Short Stack Strategy: Outs and Odds
Introduction
In this article Which cards help you?
 Learning to balance risk and reward
 Not every helpful hand is that helpful
Draws, or drawing hands, are incomplete hands which have to be complemented by one other community card in order to be defined as made hands. The strategy from the beginner section doesn't clearly define how to handle these kinds of hands.
In this article you'll learn the mathematical basis of poker. You'll learn how to figure out the winning percentages of your draw and how to determine whether it's profitable to play the hand or not.
The article is based upon the explanation of three central terms:
 Outs
Outs are all the cards which can improve your hand.
 Odds
Odds show the probability of one of the next community cards being one of your outs.
 Pot Odds
Pot odds show the relationship between the possible profit and the bet which you have to make. This can be seen as the riskrewardratio. If these are compared to the odds, it is possible to judge the worth of calling a bet to complete your draw.
Attention: This article is available in multiple versions, customised for each given poker style and format. If you want to read the odds and outs article for Big Stack Strategy, you can find it through this link to the article: Mathematics of poker  Odds and Outs for the Big Stack Strategy.
Outs  Which cards help you?
Outs are cards which, if dealt as community cards, improve your hand and possibly make it the best hand on the board. An emphasis is placed on 'making it the best hand', which we will discuss later.
EXAMPLE A 
At first, you have a seemingly worthless hand. You can't win a showdown with this hand. However, you do have the chance of making a strong hand, namely a straight, if either an ace or a six is dealt on the turn or the river.
These cards, the ace and the six, are your outs (they are still in the deck). The question is: how many outs do you have in total? The answer is relatively easy if you consider how many aces and sixes there are in a card deck. In each case there are four cards of one value, which makes a total of eight outs. Only one of these eight cards has to be dealt in order to improve your hand.
Your Outs
EXAMPLE B 
This situation is even better. Not only will every ace or a six help you make a straight, but every club will give you a flush.
The number of outs has therefore increased. On the one hand, you can allow for all the remaining club cards in the deck to be your outs. There are 13 cards of one suit in a deck, four clubs that have already been dealt, so a total of 9 (134=9) outs remain to complete your flush. The eight outs mentioned in the example above are added to this .From the eight outs mentioned in Example, two are subtracted, namely the ace and the six of clubs because they have already been taken into account as the flushdraw outs. This makes a total of 15 (9+6=15) outs:
Your Outs
FURTHER EXAMPLES 

Flushdraw  9 Outs
There are 13 cards of one suit in a deck; four have already been dealt. Therefore 9 outs remain which would complete the flush.

OESD (openended Straightdraw)  8 Outs
Any 4 or 9 complete the OESD to make a straight. Therefore an OESD always has 8 outs.

Two Overcards  6 Outs
There are 3 aces and 3 queens left in the deck which would make a top pair. You therefore have 6 outs in this example.

A pair as a three of a kind or a two pair draw  5 Outs
2 eights are left in the deck which would make three of a kind. One of the three remaining kings would make a two pair. This adds up to a total of 5 outs.

Gutshot  4 Outs
A gutshotdraw means that you have a chance to make a straight if the missing 'inner card' of your straight is dealt. There are exactly four cards which would do this; here it would be any deuce. You therefore have 4 outs with a gutshot.

Odds  How likely is it that I complete my draw?
So what does the term 'odds actually refer to? It is a commonly used term representing the probability of completing your hand.
This type of notation is called Odds against, because it shows the probability of not making your hand. It's the number of times you do not complete you hand against the number of times you do. What does your ratio look like? These odds display your probability, in order to ease the process of determining whether it is profitable to continue playing the hand or not, as you'll see in the next chapter.
