Joined: Mar '11
Location: Canada
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Okay, so I'm working on a little something, and wanted to post this, kind of to make sure I have all the math correct. Please comment and let me know what you think, and if I've made any mistakes.

------------- Pot Odds ------------------------------

Calculating pot odds is relatively straight forward. You take the total pot size, and divide it by the bet you need to call. For example, if the pot is $5 and your opponent bet's $2.50, then you need to call $2.50 into a pot of $5. This translates into 2 to 1 odds.

Implied odds take pot odds a step further. Instead of merely calculating the odds for the bet in proportion to your outs, you need to calculate what you expect the pot to be by showdown. So if you're facing a bet of $5 into a $15 pot, you're getting 3 to 1 odds. Instead, if you think your opponent will bet on the next streets as well, you calculate what the pot will be based on those bets. So essentially, if you're facing a bet of $10 into a $15 pot, but you think the pot at showdown would be $50, then you can figure you have 5 to 1 odds instead.

This is especially useful, if you're facing a pot with multiple players in it.

----------- Implied odds - hand 1 ---------------------------

We're 4 handed with 98d on the button. It folds to MP who 3xs. 1 caller in LP, folds to us and we limp. SB and BB also Limp.

Board comes AH 6d 7H. SB immediately bets $400, SB and MP fold and it's on us.

Here we're facing a bet of $400 and a call. We're facing a call of $400 into a pot of $750, which is less than 2 to 1 odds. Very poor odds considering we're likely drawing to only 8 outs. which works out to be about an 16% chance to see our draw on the turn. To make it a profitable draw, we'd need around 6 to 1 odds.

But if we consider what we expect the pot to be by showdown, this is a profitable situation to call. Given the stack size in relation to what the pot will be, we can safely assume that the bet on the turn will likely put at least one of the players all in. That means realistically, we can expect the pot to be at least $4350, so we're calling $400 to draw to a $4350 pot. this works out to be around 10 to 1 odds. Keep in mind, if we blank the turn, we can easily fold and it'll still have been a profitable play.

Calculating Implied does take into consideration that you are making assumptions, so realistically you have to consider your opponents, and how you think they may react if a potential scare card hits the board.

--- Draw odds ---

Drawing odds are relatively simple to factor. You Take the number of cards you think will give you the best hands, these are your "outs". On the flop, you'd take the number of outs you have, and multiply it by 4 if you chase to the river. So if you had 12 outs, you'd have roughly a 48% chance of improving, or approximately 2 to 1.

On the turn, you take the number of outs you have, and multiply it by 2. So again if you had 12 outs, you'd multiply that by 2 which would give you a 24% chance, or roughly 4 to 1.

To calculate 1 card ie: on the flop or on the turn, you'd take your # of outs and multiply by 2 since you're only drawing 1 card.

We're heads up in the SB with QJh, and we 3x it. BB calls with AcAs and we see a flop of 10h 9c 2h.

We're behind in the hand, but we've got a LOT of outs. Any heart, any k or any 8 will give us the best hand.

In total we've got 16 outs. We don't count the Kh or 8h twice since they're already calculated. 16 x 4 = 64% chance of making the best hand. Approximately 2.5 to 1 odds

----------- Calculating Outs - Hand 2 Flush draw and mid pair --------------

Again, we're heads up, this time in the BB with 10d 10h. SB 3x's with kc kd and we call and see a flop of Ah 5h 9h.

Again, we're behind in the hand, but have some outs. Any heart or 10 will give us the best hand. In total, we've got

11 outs, 11 x 4 = 44% chance of making the best hand. Approximately 2.2 to 1 odds.

--- Discounting outs ---

One important thing to consider, when calculating your outs, is to consider if one of your outs will give your opponent a better hand.

If you think your opponent is drawing to a flush, you need to discount the cards of that suit that make your straight as either of those cards would give him a better hand.

For example in this hand, we have an open ended-straight draw, which normally gives us 8 outs, however since either the k or 8 of spades gives our opponent a flush, we've only got 6 outs.

In this scenario, you'd have 6 outs instead of 8 for a total of 6x4=24% chance of hitting your hand, giving you 4 to 1 odds.

Joined: Jan '10
Location: Indonesia
Age: 53 (M)
Posts: 1463

Good article Retribution though I ever read it before, Thanks you remind us. But I want to ask your ( and mobster) advise . How far pot, implied odd etc effective ? in context bring us to win. My experience told me that's not good enough, time in online poker games too fast to make complete analysis and didn't give me winning decision Should be compare pot odds with our outs, right? Even many times we had better outs but lost to opponent who had little out ( ex, I had 12 out - the villain had 2 outs at turn - but river give villain's card )

Or I lost understanding about pot / implied odd - outs relationship. please share and advise.

Joined: Oct '09
Location: Belgium
Age: 53 (M)
Posts: 2847

Nice article, but an important remark:

Odds.

"So if you had 12 outs, you'd have roughly a 48% chance of improving, or approximately 2 to 1.

On the turn, you take the number of outs you have, and multiply it by 2. So again if you had 12 outs, you'd multiply that by 2 which would give you a 24% chance, or roughly 4 to 1. "

48% = 1.1 : 1 odds 24% = 3.1 : 1 odds

The "1" are the odds in favour of... The "3.1" are the odds against of...

So 3 to 1 means roughly 24% times 3 against = 3.1 24% times 1 in favour of = 1 3.1 : 1

Joined: May '09
Location: Spain
Age: 41 (M)
Posts: 1261

Hi guys!

