Mathematics of Poker: Odds and Outs
by Sammy
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Video to the Article
Introduction
In this article
The cards that are helpful to you (outs).
Balancing risk and reward
Not every out is actually helpful
A draw is a hand that isn't made yet, but would be if another helpful card c…
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#1
mouse89, 05 Oct 08 15:04
ok#2
AATACK, 04 Jan 09 01:28
I'm a little bit confused about one thing - how do they calculate $14:$2 to become 3.5:11 - isn't it 7:1? - this is the one thing I have had a hard time to understand - could somebody please show me the calculation model for this, so that I'll be able to practise this kind of calculation - I've pasted the chapter that the calculation came from - What if the opponents were to bet $4 instead of $2? There would now be $14 in possible winnings. Your pot odds, however, would now be at $14:$2, or roughly 3.5:11.#3
gheecko, 08 Jan 09 23:47
nice#4
zipenkoff, 20 May 09 18:22
im sorry, but i dont understand, what exactly i must look, at the chart, to get info how many odds do i need, to call exact situation, or not, my english is not so good, so if somebody would explain it to me a little, i would really be grateful.#5
Smileyphil, 18 Jun 09 18:36
Basically zipenkoff you have two different figures.Firstly the odds that you make your hand. Say a flush draw on the turn. You have 9 cards left to catch the flush out of a deck of 46. This means your chance of making you hand is ~20%. (9/46)
Secondly the odds you are offered in the pot. If there is $8 in the pot and the villain makes a bet of $1 then you have to call $1 to potentially win $10. Your pot odds are then ~10% (1/10)
If the pot odds are lower than the chance of making the hand then you can make a strong call.
Another way of thinking is that 4/5 times you lose $1, but 1/5 of the time you make $10. So your profit = (1/5 x $10) - (4/5 x $1) = +$1.2
Someone correct me if I'm wrong.
#6
tomzs, 01 Jul 09 11:27
#5 Smileyphil, 18 Jun 09 21:36"If there is $8 in the pot and the villain makes a bet of $1 then you have to call $1 to potentially win $10. Your pot odds are then ~10% (1/10)"
No, your pot odds are 9:1 , you have to call $1 to potentially win $9 pot
#7
Primezipper, 02 Sep 09 03:38
ok so what im confused about is the flush draw odds concept. if i have a flush draw on flop i have 9 outs. which would mean im a 38:9 or about a 4:1. if im 4:1 that means im likely to make my hand once out of 5 times which means i will hit my flush only 20% of the time. ive always thought flush draw on flop means 35% likely to hit. someone please explain.#8
loldaklol, 11 Sep 09 04:10
i think thats because your only calculating from flop->turn or turn->river, in that case it would be 20%, but if your calculating from flop->river you have 2 chances to hit your flush which would raise your chances to 35%#9
xponentx, 20 Dec 09 00:50
I have a question about example 1, if anyone is able to clarify."The same calculation applies on the turn. However, now you only have pot odds from 2.1:1. However you cannot give yourself 12 outs anymore, as the pair in the community cards doesn’t make a full house probable, but possible. You still got 8 outs left, you’d need pot odds 5:1. Your decision is made. You fold."
Now, you are still drawing to the flush and straight, but now it's possible both these hands are already beaten by a full house. So which outs are we discounting here? How are we reaching this figure of 8 outs?
#10
Maldoneves, 11 Jan 10 02:01
xponentx! I have the same question...For me, the outs would be 11 not 8, cuz u still have 9 (less the As - ace of spades) + 4 (kings) to hit gutshot.
It would give you almost the same 3:1, what would take you to the same action btw: fold!
Can someone clarify the real out count for the turn round on exercise 1?
#11
Maldoneves, 11 Jan 10 02:03
opps... my mistake above: its 8 (9 less As) + 3 kings (not 4) (since the Ks is already on the count of the flush).but my doubt is still on...
#12
Koshburger, 15 Jan 10 10:26
ok#13
Navrark, 01 Feb 10 13:00
The way I learned pot odds was by using multipliers, and I am sure the result is the same.If the number of outs is 8 on Turn for example - with an OESD - then I divide 8 by the number of cards remaining in the deck to get a percentage:
8/46x100=17.39%
Then I take the number 100, and divide it by the percentage:
100/17.39=5.75
So as long as the pot is 5.75 times larger than the bet I must make I am good to go. Of course I round up to 6 in order to give myself a safety cushion and to make the math easier.
As well, the majority of people who calculate odds also add their current bet to the total, so if the pot is $60 and I need to call $10, the pot will be $70 after I make the call so they would give 7:1 odds.
#14
Hennung, 24 Feb 10 14:00
If I've understood this article correct, I believe #13 is wrong in his calculation of his example. Let's take a look at it:You're on the TURN, got an OESD = 8 outs. There are a total of 46 remaining cards in the deck. Out of those, only 38 cards are helpful to you (46-8 = 38). This gives us 38(unhelpful):8 outs. Now what you want to do is getting the ratio to x:1, so you divide both sides with 8 giving you a 4,75:1 ratio of making your hand. Which is rounded up to 5:1, just as the "outs & odds-chart" clearly shows.
The same calculation applies to the pot odds. Let's say there is 20$ in a pot, and the villian bets 8$, giving you a total pot of 28$. It will cost you 8$ to call, which gives the ratio 28:8, and again you want to the right-hand side to equal 1. Thus 28/8 : 8/8 = 3,5:1.
If we combine the two examples we now got 5:1 odds on hitting our draw, and 3,5:1 in pot odds.
As written on page #2 in this article: "If the pot odds are higher than the odds against you, it is profitable to stay in the hand. If they are lower, you will lose money in the long run by staying in the hand."