Let's look at the previous example one more time:
You already know 5 cards after the flop: your two starting cards and the three flop cards. Any of the remaining 47 unknown cards can still be dealt (52 cards in a deck). 8 of these 47 cards help you to complete your draw, while the other 39 (478=39) cards would not complete your draw and are therefore unhelpful. In short, your odds from the flop to the turn are 39:8, which is the same as about 5:1
As you know 5 cards on the flop, your own two cards and the three community cards, there are 47 (525 = 47) unknown cards. Consequently, after the turn card is placed on the board, there are 46 unknowns after the turn. The helpful cards are your outs. From this logic we can derive the following equation:
A standard scenario for the application of odds from the flop to the turn occurs in the shortstack strategy if you are holding a draw in a freeplay position (in the Big Blind where you don't pay any extra to see the flop).
Outs and Odds

Pot odds  Can I play my hand profitably?
As you can now determine the probability of completing your draw by making use of odds, the only question that hasn't been answered is how to apply it practically in a game.
Let's make use of the old example again:
We are looking at a true situation from a real money nolimit game. You are on the flop with one opponent and you are holding the cards shown above. The pot is now at $10. Your opponent bets $2. Is it worthwhile to call this bet and pay $2 to see the turn card?
 Pot before the bet from your opponent: $10
 Bet from your opponent: $2
 Possible profit for you: $12
 Bet (which you have to call): $2
As we now know, the odds of hitting your straight on the turn are roughly 5:1 against you. This means that you'll complete your hand one in six times. Let's assume that you'll definitely win the hand if you hit one of your outs. So you'd win $12 one in six times, whereas the other five out of the six times you would lose $2. This is assuming that you would have to give up your hand on the turn if it doesn't improve.
On average, if you call the $2 you would lose $2 five out of six times. In total this is $10. However, you'll win $12 once, so the net profit, which is calculated as the profit minus the losses, is: $12  $10 = $2. It is therefore profitable in the long run to call your opponent's in this situation. As a rule you win 0.33$ (= $2 / 6 hands) in every repetition of this situation.
In this example the pot odds and pot chances come into play. They represent the relationship between the possible profit and the bet which has to be paid and are therefore an expression of the benefit/cost ratio.
In this situation, the pot is at $10. In addition, the $2 which the opponent bet are added to the pot, resulting in a total pot size and possible profit of $12. You have to pay $2 to stay in the game to see the turn card. The pot odds are now $12 : $2 or 6:1.
Like the numbers 6:1 and 5:1 suggest, a simple rule applies:
Since 6:1 is bigger than 5:1, the situation is profitable.
What would happen if your opponent bets $4 instead of $2? On the one hand the possible profit would rise to $10 + $4 = $14. On the other hand, your pot odds for calling the bet would be $14 : $4, which is a ratio of 3.5:1. It would therefore be unprofitable to call the bet. You'd be best advised to fold your hand in this situation because you will lose in the long run.
To explain the calculation: you win $14 one out of six times, and lose $4 five out of six times. This means you lose $4 = $20 five times and win $14 one time. This amounts to a total longterm average loss of 1$ (= $6 / 6 hands)
Discounted / modified outs
Let's go back to the topic of outs and slightly modify the introductory example:
In the part about outs, you have learned that you have eight outs in this situation: any ace or six will make a straight.
Your Outs
What would happen if you encounter an opponent holding the following cards?
The ace of hearts and six of hearts would give you a straight, however these would give your opponent a flush and therefore the better hand. These two cards are no longer of value to you, so we calculate only six outs instead of the original eight. These are called discounted or modified outs.
Your discounted Outs
You obviously don't know your opponent's cards, but there is a certain chance that he is holding two hearts. You cannot assume that you have eight clean outs to make your straight. You have to subtract the number of outs by the number of cards that give your opponent the better hand.
In this example, it is very unlikely that you can give yourself the full number of outs due to the large number of opponents in the hand. The way your opponents play the hand could give away whether they are holding a flushdraw or not.
Another reason to discount the outs is that your opponent could be holding a hand such as:
Hence the four sixes aren't clean outs because they would give your opponent a stronger straight. Only four outs therefore remain.
Your discounted Outs in this case
It is necessary to realistically discount your outs, in order to make a correct estimate of the odds in an incomplete hand. You can almost never give yourself every out, especially if you are playing against several opponents. It is always possible that they are holding a better incomplete hand. They could even be holding your same hand. Many things can happen in a poker game leading to you losing the hand, even though you hit one of your outs.
