The Basics: Odds & Outs
Before this lesson you should have read:
In poker, you are often behind with an incomplete hand, but you still have the chance to surpass the hand of your opponent. On the turn or river you need one card, which improves your hand into a made hand, e.g. into a flush or a straight.
A card that makes a draw into a made hand is called an out. When such a card appears on the turn or river, it is called "hitting an out".
In this lesson, you will learn how to determine the probability to hit an out. These are called odds. You will learn how to calculate if you can profitably call a certain bet of your opponent with a certain draw using odds & outs as per the chart below.
Outs improve draws into made hands
It is called a draw, when you probably do not hold the best hand after the flop, but still have realistic chances to improve your hand into the best one. Typical draws are flush draws or straight draws. The cards that complete your draw are called outs.
Example: You hold and the flop is . You have a flush draw. Every heart on the turn gives you a flush. The deck includes 13 hearts. Two of them are in your hand and two are in the flop. So there are nine hearts remaining, that can give you a flush on the turn. This means you have nine outs.
The more outs a draw has, the stronger it is. Remember only to count those cards as outs that really improve your draw into the best hand with a high probability. If an 8 appears on the turn in this example, then your hand improves into a pair, but it is anything but sure, that you will be ahead with this holding.
Draws and their outs 

Draw 
Outs 
Flush draw: on 
9 
Openended straight draw: on 
8 
Two overcards: on 
6 
Two pair/trips: on 
5 
Gutshot: on 
4 
Texas Hold'em odds are the probability to hit an out
In order to be able to make the right decision with your draw you need to know the probability to hit an out on the turn or the river. This is calculated as follows:
 Step 1: Determine the number of outs, that complete your draw.
 Step 2: Divide the number of your outs by the number of possible cards that might appear on the next street.
Back to the example: You hold on the flop and you have a flush draw. You already know that you have nine outs by this. In the next step you have to divide the number of your outs by the total number of turn cards.
The deck has 52 cards. Five of these are already known to you. Two of them you hold in your hand and three are in the flop. So there are 47 unknown cards left that can appear on the turn. So the probability to get the flush on the turn is:
9 outs / 47 possible cards = 0,19 = 19% ~ 4 to 1.
The probability is called odds. In Texas Hold'em, odds are regularly given in the notation "x to y". A probability of 19% means that you will hit an out on the next street in about one out of five cases. This is given by "4 to 1". An average there are four misses opposed to one hit.
In the following chart you find poker odds for typical situations. It also includes Texas Hold'em odds from the flop to the river. For example, these are important in an allin situation, since in an allin you will see the turn and river for sure.
Poker Odds Chart
Odds and outs 

Outs  Odds: FlopTurn / TurnRiver 
Odds: FlopRiver 
Example 
1 
46:1  22.5:1  Backdoor flush draw 
2  22.5:1 
11:1  Pocket pair to set 
4  11:1 
5:1  Gutshot 
5  8:1  4:1  Two pair/trips 
8  5:1  2:1  Openended straight draw 
9  4:1  2:1  Flush draw 
12  3:1  1:1  Flush draw + gutshot 
13  2.5:1  1:1  OESD + pair 
14  2.5:1  1:1  Flush draw + pair 
15  2:1  1:1  Flush draw + OESD 
Pot odds – Can I profitably play my hand?
Pot odds are the ratio of the possible reward compared to the stake you have to place when confronted with a bet. Thus they can be seen as a risk/reward ratio. By comparing the pot odds with your odds, you can estimate if a stake for a draw is worth it.
Again, we take a look at the example:
Your required stake is $2, the pot previous to the bet is $8, your possible reward is $10. The odds to hit your flush are about 4:1 against you.
Let us assume that in this case you will win the hand. This means that in one of these 5 cases you win $12. In the other four cases you will lose $2 respectively. Again under the assumption that you have to fold your hand on the turn if you can not improve it.
When you call the $2, on average after five occasions you have lost $2 four times and won $10 once. Your total profit, which is calculated by profit  deficit, is thereby at $10  $8 = $2.
For this reason in the long run, it will pay off to call your opponent's bet in this situation. On average, you will win $0.40 (= $2 / 5 hands) every time.
