About Pot Odds and Implied Odds When Playing Draws

Surprisingly I couldn't find any posts detailing this, so I'm going to do my thing.

A Common Scenario

With 100bb effective stacks, EP opens for 4x preflop, there are 2 callers, and we call on the button with 9 8 . Both of the blinds call. The flop pot is now 24bb. The flop comes T 7 2 , giving us an open-ended straight draw. The BB bets 16bb and it folds to us. To decide if a call is +EV, we need to understand a little about pot odds and implied odds.

Pot Odds

Our pot odds are a ratio of the current size of the pot (before we call) to the size of bet we are calling. In our above example, after the BB bets the pot is 16bb + 24bb = 40bb and we have the option to call 16bb, making our pot odds 40:16, or 2.5:1.

Our Chance to Hit

There are 47 cards in the deck that we haven't seen yet. Of these 47 cards, 8 will complete our straight. We call these 8 cards our "outs". Since 8 cards will complete our straight, that leaves 39 cards that do not complete our straight. The ratio of cards that aren't outs to cards that are outs are the odds against us hitting. Here those odds are 39:8, or about 4.9:1.

Putting 2 And 2 Together

Our odds of hitting are 4.9:1 against, and our pot odds are 2.5:1. Since our pot odds are lower than our odds against hitting, we are going to be losing money if we don't get more bets from our opponent the times we hit. To illustrate this, realize that for every 1 time we hit our draw on the turn, there are going to be 4.9 times that we miss our draw. When we hit our draw, we are winning the 2.5 units (40bb) in the pot, and when we miss our draw we are losing 1 unit (16bb) that we called. For every 1 time we win 2.5 units, there are 4.9 times that we lose 1 unit. Clearly this is a losing proposition if we don't make more money the times we hit.

The Role of Implied Odds

Implied odds are like pot odds except they consider the money we would win from our opponent the times that we hit our draw. Suppose in our example we think that we will get an additional 50bb on average from our opponent the times we hit. This means that in addition to the 40bb pot, we will get another 50bb from our opponent the times that we hit our draw on the turn. Now we are calling 16bb to win 90bb (the 40bb pot plus our opponent's additional 50bb), making our implied odds about 5.6:1. Since we are about 4.9:1 to hit our draw on the turn, and our implied odds are higher than that, it is a profitable play.

The Key

The key to making +EV decisions based on implied odds is to have a realistic idea of how much you stand to gain from your opponent(s) when you hit your draw. You cannot assume that you will always stack them!

Another Basic Example

On the turn you have the nut flush draw. Your opponent bets 36bb into a pot of 50bb and after you call his bet you will have 45bb left behind (and you have your opponent covered). You have 9 outs and there are 46 cards left in the deck, so that leaves 37 cards that don't help you, so your odds against hitting are 37:9 or 4.1:1. You must fold here since the best implied odds you could be getting are 36+50+45:36 which is 131:36 or about 3.6:1.

An Example That Most New People Don't Play Correctly

On the turn you are heads up in position and have your opponent covered. You hold 4 3 on a board of Q 8 2 7 . Your opponent bets $5.60 into a pot of $8. You figure that the times you hit a flush you will get your opponent to pay off another $10 when you hit, giving you implied odds of about 4.2:1. You must fold! While this might seem like a slightly +EV call since you are about 4.1:1 against, your odds aren't as good as they seem. First, you're always losing against bigger flushes. Second, the 2 and the 7 could give your opponent a full house. The lesson to be learned here is that if you're not drawing to the nuts, you need much better implied odds.

Now go forth and make money.