You always have to ask yourself the following question: which one of my outs actually makes my hand the best hand? If you are holding an OESD and there is a flushdraw possible, you would only be able to give yourself 6 discounted outs by default, rather than the total 8 outs.
Especially on the lower limits, players like to play suited cards because of the chance of making a flush. You therefore need to be relatively strict with yourself and consistently subtract two outs, especially against several opponents.
If you are faced with the question of how many outs you can give yourself, you have to answer the following question first: which better hands are possible and how likely are they? The more opponents on the table, the more likely these hands are. In the lower limits, connected cards like 87, 54 or 76 and suited cards are frequently played, so you need to take this into account.
Conclusion
 Odds are the relationship between: unhelpful cards : helpful cards.
 Pot odds are the relationship between: possible profit : input (bet which has to be paid).
Essentially, a draw can be played profitably if your pot odds are better than the odds for your hand. These are situations in which you can win more by completing your draw than you can if you don't complete your draw.
It is essential for your longterm profit to have understood and learned the concept of odds and pot odds and with them the mathematical basis for poker. Knowing when it is worthwhile to call a bet and knowing how much to bet to make an opponent's draw unprofitable (give him the wrong odds) are fundamental strategic elements of the game. Take the time to really grasp this material, because it will certainly help push your game and your bankroll forwards.
LINKS  

#1 AcessUP, 17 Apr 08 23:44
i dont understand.. if the OESD is 5:1 how come it says that your chances are 1 out of 6? Im a beginner so sorry =/#2 EnRaged, 19 Apr 08 16:56
AcessUP, the original equation is "not helpful cards : helpful cards", hence 5:1 means that on every good outcome there are 5 bad outcomes. But since overall we have 6 possible outcomes (sum of both good and bad ones), the chances are 1 out of 6.#3 megaworld0, 06 May 08 01:31
1 chance out of 6 possible = 5 bad to 1 good. 5+1=6  all possible outcomes ;)#4 gonetrolling, 17 May 08 03:45
why are the odds for a flush draw 2:1 from the flop to the river. I was under the impression that it was still 4:1 could someone still explain.#5 gonetrolling, 17 May 08 04:10
why do the odds change when they are calculated from the flop and then recalculated on the turn. I understand that u only get 1 more card, but if the odds of hitting on OESD are 5:1, should you not call if the pot odds on the turn are at least 5:1 if you had the OESD on the flop?;
#6 matt1234, 18 May 08 17:25
gonetrolling:odds for a flush draw are, you hold 2 flush cards, and you can see another 2 which leaves 9 outs. 9/47 x 100 = 19.1% from flush to turn.
If you dont hit (81% chance) then you have a 9/46 x 100 chance of hitting on river = 19.6% chance. 19.1 + 0.81(19.6) = 34.5% chance from flop to river. This is just over a 1/3 of a chance, hence 2:1
#7 Werkon, 23 Jul 08 10:51
gonetrolling : it is 2:1 because it is flop to river (not flop to turn). Thus 2 cards are dealt which increases your odds about 2 times.#8 Werkon, 23 Jul 08 10:53
I'm sorry for answering again, didn't see that answer. If any mod sees that, please delete my 2 comments, thanks.#9 ole435, 24 Jul 08 09:40
Hi , can someone help me with question 8 and 9 , why is it yes 4:1 and no 5:1 , i mean how do you solve it ?? thanx :)#10 nickital, 18 Aug 08 16:50
hi all!concerning outs and odds, why are cards dealt to other players never included into calculations?
Example: 7 players sitting down; 2 cards per player = 14 already dealt before flop; or even more 14 + 3 community cards = 17 cards after flop. When calculating outs and odds, why shouldn't we consider these cards for calculation too? Thanks a lot!!
#11 nickital, 18 Aug 08 16:55
sorry all, hadn't read the article "discounted outs" yet! just for info, what kind of rule to you apply when discounting outs? Thanks again!#12 TheBrood, 26 Aug 08 00:31
Ole: I was stumped here for a minute too.8. states a bet on the flop. Plus if we call all in we are seeing the river (two cards). Pot odds are 2:1 from flop to river.
