# Poker odds

#### dj11

##### Legend
Silver Level
As I started reading this I thought to my own self "DJ, try and get a poker odds for dummies type thing going".

I didn't hate math, it was my favorite subject in school, until I hit the Calculus wall. I even aced my inductive logic final. With age however my whippersnapper like mind has dulled to a tongue depressor like edge on math issues.

The bigger reason for me to get Super System was the odds section. Problem there is the intrepretation of those table takes a long time to master.

What I think is needed is a clear narrative of not only quick easy ways to deduce odds, but how those odds relate, and why they are pertinent. It will be the clear narrative part that is the hardest.

After 15 months or so of intense online playing, I have developed an intuitive grasp of the odds. This is where I need to fine tune that grasp. The end result will be that though I could not spout off the odds for any specific situation, I intuitivly know them. Watching Chris Ferguson, math doctorate, do no better than others partly because he seems to rely to much on odds, suggest they are not the be all and end all of play. But no one will deny the importance of long term thinking in poker.

#### medeiros13

##### Rock Star
Silver Level
I think Medeiros' post has helped a little though. So, if you have a 36% chance of making your hand, you shouldn't call off more than a 36% size of pot bet? Did I read that right...

You've got it JQ. Not that I want to confuse anyone but sometimes you may call if pot odds are slightly off if you think you can earn a bet on the river on your made hand. To be honest though, I'm not all that good on explaining implied odds. Maybe someone can help with that explaination.

#### bubbasbestbabe

##### Suckout Queen
Silver Level
Let me see if i have that right. Say a pot is 1500 chips. You have a flush draw. (4 cards on flop). What you are saying is that I should call any bet of 540 and less? Then what happens on the turn for the odds?

#### NineLions

Silver Level
TSo if I'm on a flush draw, I know I have 9 outs (2 on the board, 2 in your hand) so I have a 36% chance of hitting on the turn.

Isn't this a 36% of hitting on the turn and river combined? A little less than 20% on the turn and another less than 20% or so on the river?

#### medeiros13

##### Rock Star
Silver Level
Isn't this a 36% of hitting on the turn and river combined? A little less than 20% on the turn and another less than 20% or so on the river?

I don't believe this is the case. I use the rule of 4 and 2 that is discussed in Phil Gordon's book. He says multiply outs times 4 on the turn and times 2 on the river to get your odds for each street.

BBB, you've got it right after the flop. Now on the turn, that number is reduced to 18% (9 outs times 2 now)

#### NineLions

Silver Level
I don't believe this is the case. I use the rule of 4 and 2 that is discussed in Phil Gordon's book. He says multiply outs times 4 on the turn and times 2 on the river to get your odds for each street.

I dunno medeiros.

Page 178:

"According to this "Rule of Four," I have about a 20% chance of catching a winning hand on the turn or the river."

Then it becomes the "Rule of Two". The difference between the turn and the river is one card, so the percentages are not going to drop in half.

#### F Paulsson

##### euro love
Silver Level
Gordon's "rule of two" is your chance of hitting your hand on the next card. So that holds true if you're on the flop and want to know if you can afford seeing the turn, or if you're on the turn and can afford to see the river.

The rule of four, besides being a weird thrille type book, is your chance of getting your hand in TWO cards. I.e. from flop to river. Not used often, since you rarely get two chances to hit your hand for the price of one, tournament all-in decisions not included.

#### medeiros13

##### Rock Star
Silver Level
Thanks Ninelion and FP, I've never seen the 4 and 2 rule explained that way. I guess you could also use "four" if you attempted to raise on the flop to try and get a free card on the turn as well as all in situations.

So FP, since you're more of a limit player, how do you use odds in LHE when you have a flush draw. Do you use 20% on the turn and 20% on the river to determine a call or fold?