Very, very good writeup Spoon.

insta-digest imo

I vote insta-digesting this post as well, nh.

nice. 2+2 should stick THIS in the front of their books.

nm look at the post right below this, Villain was drawing to 65

Converted

PokerStars No-Limit Hold'em, $1.00 BB (8 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com

Hero (Button) ($100)
SB ($110)
BB ($104)
UTG ($32.70)
UTG+1 ($126.70)
MP1 ($156.05)
MP2 ($60)
CO ($61.95)

Preflop: Hero is Button with 5, 7
UTG calls $1, 4 folds, Hero bets $5, 2 folds, UTG calls $4

Flop: ($11.50) 4, 2, J (2 players)
UTG checks, Hero bets $6, UTG calls $6

Turn: ($23.50) 3 (2 players)
UTG checks, Hero bets $14, UTG raises to $21.70 (All-In), Hero calls $7.70

River: ($66.90) 9 (2 players, 1 all-in)

Total pot: $66.90 | Rake: $3

Originally Posted by spoonitnow

The key to making +EV decisions based on implied odds is to have a realistic idea of how much you stand to gain from your opponent(s) when you hit your draw. You cannot assume that you will always stack them!

When I started learning about implied odds a while back, I went through this phase where I'd start calling way more than I should have because I always though I'd get paid off. This wasn't the case and I was rewarded with a nice downswing and a healthy dose of tilt to go with it. Spoon is spot on about this being the key to implied odds. You left out any mention of stack sizes, but I hope most of us here would think of that anyway.

nh

In IRC today, CrazyAndy27s suggested he didn't understand implied odds, and was asked to read this thread. This is what he learned.

<CrazyAndy27s> you work out a conservative estimate of how much more you will get on later streets if you do hit then add that into your pot odds equation, to see if you are getting the right implied odds to call
<CrazyAndy27s> that right?
<spoon_brb> NO
<spoon_brb> YOU SUCK
<spoon_brb> QUIT POKER
<spoon_brb> AND DIE
<spoon_brb> AND BURN IN HELL
<spoon_brb> Actually yeah you can do it like that
<Stax> QFT
<Stax> well the burn in hell part

You forgot to mention bluff outs and the chance you're ahead or have other outs.

I won a $2.5k pot once with QJs unimproved...

Originally Posted by Fnord

You forgot to mention bluff outs and the chance you're ahead or have other outs.

I won a $2.5k pot once with QJs unimproved...

It's a good point. One thing about implied odds is that it helps to have good reads on your opponents, in 2 respects:

1. Do your opponents have a showdown hand, or are they bluffing or on a draw like you are? (Fnord's QJs won because his opponents were either bluffing or semi-bluffing.) And related to this, do you have a showdown hand (for instance, if you have a pair and a straight draw, sometimes your pair is good even if you miss the straight)?

2. Are your opponents likely to pay you off if your draw comes in and it is fairly obvious? For example, if you have the ace of clubs, with 3 clubs on the board, and a fourth club comes, is this villain likely to pay you off or to put you on a big club and fold?

As a general nature, the less obvious your draw is, the greater implied odds you have. For instance, one of the least obvious draws is the straight draw with suited one-gappers. Say you have T8 and the board is A97. If a jack hits, and your opponent has TPGK, he or she will probably pay you off.

On the other hand, the most obvious draws are things like 4 cards to a flush, and 4 cards to a straight. 3 cards to a flush falls somewhere in the middle, along with a sequential 3 cards to a straight (i.e., 987).

Similarly, trips (I mean a second card on the board to match the card in your hand, not a set) are pretty obvious, whereas 2 pair (made by pairing each of your hole cards) is not.

The less obvious your draw is, and the more likely your opponent is to pay you off, the greater your implied odds.

This is great stuff.

It's telling you things you already know, but in a way that makes you really think about and appreciate them. So you understand something afterwards, that you thought you did before, but now realise that perhaps you didn't quite.

I think that after I am done re-reading all the digest articles, I am going to find all of spoons & rentons posts and real all of them (and the posts that respond) as I am sure their will be some real diamonds of strategy hidden amongst them.

Great Post!

brilliant thread... cheers

added to favourites!!!

Calling flop bet ip you can sort of discount chances that you will get outdrawn to a better flush a little cause there's a chance you can get a free card on turn. Also note that one important spot to discount your implied odds a little is when you have an OESD on a two to a flush board because when it comes out with the third flush card people will be wary of draws and you will have pretty big reverse implied odds.

Good thread btw

Good thread

Lots of good info I can use.
Thanks

Very nice! Thanks spoonitnow, I understand it a little better now.