9. states a bet on the TURN. So we only see one card. Pot odds are about 5:1 from turn to river.
#13 djflocibus, 19 Sep 08 18:23
I can't understand the answer to Question 8.pot odds= 3:1
Flushdraw odds= 4:1
pot odds < odds
So the answer should be NO.
Why the answer is yes? Please help me!!!!
#14 Aitchy, 20 Sep 08 16:29
sound thanks for the help#15 Skraggy, 01 Oct 08 11:17
nickital:You can't include your oppenents cards in the equasion because you don't know what they are!
#16 mouse89, 05 Oct 08 15:00
cheers#17 c4lyps0, 22 Oct 08 21:49
A great article. I seem to have grasped the concept finally. Now I should work on my arithmetics. :D#18 1pokerpro1, 29 Oct 08 11:40
to djflocibus:the bet is profitable, because you go allin after the flop. your pot odds are 3:1, flash draw odds are 4:1, yes, it seems like a fold, but you have to realize, that you ll see turn and the river card for your call and you wont have to put another money to pot, because you r allin. That makes your flash draw odds 2:1.
pot odds 3:1 > flash draw 2:1
call is right decision
#19 Harold1, 21 Nov 08 16:05
the math doesn't add up.5:1 means you'll win one out of six times, o.k.
2.00 to call means you will win once out of evry six times meaning you have to invest twelve dollars to clear twelve dollars with those odds?
The instruction says you will invest ten and make two dollars profit one out of six times.
Not the way I add it up, that's just bunk and bad instruction.
what crap
#20 Harold1, 21 Nov 08 16:34
I rechecked and the math is wrong. You do not win 2.00 one out of six times in your example on page 4.Ypou have to invest twelve dollars to win twelve dollars.
Which is good enough odds to call with but you do not make "a two dollar profit five times out of six' you will only break even, or even odds with a two dollar bet.
Any profit would only comes if you survive the river and only if your straight holds up otherwise you will only break even one time out of six.
I think the math is going to confuse many.
Even though the call would be right, the instruction is wrong and should be clarified or corrected.
#21 Harold1, 21 Nov 08 16:56
'On average' this means if you call the $2 you'll lose $2 five out of six times. In total, this is $10. However you'll win $12 once. The net profit which is calculated by the profit  the losses, is therefore $12  $10 = $2. Due to this, it's profitable to call the bet of your opponent in this situation in the long run. On average, you'll win $2 every six times in this situation.'My math says you have to invest 2.00$ 6x to win one time which means you only break even. 12.00 invested to win twelve dollars?
Good calling odds but you only break even one time out of six with 5: 1 odds?
#22 Blackov, 06 Dec 08 13:53
The math is correct here. You invest 2$ six times, that makes 12$. But you one time of six you win 14$ (10$ pot + 2$ opp bet + 2$ your call).#23 SadisticNature, 02 Jan 09 19:06
You might want to change the example hands for the discounted out sections. The hands you give as examples discount some outs but also add some outs which makes them misleading (i.e. vs any of the example hands pairing your 2 or pairing your 3 will win the hand). Changing the QJH to the KQH solves the first one. The second one you could use something like 458 when opponent has 87 and you have 32, although this isn't ideal because you could already be dead to 67 and gets a little complicated for beginners on the math.#24 the182guy, 04 Jan 09 16:15
One thing that should be noted, calculating your outs is not 100% accurate because some of your outs might have been dealt to the other players. So say you're on a 10 handed table and have a flush draw on the flop, you can say you have 9 outs but the chances are, some of those would have already been spent because 18 cards from the deck have been dealt to your opponents.So in short, yes calculate your outs but also consider how many cards have been dealt where some of your outs could be dead.
#25 MG815, 07 Jan 09 07:19
I couldn't agree more with Blackov. The math is correct.#26 nikoz07, 21 Feb 09 15:11
Regarding questions #8 and #9:The conditions are just the same, you're going allin on the turn!