#### bubbasbestbabe

##### Suckout Queen
Silver Level
I'm posting a hand here just for the odds discussion. I just wanted to see how I figured them out to what the math whizzes do. On each turn what are the odds for calling and why? I also know the comments about folding and all the other yada-yada. I just want to know how odds would figure into this hand. This isn't the greatest one to do it with but it will work.

pokerstars Game #8247939395: Tournament #42068918, \$4.00+\$0.40 Hold'em
No Limit - Level I (10/20) - 2007/02/02 - 18:27:20 (ET)
Table '42068918 4' 9-max Seat #9 is the button
Seat 1: ZacharyPants (1420 in chips) is sitting out
Seat 2: klitkat (2600 in chips)
Seat 3: annazara (1450 in chips)
Seat 4: newfie4life1 (1820 in chips)
Seat 5: billybuster (3090 in chips)
Seat 6: aknewbie (1420 in chips)
Seat 7: tyoung12 (2140 in chips)
Seat 8: Bounty4me (2100 in chips)
Seat 9: riverme204 (1220 in chips)
ZacharyPants: posts small blind 10
klitkat: posts big blind 20
*** HOLE CARDS ***
Dealt to klitkat [Qc Th]
annazara: folds
newfie4life1: raises 100 to 120
billybuster: folds
aknewbie: folds
tyoung12: calls 120
Bounty4me: folds
riverme204: folds
ZacharyPants: folds
klitkat: calls 100
*** FLOP *** [Ah Ts 4c]
klitkat: checks
newfie4life1: bets 100
tyoung12: calls 100
klitkat: calls 100
*** TURN *** [Ah Ts 4c] [Ks]
klitkat: checks
newfie4life1: bets 1600 and is all-in
tyoung12: calls 1600
klitkat: folds
*** RIVER *** [Ah Ts 4c Ks] [Jc]
*** SHOW DOWN ***
newfie4life1: shows [Kc Kd] (three of a kind, Kings)
tyoung12: shows [As Kh] (two pair, Aces and Kings)
newfie4life1 collected 3870 from pot
*** SUMMARY ***
Total pot 3870 | Rake 0
Board [Ah Ts 4c Ks Jc]
Seat 1: ZacharyPants (small blind) folded before Flop
Seat 2: klitkat (big blind) folded on the Turn
Seat 3: annazara folded before Flop (didn't bet)
Seat 4: newfie4life1 showed [Kc Kd] and won (3870) with three of a kind,
Kings
Seat 5: billybuster folded before Flop (didn't bet)
Seat 6: aknewbie folded before Flop (didn't bet)
Seat 7: tyoung12 showed [As Kh] and lost with two pair, Aces and Kings
Seat 8: Bounty4me folded before Flop (didn't bet)
Seat 9: riverme204 (button) folded before Flop (didn't bet)

#### NineLions

Silver Level
If you don't mind me taking a stab at it (I'm one of the ones still trying to learn myself):

First off, ignoring your call of the 6x BB raise from early position w QT,

I'd assume one or both villians have at least paired the ace or have a high pair. You have middle pair so you're probably behind. Any Q or T helps you, and there are 3 Qs and 2 Ts left so that's 5 outs. There are no flush draws to worry about that might cancel the value of your cards. You have a runner-runner straight possibility, but that's not worth considering at this point but the 3 Qs may become dangerous as it might help someone else get the straight instead of you. AT really has you beat and if someone has that, then only at least 2 Qs or the runner-runner helps you.

Still, (as as a non-expert) I'd read it as 5 outs, meaning 5 x 2 = 10% chance of you getting one of these cards. You could also use the 4 rule since it is the flop and say 5 x 4 = 20% of getting either a Q or T on either the turn or river combined.

When it comes to you you have to call 100 to an existing pot of 570, so you have pot odds of 5.7 to 1. With the 2 rule you have 10% or 9 to 1 (90% to 10%) so don't have the odds to call. By the 4 rule you haev 20% or 8 to 2 or 4 to 1 so you do have odds to call.

