, gives you 2 to 1, right? But you only get one card for that bet, and your equity is 31.9%, not 53%. 53% is for 2 cards, not 1, so you’re required to make another bet, so your equity is much lower each bet(than the 53%). On the turn bet, it’s 32%. So, for your $100 bet, should he call, you really only have 31.9% of $300, or about $96 for your $100 bet, slightly more with 1 card removed for the turn bet. How to avoid this and get 53%? 1. Shove 2. be last to act and check the turn, if possible.
When you are playing Omaha with nine or ten players, with ten after the burn and flop
you only have eight cards left. When you have a hand with fifteen outs, how does that
work with only eight cards left in the deck?? Thanks to anyone who can reply.
pot odds formula??? from “jonthan little” vol 1,page 29, paragraph 2. 42%= 0.42=100/(100+x). what is x??
then you have 42+0.42x=100, so x=58/0.42=138 chips in to make worth your call..?? how would one figure it if there was a bet of 375 or any other then a 100 bet? i think i would multiply 0.58 times the bet or 0.42 times bet ??? algerbra???
Maybe I’m just stupid, but I want to post this question anyway;
To calculate your equity there are multiple ways:
All of them give another value of your equity.
As for an example:
Number of outs: 10
-Your method gives us;
-2nd method I described above gives us;
(10/(47-10))*100=27% (times 2 for T&R = 54%)
-3th method I described above gives us;
(10/47)*100=21% (times 2 for T&R=43%)
Just because yours is a shortcut, I wonder which one it’s based on. I figure the 3th one, which would be the one I would use for more accurate odds.
Awaiting your reply,
Maybe I’m too new at calculating my outs, but I have read two different ways to do it, and both give different ratios.
The first being the one described above.
The second being: If I had 8 outs on the flop. I would take 47-8, then 39/8. Giving me 4.8-1 instead of 2.1-1 described in this article.
Am I just missing a step??
Call me stupid, or just new at poker, but I don’t understand half the stuff you’re talking about….
You’re absolutely correct. Dwan had about 16% chance of hitting his straight, and about 3% chance of winning by making a running two-pair or trips.
I saw an interesting hand in the Durrrr challenge in which Dwan held 75o to a board of Q36 rainbow to Sammy’s QJo.
Durrr’s hand was 20% to win – but using this formula I thought he would only be 16% to win with his 4 outs. I’m guessing the extra 4% was for the possibility of a running pair, but the formula does not account for that – care to explain? Just an exception or what?
I’d recommend you read the “how not to suck at poker” series. This one explains how to count your outs.
What the hell is equity… and what the hell is an out?
This isn’t really going to be the answer you want to hear, but here you go:
When you make a bet too large to give sufficient odds to a player on a draw, and they call anyways, that’s good. Even though it means you lose A LOT, you make money in the long-run.
But, you have to make sure you don’t pay out the value bets of players when they do his their flush or straight. If you lose money after the player has already made the hand, then you’re the one making the mistake, and they were correct in calling (assuming they knew you would pay them out if they hit).
Cheers!im really finding your articles this stuff usefull, the only problem im having is when playing low stakes online, lets say the flop comes 10h kh 4d and i hit 2pair with 10s ks, and its checked round to me but its possible other players could be on flush draw so i try to price them out,
in theory the only people who will call is people with trips or also 2pair or even aces,
but i find some people will still call with flush draw probably because they they dont understand the concept of pot odds and equity so trying to price people out only works with people who know what they are doing!
You are correct that your equity is 53% with a 15-outer. Anytime your equity is more than 50%, you will ALWAYS have pot odds to call, no matter what the bet.
If your heads up opponent moves all in, you’re getting 1:1 on your money for the all in, plus all the money already in the pot, so you’re getting more than 1:1 on your money with > 50% odds.
So yes, with a 15 outer, the only mistake you can make is folding.
One thing to note, that formula gives you your equity for seeing both the turn and the river. you’re only around 30% to hit your hand on just one card. but since you’re 53% to hit by the river, it doesn’t really matter when you look at the hand as a whole.
Just to be safe, you should be looking to win the pot, or get it all in on the flop. either you get it all in good, or you win the pot with 0 risk.
sorry thats supposed to say open ended straight flush draw
hi im a beginner poker player and its a great article, so if i have an open ended straight draw (15 outs) that makes it 53% in my favour which would be odds of 0.7-1 ( i think im right)
so lets say there is 2 of us in the pot to make it simple, no matter what bet my opponent makes (assuming he is to act first) the pot odds will be greater that the card equity, even if he pushes all in the pot odds will be greater than 0.7 – 1. is this correct?
They’re actually both correct, depending on the situation.
(10 * 4) – (10 – 8) = 38%. 62/38 = 1.6-1
This is your odds for making your hand by the river (on either the turn, or the river)
While the other method
37/10 or 3.7-1 are the odds of you making your hand on the turn specifically.
So if someone goes all in on the flop, you want to use the (X * 4) – (X – 8) formula, while if someone makes a bet on the flop with 400bb behind, you want to use the other formula, since you might have to call a huge bet to see a river.
in the artical “calculating-pot-odds-a-beginners-guide” a 10 out on the flop is a 3.7-1. using this formula, (10 * 4) – (10 – 8) = 38%. 62/38 = 1.6-1. 3.7 vs 1.6 is a big difference. one of these methods has to be wrong. which one is correct?
I’m confused about one thing though. The odds sound great with 2-1 against you and getting paid 3-1. But if you flopped the open ended straight draw, then you only have 16% of hitting on the turn.
This calculation assumes you get to see the river for free as if the other players were all in. But if they aren’t all in and have large stacks, then it’s 4.5 – 1 against you on the turn. What if you miss on the turn and have to pay another big bet on the river? I guess this is where implied odds come in.
This is a great article. Thank god people don’t understand this stuff. I’m scared of everyone getting good at poker.
Hear that everyone? STOP READING POKERLISTINGS!
Great post. Sound advice. Confusing at first, but practice makes it perfect.