Which means 3:1 against 2:1 for both OESD and flushdraw.
Why are the answers different?.. O_o
#27 Rakijan, 23 Feb 09 16:28
What do points 3, 6, 7, 10 and 11 in Outs and Odds chart stand for?#28 LegoMann999, 17 Mar 09 16:24
Very nice article, i am sure this will improve my play a lot#29 Bomberclad, 17 Mar 09 21:05
this article and comments confused me even more. i suggest you improve it.#30 Protagoras, 19 Mar 09 21:22
At first i had the same problem as harold1, but as Blackov mentioned, the TOTAL pot is indeed 14, not 12. I think, however, maybe its useful to clarify that fact in the article to avoid further confusions. But otherwise, i've been a member just a week and my games are already improved significantly!#31 connect1337, 01 May 09 14:58
Oh my head :(:p
#32 Donaldc, 28 May 09 16:40
I was told by a friend who had read many poker books that you can calculate your odds easily by taking your outs and multiplying by 4% to hit on the turn and 2% to hit on the river. Is this applicable?#33 bax14, 07 Jul 09 10:27
hmmm well that was easy.... next..not
#34 yourcashgohere, 10 Jul 09 18:06
and what is the conclusion...you can't make so many calculations when you are playing..therefore this strategy is in many cases unhelpful...#35 theboydave, 20 Jul 09 15:36
The maths and ratios can seem a bit difficult but if you can learn this stuff it will give an edge also makes you think that some of your outs are can be opponents outs also.#36 Ciduletz, 22 Jul 09 21:14
Pot before the bet from your opponent: $10Bet from your opponent: $2
Possible profit for you: $12
Bet, which you have to call: $2
I have OESD in my hand. My question is: the 10$ POT that remains for me and my opponent.. is a pot that i contribuited with what sum ? Because to see the FLOP i need to pay, my question is that.. the math is made without counting to what i contribuited to that 10$ pot to see the flop ?
#37 johnboy1, 28 Jul 09 21:44
bloody hell i need bronze level to read this i even ant got that as well as my bonus what a joke carnt even learn poker what a blag!!!!!!!!!!#38 bakoy, 20 Aug 09 04:01
lol @ 37 who is silver#39 revorx, 20 Aug 09 08:36
Hmm i missing something ? In some comments peoples are asking about the answers in some numbered question. Is here some kind of quiz with questions what i`m missing or they are talking about the examples in the article ?#40 mihahr, 24 Aug 09 23:36
Interesting to see quite a number of people doubting the math and written facts in this article  since I have just read the previous article about most common mistakes of players, one of them being not believing the pokerstrategy.com :)Anyway, this definately looks like a science fiction, before you put all of your thoughts to it. This must be one of the earliest 'filters' for good and bad (or let say casual) players.
#41 KalilTactuk, 26 Aug 09 04:42
@36It is true. Here it says you need to invest $2 to win $14 one time out of six attemps. But this makes no sense, you'll be losing all you have invested so far in the pot five times and winning it only once, i dont think theres a way to make a profit out of this. I know the example is just to be clear about when you should call or fold, but the math is erratic.
Let me know if im wrong. Thanks.
#42 kriuks, 30 Aug 09 18:13
Kalil, winning EVERY pot is impossible. Poker profits in a long term.#43 chanwaiki6203, 31 Aug 09 12:25
how can i see0#44 Lizocain, 01 Sep 09 14:39
The second example:"In addition, the eight outs for the straight mentioned in the previous example are added, from which two have to be subtracted, namely the ace and the six of clubs because they have already been taken into account in the outs for the flushdraw. This makes a total of 9+6=15 outs:"
9+8=17 outs.
#45 thejugador, 18 Oct 09 15:54
Hi,I've read somewhere for a ruff estimate after the flop to multiply the outs by 4.5 and add 2 for turn odds%.and after the turn to multiply the outs by 2.5 and add 2 for river odds%
Is this good does anyone know,I hope it is!