Now at the turn you now have a straight draw so all 4 J's now help you, but, the three Qs may give someone else the straight so it's more complicated to value. Plus, since it was raised preflop, an AK or even KT has 2 pair which your potential QQTT pairs won't beat. I'd now dismiss the Qs but add the Js and calculate 4 Js plus 2 Ts remaining will help you, so now 6 outs. (as it turns out, getting one more T wouldn't help 'cause now you've got to beat a set of Ks)

So betting at the turn with only the river to come you have to use the 2 rule, so 6 outs x 2 = 18%. The pot when it gets to you is 3,870 and you have to call 1,600, so I'd estimate that by calculating 1,600 x 2 = 3,200, so around 2.3 to 1 pot odds. 18% is less than 20% = less than 4 to 1 which is less than 2.3 to 1, so you don't have the odds to call. On top of which, if someone has AA or KK, another T doesn't help you in which case you only have 4 outs.

Okay, that's my guess. FP, or someone, want to correct me?

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#### F Paulsson

##### euro love
Silver Level
I don't think I ever fold a flushdraw on the flop in limit hold 'em. Keep in mind that my odds can never, ever, be worse than 3:1 and it would be nearly impossible for me to mess up and not be able to get the rest in using implied odds.

Edit: I started writing this reply a long time ago, so I missed the posts that came in while I was waiting to post it. I'll address those when I get back home!

#### F Paulsson

##### euro love
Silver Level
Okay, in regards to BBB's post:

The first thing we must remember is that when we're counting outs, we're in reality making an estimate based on our opponent's range of hands. For the sake of simplicity, let's say that our opponent accidently showed us his cards and we know that he has AK in the above example. How many outs do we have, then?

On the flop, we have 5 outs: Any queen and any ten will give us the best hand. We have a backdoor straight draw as well, but that's rare enough to not really bother with (probably comes out to about half an out) at this point. Five outs, and using the "rule of two," gives us about 10% chance. So 10% of the cards will give us the best hand, and 90% of the cards will do it for him. The odds, then, are 90:10 or nine-to-one.

(If someone's unsure of why 90:10 = 9:1 let me know and I'll explain that, too.)

On the flop, we can profitably call one bet if the pot is at least 9 bets.

On the turn, things suddenly change. He hits two pair; us hitting a lower two pair is clearly useless so the three queens that earlier were good for us are now useless. However, the king on the turn gives us an inside straight draw. That's four new outs, that weren't there before. Plus, the two remaining tens are good for us.

So that's six outs. Now we're looking at (2*6=)12% chance to win. 12% will make us win, that leaves 88% to make him win. 88:12 = 44:6 = 22:3 = 7.3:1

We need a little over seven bets in the pot to profitably call the turn.

It really just comes down to counting your outs and multiplying them by two to figure out the percentage, but once you have that down pat - you can essentially memorize it for everything up to 10 outs if you want; in a limit game, you're unlikely to be in a situation where you should fold something with more than 10 outs anyway - the difficulty becomes correctly counting your outs, which in turn takes hand reading skills.

Counting your outs is one of the most essential skills of limit hold 'em, and is the thing that the really bad players - most players, actually - suffer the most from. Either because they do it poorly or because they don't do it at all; I'm not sure.

#### NineLions

Silver Level
If you don't mind me taking a stab at it (I'm one of the ones still trying to learn myself):

So betting at the turn with only the river to come you have to use the 2 rule, so 6 outs x 2 = 18%.

6 x 2 = 18? No wonder I keep getting beat on the river. Sheesh

U

##### Rising Star
Silver Level
Hi...

I'm new to the forums but am a math guy and I usually play by the odds (though not always) depending on the table. I prefer 6-player games for that reason.

Anyway here is my take (and sorry for the length of the post as I just kept rambling)

Dealt to klitkat [Qc Th]
*** FLOP *** [Ah Ts 4c]

A 6-bet preflop probably means a high pair or 2 big cards, or a bluff, but with a weakish hand like QTo I would generally credit the hand.

So at this stage (ignoring T4)...

You're behind against Ax, KK, KQ, QQ, QJ, JJ, TT, and 44. While it's possible the raiser could have a smaller pair it's pretty likely he (or the other limper) has one of these so it's a good idea to assume you're behind here and base a decision figuring you have to improve to win the pot without bluffing.

If opponent has AA you need runner runner (see bottom).