Now we introduce the socalled pot odds. They give the ratio of the possible reward compared to the required stake, so they are a reward/risk ratio.
Pot odds = possible reward : needed stake
In the aforementioned situation, the pot contains $8. You have to add the $2 that are placed by your opponent which makes a total pot and a possible benefit of $10. You have to pay $2 to stay in the game and see the turn card. Therefore the pot odds are $10:$2 or 5:1.
Thus your pot odds are 5:1 and your odds are 4:1.
Now you have to consider the following rule: if the pot odds are higher than the odds of an incomplete hand, you will win in the long run. If they are lower, you will lose.
What would happen if your opponent bets $4 instead of just $2? The possible benefit would rise to $8 + $4 = $12. But at the same time, your pot odds would turn to $12:$4 which is a ratio of 3:1. Therefore it would not be profitable to call the bet, since your odds are 4:1 and your pot odds are lower than your odds. At this point you should fold your hand, otherwise you would lose in the long run.
Equilab  Improve your knowledge of odds and outs
You can get a better understanding of odds and outs, and your chances to win the hand in various situations, with our free PokerStrategy.com Equilab software. The PokerStrategy.com Equilab can analyse the range of hands an opponent will likely hold in a given situation, then provide you with equity figures so you can deduce the profitability of any given situation.
Download the PokerStrategy.com Equilab for free
Summary
Using poker odds & outs, you can calculate if you can profitably call a draw. Outs are cards which complete your draw. Odds are the winning probabilities to hit an out. In Texas Hold'em odds = outs / possible cards.
Pot odds give the ratio of a possible reward compared to the stake you have to place. They are produced by: pot odds = possible reward : stake. If the pot odds are higher than the odds of a hand, you will win in the long run. If they are lower, you will lose in the long run.
Next steps
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Discussion
#1 acephalia, 23 Oct 13 16:08
thank you. this helped a lot.#2 ocendie, 29 Oct 13 19:17
nice job#3 dimas2345678, 10 Nov 13 09:23
thanks#4 yuli06, 10 Nov 13 13:55
Nice#5 audzejs, 07 Dec 13 22:11
I really can't understand why 9/47 is 4 to 1 . Isn't ir more like 5 to 1?#6 dgelashvili111, 12 Dec 13 23:09
A probability of 19% means that you will hit an out on the next street in about one out of five cases. This is given by "4 to 1". An average there are four misses opposed to one hit.#7 dgelashvili111, 12 Dec 13 23:10
A probability of 19% means that you will hit an out on the next street in about one out of five cases. This is given by "4 to 1". An average there are four misses opposed to one hit.#8 dgelashvili111, 12 Dec 13 23:11
A probability of 19% means that you will hit an out on the next street in about one out of five cases. This is given by "4 to 1". An average there are four misses opposed to one hit.#9 Gadgaard, 13 Dec 13 13:30
simply said if you run it 5 times, you lose four times and and you win once hence 4:1<br /> (variance not included)#10 Norgul, 27 Dec 13 16:11
Isn't the possible reward $12? If you enter the pot $8(pot)+$2(him)+2$(you)...however, if you don't enter the pot, your possible win isn't $10 since you are folding?#11 Norgul, 27 Dec 13 16:14
Oh...unless $8 is the total pot after the Villain raises#12 Frannie1969, 29 Dec 13 10:22
What a interesting lesson this was and also it gives me a very good reminder of the BRM!#13 Ashkin7, 31 Dec 13 17:43