Good article retribution. Maths are important in poker. Maths are almost all in poker. An right use of it make us better players. Specially the implied odds, concept without no one must play poker.

Joined: Apr '09
Location: Portugal
Age: 36 (M)
Posts: 4764

This outs calculation is very useful. I have never thought about it that way, always thinking this data was only possible to have with poker odds calculators. Instead, if we use our brains while playing, we are making a lot better to ourselves. We are exercising our maths and at the same, we are having fun with the game. Thanks for the explanation. Now for admin, it could be useful if it was created a personal segment in BRM site where we could put our preferred forums/news/polls, in case we would like to consult them in the future. It would be a lot more easier to find them. I am saying this because this thread is really useful and I believe, in the future, this can be extremely helpful for the game and also for showing new mobsters good work that has already been developed around here.

Joined: Jan '12
Location: United Kingdom
Age: 28 (M)
Posts: 1204

Falkiry there already is a section of the forums for threads like this. Retribution should have posted it in 'poker strategies' instead of 'poker forum.' Really good thread though reritbution, should help new members learn some moves such as floating, even though I already know this, its symbiotic to me.

Edited by sadamman (Thursday, March 22, 2012 @ 13:48 GMT)

Joined: Mar '11
Location: Canada
Age: 37 (M)
Posts: 1490

Posted by IslandJack: Nice article, but an important remark:

Odds.

"So if you had 12 outs, you'd have roughly a 48% chance of improving, or approximately 2 to 1.

On the turn, you take the number of outs you have, and multiply it by 2. So again if you had 12 outs, you'd multiply that by 2 which would give you a 24% chance, or roughly 4 to 1. "

48% = 1.1 : 1 odds 24% = 3.1 : 1 odds

The "1" are the odds in favour of... The "3.1" are the odds against of...

So 3 to 1 means roughly 24% times 3 against = 3.1 24% times 1 in favour of = 1 3.1 : 1

Roughly....

I don't know if that's right or not. You need to factor odds out of 100. Thus, if you're a 50% favorite, you SHOULD have 2 to 1 odds. Same as, if you must see a $2 bet into a $4 pot, $4/$2 = 2 to 1.

The thing is, there's conflicting information on how odds are calculated precisely. The majority seems to assume that pot odds are an equation of bet to call vs pot, however there are a few examples I've come across, where ithey calculate bet to call vs pot + bet to call.

Ie: If the bet is $2 and the pot is $4, then you'd factor it as $2+$4 = $6. $6 / $2 = 3 to 1.

Of course I want to be 100% sure the math is correct before I publish anything concrete, thus why I posted this for scrutiny

Joined: Aug '10
Location: Germany
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Posts: 1615

Pot odds or odds and outs are the standards in poker and every player must calculate them if they want a winning player longterm. And there are enough poker schools to lear about that and everybody can download start hand charts etc.

Joined: Jan '11
Location: United States
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Damn good article and hard to retain being relatively new. Will print this one out to reference and learn by heart. It's good to post topics like this for some of the inexperienced players that spend time reading in the forum. It's made me a better player! At least I win on a regular basis although I don't play for big stakes. Thanks and Good Luck to All!

Joined: Mar '11
Location: Canada
Age: 37 (M)
Posts: 1490

Here's an excerpt I found on wikipedia:

Odds are most commonly expressed as ratios, but converting them to percentages will often make them easier to work with. The ratio has two numbers: the size of the pot and the cost of the call. To convert this ratio to the equivalent percentage, we add these two numbers together and then divide the cost of the call by this sum. For example, the pot is $30, and the cost of the call is $10. The pot odds in this situation are 30:10, or 3:1 when simplified. To get the percentage, we add $30 and $10 to get a sum of $40 and then divide $10 by $40, giving us 1/4, or 25%.

To convert any percentage or fraction to the equivalent odds, we subtract the numerator from the denominator and then divide this remainder by the numerator. For example, to convert 1/4 (or 25%), we subtract 1 from 4 to get a remainder of 3 (or 25 from 100 to get a remainder of 75) and then divide 3 by 1 (or 75 by 25), giving us 3, or exactly 3:1.

Joined: Nov '09
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Posts: 2367

Posted by Greenmohave: Damn good article and hard to retain being relatively new. Will print this one out to reference and learn by heart. It's good to post topics like this for some of the inexperienced players that spend time reading in the forum. It's made me a better player! At least I win on a regular basis although I don't play for big stakes. Thanks and Good Luck to All!

Over time you would be surprised how quickly you can make these calculations while playing, it really becomes second nature.

Interesting thread overall retribution, always good to see poker threads on the Bankrollmob forum. One of the things to remember when you are calculating pot odd and such is that it is reliant on how accurately you have put somebody on a hand. For instance, if you raise in middle position with mid pocket pair, and the small blind reraises you substantially and you put him on AK/AQ you might make a call you think is profitable, when actually he has AA/KK/QQ. Again, more playing time and familiarity with your opponent will let you make that decision more accurate.

Joined: Apr '09
Location: Portugal
Age: 36 (M)
Posts: 4764

Posted by sadamman: Fakiry there already is a section of the forums for threads like this. Retribution should have posted it in 'poker strategies' instead of 'poker forum.' Really good thread though reritbution, should help new members learn some moves such as floating, even though I already know this, its symbiotic to me.

You know you’re right, but if you look for it you will not find that may articles written as well and as clear as this one. Retribution put everything in simple words, avoiding massive lecture to understand what, in fact, is simple. But it would be nice if we, as users, have our own case/box/segment, so we could put apart anything we wanted to.