The odds from the rule of 2/4 are only that you improve your hand not that you'll win the pot so reads are critical in figuring the real odds. You might have 5 outs to improve your hand (3 queens and 2 tens) but against certain hands not all of them will help you.

For example, if opponent has QQ, TT, AQ, AT then you only have 2 or 3 outs which means a 4%/6% chance to hit the card on the turn or 8%/12% by the river. At best this translates to about 7.3:1 (at 12% you win 12 times out of 100 so you lose the other 88 times so your odds are 88 against 12 or 7.3:1). Your real odds would usually be worse in this situation since you're unlikely to get a free card here.

Otherwise you have 5 outs which means roughly a 10% chance to hit the card on the turn or 20% by the river so at best you'd have a 4:1 shot if the turn is free*.

Since you're up against 2 players, you might already be drawing dead since even if the turn misses the raiser and helps you, the other limper might improve from it also. As a charter member of the paranoia patrol I view the odds above very conservatively if I'm not heads up. To call the bet, not to raise, I might assume the 7.3:1 odds against me increased by half to maybe 10:1 or even 15:1.

*** TURN *** [Ah Ts 4c] K♠

This wasn't a good card since now Kx and QJ also has you beat. But at least you picked up a gutshot straight draw though any player with a queen or jack also has one. Remember that if a queen falls on the river you might have 2 pair but it could have given someone the straight. So the fact that you had around a 4*3=12% chance of picking up 2 pair by the river it might actually cost you money against hands like JJ, QQ, QJ. This is where playing by the odds is really tricky.

You can't expect someone to hit a runner runner straight of course but it's something I keep in mind after I see this flop, especially if I think an opponent has a hand like KQs or QJs where he might have a fairly decent chance of hitting runner-runner to a good hand.

As the above posters mentioned any of the 4 jacks gives you a straight, but there is also a flush draw now and a J♠ might give someone a flush which beats you so rule #7 of the paranoia patrol says to only use 3 jacks as outs in this case. The difference is pretty small though (8 outs vs 9 outs or about 5.3:1 vs 4.6:1) so in most cases it wouldn't affect my betting too much. At worst I might just call with a straight if the J♠ came instead of raising.

Something else to consider is that someone might already have the straight (QJ) and you are drawing to a split pot which potentially cuts the odds the pot is giving you in half. If the pot is 1000 and there is a 200 bet you are getting 6:1 pot odds which migh be worth calling. But if you are drawing to a split pot then you are betting 200 to win 600 which is only 3:1. While a split here is unlikely, it happens a lot in Omaha so it's just something to keep in mind when figuring what odds you really need.

*** RIVER *** [Ah Ts 4c Ks] J♣

OK you would have made the runner-runner straight and won the full pot if you stayed in. But I wouldn't look at it that way since you made the right decision considering the odds as you miss it the vast majority of the time. We always look back and think of the pots we could have won but rarely look back and think what a great fold. Anyway, look at it as getting to see how your opponents play AK and KK!

Now if you want to figure out your chances of hitting runner runner from the flop, there are about 1,100 possible combinations of turn+river cards (1,081 actally) so count the number of combinations that works for you.

KJ -> 32 possibilities
QT -> 12 possibiliies
QQ -> 3 possibilities
TT -> 1 possibility

That's a total of 48 ways you have of hitting runner-runner. (am I missing any?)

So you have a 48 out of around 1100 chance of hitting a big hand by the rivver which is about 4.5% (or around 21:1 which partly explains why I get beat by runner runner so often in limit games). This is only worthwhile if you are looking to figure the odds of making a hand at the river when you see the flop. This is the same for the rule of 4 which also looks at both cards. When you think about it though, runner-runner is both cards helping you while the rule of 4 is the chance of just 1 of the 2 cards helping you.

So if you have 5 outs on the flop, then your chance to get 1 card to improve by the river is 4*5=20% so figure that half the chance of hitting that big hand is already in your rule of 4 odds so add 4.5%/2 to get 22.5% which lowers the odds from 4:1 to about 3.5:1. It might not seem like much but it really comes into play when you have a suited hand and/or overcards where you get more outs and more runner-runner possibilities. For example, if you have 3 of a suit on the flop there are an additional 45 ways of hitting the flush (about a 4.2% chance).