This means that if you look on the left-hand side of the pot odds, and compare it to the left-hand side of the odds of hitting your draw, you will only call if the pot odds number is higher than the odds number. In our example 3,5 is NOT higher than 5, thus you FOLD!
Please correct me if I'm wrong here! And if this is one of the correct ways of thinking, please write a comment about it to help other players.
#15
mancamanca, 26 Apr 10 17:49
kk#16
VlatkoCRO, 19 May 10 18:07
12$ : 2$ is in the case the opponents raises 2$ - 6:1 pot odds14$ : 4$ is in the case opponents raises 4$ - 3.5:1 pot odds
(if pot on the flop is 10$, opponent raises 4$ --> 14$ pot, bet is 4$)
#17
PaTaPaTaPoNn, 13 Aug 10 07:06
this is the hardest part for mei can never count the odds before my waiting time went out
#18
keviginge, 01 Sep 10 23:34
I think it may just be an error ( Typo )on the article,$14 : $2 = 7:1
#19
trikornepenal, 10 Sep 10 10:14
"However you cannot give yourself 12 outs anymore, as the pair in the community cards doesn’t make a full house probable, but possible. You still got 8 outs left, you’d need pot odds 5:1."I don't understand how we get 8 outs...
#20
Ectoz, 23 Oct 10 09:48
seriously now,who will bet 2 dollars into a 10 dollars pot? :D i faced quite the lot of draws and you almost always face 1/2 pot bet or 2/3,even worse a pot bet.So you almost never get right odds.Implied odds are vital.#21
WillShakes, 15 Dec 10 21:16
This is great stuff, and it is good to get back to basics often with odds and outs. However, my problem is that I often get called by idiots who don't know this info, even though I've bet enough to NOT give them pot odds, and then they hit! Which unfortunately negates the whole ratio of profit over time because I get more losses. Last year things were going well, but this year it seems bad beat after bad beat. Sorry for the moan. I guess my question is, is there an easy way to deal with this? Or should I just play higher stakes than my bankroll so that I know players will play proper poker instead of coin tossing?#22
WillShakes, 15 Dec 10 21:31
As an example. Just watched a hand that I often suffer.All fold to MP1 where a guy limps (600).
MP2 raises 2700 (donk)
all folds back to limper who re-raises 10,200.
Pot odds for anything other than AA or KK are null and void, right?
MP2 calls... (sigh)
flop comes A-high
Now, admittedly the rest of the hand by MP1 was tilted as he only had QQ, but pre-flop he shoulds been safe with the re-raise.
He bet 5K into the flop, and MP2 went all in, which was called by MP1 (QQ).
Turns out MP2 only had A10o!!!
For gods sake! What's the point learning these techniques if donks-r-us come in and ruin it all?
#23
WillShakes, 15 Dec 10 21:34
Or does MTT strategy on odds and outs require different thought? I have had this at cash tables too where play tends to be looser, as usual. So you would expect better. This is in a tourney where either player could've gone out (similar stacks), started with 1989 players, and at this stage only 300 left.Incidentally when I say this happens to me often, when it does I get out after the flop, rather than lose all my chips with QQ against an A-high flop.
#24
paksrott, 30 Dec 10 17:17
lissen me guys 1 example was pot 10 and bet 2 that means 12 pot and ure call 2 means 12:2 and answer is 6:1 and now read good second example pot 10 bet 4 that means 14 pot and ure call 4 means 14:4 answer is 3.5:1 all u guys who get that second answer is 7:1 made wrong math u putdet 14:2 but in example was 14:4 so that means u failed and example rules XDXD#25
belayd, 22 Mar 11 10:50
One thing I need clarification on: If the pot is $10 and villain bets $2, that makes the pot $12. But if you also call $2, doesn't the pot increase to $14? So how is it that you're paying $2 to win $12 rather than paying $2 to win $14?#26
winmaster76, 31 Mar 11 01:54
In pot odds of 12:2, the 12 means the POSSIBLE WINNINGS, not the amount that will be in the pot, since the $2 is invested by you it doesn't count as winning it.#27
hurla, 01 May 11 09:20
@WillShakes. It doesn't matter if someone calls your bet eventhough they weren't getting the right odds for a flush draw. And it doesn't matter if they get lucky and hit it. What matters is that you made the correct play, a play that has a positive EV over time. Your bet forced them to make an incorrect call. If you make that play 100 times, you will show an overall profit, eventhough sometimes your opponent will get lucky. It's frustrating when you make the right play and still lose the pot, but take comfort in the fact that you will profit from this play over time.#28
brobz, 05 May 11 16:13
hand odds are easier with the Rule of Four and Two, Take your outs on the flop and multiply by 4 to get your chances of hitting on the turn, on the turn multiply your outs by 2 to get you chances of hitting on the river. this rule works really well and is only ever a percentage or two off. Then you look at your pot odds and get a percentage out of that. By like somone said you almost never get your odds to draw, Implied odds are key#29
shakalak, 16 May 11 00:01
yeah, the Rule of Four and Two is a great short cut. However I think you multiply your outs by four on the flop to determine your percentage chance of hitting by the RIVER and by two on the turn for chance of hitting on the river#30
ssopht, 12 Jun 11 11:57
I don't understand example #5 and the discounted outs:"You have 8 outs and two over cards, which allow you to add another 2-3 outs."
Does it mean 2 x 3 ? If not, then which are the still viable outs after the turn:
"You only have 9 remaining outs that would be certain to give you the best hand."
#31
Tr3LoS, 27 Jun 11 07:20
Really helpful article, I should practice my calculations a bit.#32
foxicoxi, 15 Apr 12 19:11
its much easier if u multuply the outs by 4 for the turn, and 2 for the river. the result is an accurate percentage that you will get a card u want