Nice#14 cosmos117, 08 Mar 14 09:39
This has helped me a lot, the quiz technique really has made it very interesting which in turn has helped me understand it.#15 dzeminis, 31 Mar 14 14:59
Helped a lot. Thanks#16 Petersey611, 04 Jun 14 15:45
decent#17 wirra, 12 Jul 14 06:52
nice#18 deekay7, 22 Jul 14 10:44
nice one#19 fililp88, 30 Jul 14 20:41
wtf "9 outs / 47 possible cards = 0,19 = 19% ~ 4 to 1."<br /> <br /> 19% i 1:5!!!#20 599ALG, 27 Sep 14 10:01
Thank you! Looking forward to the next test!#21 SLYDOC11, 04 Oct 14 02:42
ok#22 tashaleigh3, 09 Oct 14 09:56
thanks!#23 catblank, 14 Oct 14 08:58
oke#24 Socialhabit, 16 Oct 14 17:28
thanks! :)#25 4s4s4s, 19 Oct 14 19:29
Ty#26 Schkisz, 14 Nov 14 00:29
@filip<br /> <br /> 1 + 1 + 1 + 1 + 1 = 5 > 20% + 20% + 20% + 20% + 20% = 100%<br /> <br /> therefore if you divide 5 (or 100%) into 5 sections (one of which is either win or lose) you get our equation to:<br /> <br /> L(20%) + L(20%) + L(20%) + L(20%) + W(20%) = 4(Ls) :(to) 1(W) (100% times), so in 5 cases you will lose 4 times and win 1 time....<br /> <br /> complicated but that's how math is... =)#27 BenBlakeIsTilting, 14 Nov 14 03:43
sweet#28 yetAnotherUsername, 22 Nov 14 05:12
?#29 Honda70, 28 Nov 14 14:11
ty#30 KosttuxxRNMD, 29 Dec 14 23:43
good to know#31 STELPPL, 20 Jan 15 05:21
thanks#32 Dolja25, 15 Feb 15 14:56
ok#33 Tomic1891, 16 Mar 15 06:26
Nice#34 prd94, 01 May 15 23:41
Nice#35 vaso014, 08 May 15 18:01
nh#36 Jepong700, 09 May 15 14:18
nh#37 marco0425, 23 May 15 12:28
nice#38 CikaMisa, 06 Jun 15 13:06
nice#39 Davidius, 20 Jun 15 22:03
So in poker odds=probability? In math and statistics its probability=desired outcome/all possible outcomes and odds=desired outcome/undesired outcome. So how come do you use them as the same thing here?#40 Davidius, 20 Jun 15 22:21
Okay I get, although it would be nice to add an explanation to the article. My last post still stands in true in math as well as poker, that is why odds are 4 to 1 while probability is 1 out of five. So you get odds=9(outs)/38(bust)=0,236 (1/4) and probability 9(outs)/47(possible)=0,19 (1/5).#41 Karla9516, 09 Jul 15 05:51
I downloaded equilab, but really can't figure out how to use it. Can someone help me where can I find guide for this software?#42 ferrye, 03 Aug 15 06:19
Important stuff, more important than you may think!#43 deniavigacil, 10 Aug 15 18:55
i use application#44 batnuuts12, 17 Sep 15 09:22
df#40 Davidius, 20 Jun 15 15:21<br /> Okay I get, although it would be nice to add an explanation to the article. My last post still stands in true in math as well as poker, that is why odds are 4 to 1 while probability is 1 out of five. So you get odds=9(outs)/38(bust)=0,236 (1/4) and probability 9(outs)/47(possible)=0,19 (1/5#45 batnuuts12, 17 Sep 15 10:45
df#40 Davidius, 20 Jun 15 15:21<br /> Okay I get, although it would be nice to add an explanation to the article. My last post still stands in true in math as well as poker, that is why odds are 4 to 1 while probability is 1 out of five. So you get odds=9(outs)/38(bust)=0,236 (1/4) and probability 9(outs)/47(possible)=0,19 (1/5#46 shesko12, 21 Sep 15 22:07
Hi there,<br /> I am a bit confused on how you got your results for the Backdoor flush draw. From my understanding the Backdoor flush should be calculated by multiplying the probability for both the turn and the river to contain the desired suit, i.e. (10/47)*(9/46) = 4.16%. 4.16 fits 24 times in 100 so the odds are 1:23. This seems close enough to your flopriver result but how do you get 46:1 in the FlopTurn / TurnRiver result? Doesn't 46:1 mean that only one card in the whole pack can lead you to your desired outcome?#47 blackdiego74, 01 Oct 15 16:32