Hope this helped - sorry for rambling!

----

* BTW this is a rule of thumb and works for typical hands but fails for certain hands with lots of outs.

U

##### Rising Star
Silver Level

KJ -> 32 possibilities -> should be 16
QT -> 12 possibiliies -> should be 6
QQ -> 3 possibilities -> should be 3
TT -> 1 possibility -> should be right.

That means 25 possibilities instead of 48 which is around 2.3% (42.5:1). Half of this is about 1.2% bringing the net change to rule of 4 odds from 20% (4:1) to 21.2% (3.7:1).

Late at night so I hope I'm right this time - will double check tomorrow.

#### withawedge

##### Visionary
Silver Level
Tenbob,

You stated earlier you could do a "Dummies" guide for odds etc.

Does your offer still stand?

Thanks

#### F Paulsson

##### euro love
Silver Level
What is it you feel is missing from the Odds for Dummies guide that is already in the articles' section? Do you want more specifics, less specifics, more examples, charts..?

#### bubbasbestbabe

##### Suckout Queen
Silver Level
Ok I'm a getting this slowly. One question, pot odds. Unmasked used this set of figures and I want to make sure I've got this right. Please bear with me because I'm handicapped,(blonde).
The pot is 1000. there are two people betting,yourself and the villian. Villian bets 200. Now let me state what I get the formula for figuring out this. 1000+200(pot and bet)/number of players=pot odds. 1000+200/2=6:1 pot odds. I don't know if this is right. But it is the only thing I can figure for the figures Unmasked used. If this isn't right, what is the correct formula for this?

#### dj11

##### Legend
Silver Level
For those of you who know odds, we that struggle with them know you have those odds, and the calculation of them internalized to the point they become intuition.

What we who have not intuitionalized (???) the odds factor yet want is a fast way to do so. Personaly, as I read Super System, I found some new ideas, but in many cases I found out what it was I was doing intuitively, and in several cases never able to rationalize.

Best quick example of that would be raising 3x the BB rather than a simple 2x raise. The difference in who stays is remarkable.

Once I had internalized that, it became intuition. Now I know I for one, need to have a much better grasp on the card odds, pot odds, implied odds, and expected value. Then I can at least have a chance to grasp reverse implied odds.

How to do this? Personaly I read as much as I can before becoming blurry eyed. I have slowed down my play online to make an effort to calculate not only the odds, but what the other player might be thinking he is thinking about what I am thinking. I am much better at the what was I thinking thing. I need to discount the him thinking about me thinking about him a bit, and increase the odds calculation part.

Thus the need for the Odds for fish story. We should probably refer to our quest this way to prevent copyright issues.

Might be a series of exercises, questions, examples. Might be that perfect description of the issue. Or 10 people saying the same thing differently collected together in an article.

FP writes very clearly, and Unmasked has a fair style. Learning, and teaching though are sometimes magical. A simple word at the right moment, can teach more than a lecture at the wrong moment.

Sorry about my rambling.

Still seeking.

Oh, Yeah!, I have no doubt that I, and probably most everyone else here will at some point get this. It just happens. We will wake up one morning and it will be there. The process of getting there is the tricky part.

#### Stefanicov

##### Legend
Silver Level
ok i got a brain and was good at maths and i get the odds to chase theories tho i dont use figures i know basically the chances in round about ways and if it is very tight i will do the maths but what i dont get r implied odds does any 1 have an easy way to explain those please

sorry if im hijacking bbb

#### bubbasbestbabe

##### Suckout Queen
Silver Level
No, any question on odds here is fair game. The only thing that should be kept in mind is to really spell out what you mean and what your answer is. Like, what are implied odds? Others may not know what you asking about. And sometimes that includes me.

U

##### Rising Star
Silver Level
Ok I'm a getting this slowly. One question, pot odds. Unmasked used this set of figures and I want to make sure I've got this right. Please bear with me because I'm handicapped,(blonde).
The pot is 1000. there are two people betting,yourself and the villian. Villian bets 200. Now let me state what I get the formula for figuring out this. 1000+200(pot and bet)/number of players=pot odds. 1000+200/2=6:1 pot odds. I don't know if this is right. But it is the only thing I can figure for the figures Unmasked used. If this isn't right, what is the correct formula for this?