#46 Chippolata, 23 Nov 09 13:52
to #22regarding the first exemple of "Pot odds  Can I play my hand profitably?"
Hmmm well if the 6 is your out it could also be a gutshot to a higher straight out for your opponent ;)
He would have needed to do a pretty brave bet on the flop then though :p
I think this is just waived regarding the low probability for it to happen.
Even though if this actually happened you would most likely lose your entire stack to your opponent...
Implied odds :D ?
#47 Thunderin, 29 Nov 09 03:33
Does anyone know of any poker tool which helps you practice and master the calculation of pot odds vs. odds so that you can calculate it very fast? I tried to Google something like that and couldn't find anything.#48 minimAlleast, 06 Dec 09 20:43
Here Phil Gordon simplified it all:http://www.youtube.com/watch?v=kn97ymhgp_w&feature=PlayList&p=2E6FDD56DBEB493D&index=2
#49 Melkboer, 20 Dec 09 01:07
thanks#50 36bullets, 21 Mar 10 12:07
Good article.I have one question though, if you have an OESD but the flop are all overcards, do you exclude the outs that will give you a pair? I think that it should be excluded but I want a pro to confirm...
Thanks!
#51 kerko13, 05 Apr 10 21:11
good article...main part of this is the math...#52 nel42988, 13 Jul 10 06:26
the ratio difference between the odds in flop and turn differ because of the number of the cards that will be show. 3 cards in the flop and 1 in the turn that is the reason why it has different ratios.nice article...i'm loving poker more and more thks to u
#53 nel42988, 13 Jul 10 07:48
#50 question im not a pro but i think it should be excluded since it will beacome underpairs..it will be put on the unhelpful outs...#54 Miske91, 01 Dec 10 17:06
Kalil, winning EVERY pot is impossible. Poker profits in a long term...#55 valivvvv, 12 Dec 10 06:54
"These are situations in which you can win more by completing your draw than you can if you don't complete your draw."well, i guess in ALL situations you can win more by completing your draw than if you don't :)
#56 steliosvol, 11 Jan 11 11:28
Why do you write 7:1 and not the graphics in % ??how match % is 8:1 for example?
thank you.
#57 pinkwille, 15 Jan 11 22:48
in outs odds table are many mistakes i think... Flushdraw + Gutshot 9 + 4 = 13 outs (not 12)
 Flushdraw and OESD (known as monster draw) 9 + 8 = 17 outs (not 15)
but what is *** and a pair i dont know...
#58 David, 17 Jan 11 10:24
@57: Hi pinkville, in case of Flushdraw + Gutshot you have to discount 1 out because we already counted it for the flushdraw. The same case for Flushdraw and OESD: Flushdraw 9 outs + OESD 8 outs MINUS 2 outs = 15 outs#59 cpers, 07 May 11 18:53
just a quick question about the charts:#1 5:1, does it mean one out of 6 you lose or one out of 5?
#2 BackdoorFlushdraw (two cards of the same suit on the turn and the river), how come the outs are 1 instead of 10? I know it should be less than 10 because it needs 2 cards. But how do you get this numbers?
#60 webbous, 15 Jun 11 13:20
When you are trying to figure out the pot odds is it not important to also take into account the money that you put in?For example, if you look at the example they used in the $10 pot and $2 bet, doesn't it matter how many opponents went into it to determine how much money you put in? Like would it make a difference if it was you and one other opponent, or if it turned out there were 5 opponents when you only put in $2 or do we disregard what you have already done?
#61 SvenBe, 15 Jun 11 17:02
webbous: only the ratio between the money you put in and the money that already is in is important for the calculation. However if you are on a draw it sometimes is better to have more opponents since that would (possibly) mean more $ if you hit#62 FruitNinja, 03 Aug 11 07:05
Hi thejugador and Thunderin, to make it fast, a quick estimate may be ok. I've read something similar, for odds% making it, multiply outs by 4 for turn and by 2 for river. Estimate but close...#63 marinank, 21 Mar 13 16:28
Can some one tell me when I`m looking odds from flop to the turn(one card) and when are looking odds from floop to the river(2 card)???