WOW!!! that make sense to me . thanks for the lesson...#48 PacMan91, 16 Oct 15 23:15
slowly understanding#49 gohomeman2690, 31 Oct 15 15:20
ok#50 corsc, 01 Dec 15 11:45
I think initially how to easily convert from 19% to 4:1 is not clear and its only very briefly shown in the video.<br /> <br /> I think it might be worth mentioning the quick way to convert from a 19% to odd is:<br /> 100 %  19 % : 19%<br /> <br /> resulting in:<br /> 81% : 19%<br /> <br /> approximated to:<br /> 4 : 1#51 Marsovac1987, 02 Dec 15 17:33
4 to 1.#52 xxxpokerxxx1, 10 Dec 15 21:56
ty for this#53 marrcio, 30 Dec 15 23:26
Certainly the lesson I most come back to, very nice.#54 jaskob93, 13 Jan 16 15:06
ok#55 akerblum, 18 Jan 16 14:32
good to know#56 bubamarasr, 20 Jan 16 18:06
Read it. Thank you.#57 DrussDLegend, 14 Feb 16 15:38
Read through twice, this is by far the party where I struggle the most in poker. Starting to sink in though. Thank you.#58 Yoshue1824, 15 Feb 16 00:45
Thanks#59 Nhoxalone, 17 Feb 16 02:33
rất ý nghĩa.#60 sahamanu, 22 Feb 16 19:15
Much to learn.#61 amzinas302, 13 Mar 16 16:39
ok#62 sedinbsng, 01 Apr 16 13:49
ok#63 Fortizr, 05 Apr 16 16:54
ok#64 pharaonsgold, 07 Apr 16 00:30
good#65 CroZoZo, 26 Apr 16 13:18
kul#66 FelixAces, 07 Jun 16 21:01
Sould we calculate in game?#67 PSICKO, 25 Jul 16 00:55
Hello All, this makes me very confused !!! <br /> And ODDS is something i really need too learn for <br /> "positive expected value"<br /> * The first chart you say you have 9 outs I think its only 8 !!!<br /> What if your opponent has pocket TENS ??? (or even 33.)<br /> Then the 3 gives him a FULL HOUSE so i wouldn't count the 3. <br /> We have too learn TELLS and decide what cards your opponent has to exclude HIS outs !!!<br /> <br /> *also The other chart with the AQ overcards, You don't count the runnerrunner OUTS ??? Howcome..???<br /> *also The Trips section the K could give your opponent (pocket JT) a straight so your/my inproved 2 pair or trips would be useless and be negative outs.<br /> (and what if he holds QQ and hits a 9 ? )<br /> *also The 3 in gutshot could give your opponent (who limped in or got called his potstealraise with 64s from OT.) a higher straight, so again negative outs.<br /> <br /> i'm curious for everyones reactions, advise, tips and hints.<br /> <br /> Because i want too sharpen my play and the math is tricky and wenn i calculate my odds at the table my hand is already sat out wenn ready. lol#68 PSICKO, 25 Jul 16 01:58
8 / 47 = 0,17 = (almost) 6:1<br /> <br /> call 6 times $2, win 1 time $10, =  $2, negative EV (expected Value.)<br /> Thus your pot odds are 5:1 and your odds are 6:1. don't call<br /> <br /> <br /> even wenn you count your $2, call within' the pot because wenn you call it<br /> it isn't yours any more...<br /> you get : call 6 times $2, win 1 time $12, = 0 so calling isn't profitable in longterm.#69 woowoo1966, 02 Aug 16 19:37
cool thanks#70 Robinsko, 09 Aug 16 16:35
time to qwiz#71 Robinsko, 09 Aug 16 16:39
blioc#72 Robinsko, 09 Aug 16 16:55
:)#73 triviums, 11 Aug 16 02:31
When I count pot odds, do I track the small bets all the way from the flop to the river? Are the bets on the turn and the river to be counted as 2 bets or 1 bet?<br /> <br /> Please advise.#74 PokerrBabe, 17 Aug 16 00:57
Nice lesson. Very valuable information. :)#75 NouNasr969, 18 Aug 16 10:22
thanks for this incredible website#76 PaintRag555, 06 Sep 16 05:04
Well done!!!#77 FussgaengerSF, 02 Oct 16 15:10
Thats a easy way to calculate the odds. Nice :) thx#78 xpoky18, 03 Oct 16 12:52
good lesson.