When I calculate my pot odds my only concern is what the bet to me is and what the pot is when I bet. The number of players and any previous bets I made don't really matter (well ok they matter but not for this).

Pot is 1,000
Villain bets 200 making the pot 1,200.
The bet to me is 200

The odds you are getting = win:lose. Here that is 1200:200 or 6:1.

Odds of 6:1 means that if you make this call 7 times, lose 6 times and win just once you break even.

Losing 6 times means you lose your 200 bet 6 times (6*200=1,200).
Winning 1 time means you win the pot (1,200).

When you calculate the odds this is a quick way to doublecheck.

Other examples

If villain bet 500 the odds would be 1500:500 or 3:1.

If villain bet 100 the odds would be 1100:100 or 11:1.

Another way of looking at it is what pot odds you are giving with your own bets which is equally, if not more important (see bottom). If you bet the pot you are always giving 2:1 to call while betting half the pot gives 3:1, etc.

Implied odds

Implied odds is more of a nebulous area since implied odds are basically pot odds that includes potential future bets by your opponents. In our example, suppose there is one other player who has yet to act but you are sure he will call and not raise if you call as well. Then you can include his 200 call and the implied odds are 1,200+200:200=1,400:200=7:1 (which happens to be his pot odds but as he is a calling station he ignores them - notice how better position gives you better pot odds).

Now suppose this betting was on the turn and you have a gutshot straight draw (e.g. you hold KJ and the board is AT73 rainbow). The only card that can help you here is a queen (which gives you the nuts) so you have 4 outs.

The rule of 2 says your chance of winning is 4*2=8% which means the odds against hitting the straight are (100%-8%):8% or 92:8 or 11.5:1 (to be exact, there are 46 unknown cards, 42 don't help and 4 do so the odds are actually 42:4 or 10.5:1). However, your pot odds of 6:1 isn't enough to call a bet when you are 11.5:1 against winning the pot, so figure you need to have implied odds of at least 12:1 to call this bet. How much more betting do you need on the river if the queen hits to get the implied odds up to 12:1?

Suppose the betting goes as follows

Pot=1,000
Villan bets 200
Pot=1,200
You call 200 (1200:200=6:1 pot odds)
Station calls 200
Pot=1,600
Queen hits on river
Villain bets 200
Pot=1,800
You raise to 1,000
Pot=2,800
Station folds
Villain calls 800
Pot=3,600.

In this example, your pot odds are 1,200:200 (6:1)

Your implied pot odds are 2,400:200 or 12:1 since you believe the station will call the 200 bet on the turn and villain will bet and call your raise on the river for an additional 1,000 (1,200+200+1,000=2,400). You don't count your own future bets in the implied odds since the assumption is you're only going to bet more if the river gives you the nuts.

If the river isn't a queen, you throw your hand away. If the river is a queen then you need to ask yourself if villain will bet and call a large enough raise to make the call on the turn worthwhile. To get the proper implied odds for your gutshot straight draw he'll need to call a substantial raise (in fact he'll need to put an additional 1,000 chips on the river). His pot odds to make this call are Pot+Your bet:His call

The pot after your raise is 1,800+1,000=2,800.
The bet to him is 800.
His pot odds are 2,800:800=7:2.

Would he call the raise?

P.S. Sorry for the long post - I often write like this just to be sure I understand something as I make loads of corrections along the way.

Last edited:

#### F Paulsson

##### euro love
Silver Level
I'll try the ultra-brief explanation:

Pot odds = the pot - to - the amount to call.

In the picture above, my pot odds are 5.5 : 3.

(I hope it works; I sat in only to take the picture, so technically, this post cost me a buck )

#### F Paulsson

##### euro love
Silver Level
Addition: This is completely regardless of how many people are in the pot with me.

Poker Odds - Pot & Implied Odds - Odds Calculator