Originally Posted by Darth Candy

Very nice! Thanks spoonitnow, I understand it a little better now.

No problem. If you need anything else I'm xojessahhox on AIM and you have my e-mail.

Originally Posted by spoonitnow

Putting 2 And 2 Together

Our odds of hitting are 4.9:1 against, and our pot odds are 2.5:1. Since our pot odds are lower than our odds against hitting, we are going to be losing money if we don't get more bets from our opponent the times we hit. To illustrate this, realize that for every 1 time we hit our draw on the turn, there are going to be 4.9 times that we miss our draw. When we hit our draw, we are winning the 2.5 units (40bb) in the pot, and when we miss our draw we are losing 1 unit (16bb) that we called. For every 1 time we win 2.5 units, there are 4.9 times that we lose 1 unit. Clearly this is a losing proposition if we don't make more money the times we hit.

1) So if we think we cannot extract anymore value from villain, we just fold? What if we have good odds, but don't think we can extract more value? Just play on and bet again, then win the pot as it stands, right?

2) Is knowing you can extract more value from Villain based solely upon our reads on him?

3) What about if we don't hit, but the turn card is one that offers a nice bluffing opportunity? How do we alter our approach then, still taking into consideration the poor odds?

4) Is converting odds to EV a simple matter of "If you aint got good odds, then it's -EV"? Seems a bit obvious, but my mind just has specific questions that it needs answering to clarify it to myself.

Thanks

1)yup
2) yup
3) you factor in scare cards as "bluff outs" into your pot odds equation (e.g you have a flush draw on a K high board and you read your opp as having 1pr ks or worse with q or worse kicker, you can factor in that you'll be able to bluff an A turn a fair portion of the time (say 75 %), you can add 75% of said As into your pot odds equation (3/4). so with a flush draw you have 12 outs- 9 to hit flush and 4 to hit an A turn where you can successfully win the pot with a bet 3/4 times.
4) kind of, but obviously we need to calculate HOW MUCH + or - EV it would be.

Wow, and all that in the quick 30s we get before we get autofolded! Guess I'll be finding the fold button a lot more until I've learnt this down to a T.

Very goood!

Thanks again spoon

Great stuff.

I was wondering, what is the % of flush or straight draws you do guys actually play in your game? All in relation to what has been written above of course. I guess in a loose/weak game you get much more implied odds than in higher stakes for exemple. Would you say 50%-75% ? Or it would be way to high a % ?

In a loose/weak game you're going to be getting more value for your hand, so you can call with less than optimal odds, in a tougher game, you'll have a lot more fold equity so if you can bet/raise that helps negate the poor odds/poor reward.

So in tougher games, semi-bluff on draws get much more value than in loose games if I get it right. Most of the time, or depending on the player, you'd better call with good implied odds in loose games than trying to make s player fold his hand...specially when they are not willing to...

Right, except in the 'tougher' games your not really getting more value from your draw, you're semi-bluffing for a couple different reasons: 1.) Villain can fold a made hand (albeit a weak one) or his air 2.) You're disguising your hand a bit for when you hit instead of taking a c/c line then waking up when the 3rd flush card hits or whatever 3.) You're building the pot so that when you DO hit, you get paid more instead of trying to take a c/c line and it happens to check down and you end up with a tiny pot with a strong hand.

And obviously with a calling station you don't have nearly enough fold equity to try to semi bluff since he's calling with any pair/any draw or even air, but at the same time you can get a lot more value from your hand when you do hit since he's probably not thinking about your range and he'll still blindly call down when we're good.

And in loose games when you finally miss your draw on the river, if the river card is a scare card giving you a good opportunity to bluff, is it worth it to give it a try? Or it's most of the time a move that has negative EV on the long run ?

Vs a calling station, you're probably not going to want to try to take it away without a hand that often, especially if you have A or K high since that will be good a fair portion of the time (if its been checked down especially). If you have like 23s no pair, then it wouldnt hurt to throw a bet out there occasionally since you have 0 chance of winning the pot if it's checked through.

Thanks for your answers dranger.

when spoon ruled the world.