Implied Odds

While looking through various entries, I found an interesting point on implied odds:

Originally Posted by Erpel

Here's what I think (using flop as an example). Pot is $X, bet is $Y, I think 10 cards (adjusted outs) will make me the winner on the next street. So my odds to win are 37 to 10 - or 3.7 to 1. To be profitable I need implied payout odds better than that. In other words, I need to win ($Y * 3.7) - $X on average on later streets for the call on this street to be profitable. It's a dead simple calculation when facing a bet and I can't understand it's not more widely used or documented.

Now many of us have an idea of what implied odds are, but in the heat of the game we need to be able to calculate these on the fly amongst other things. Now none of us want to be losing players, let alone break even, but without being able to calculate the implied odds to pay us off, it seems inevitable to happen. Now in the brief time playing I've taken notes and used round numbers to simplify it and help make plays more profitable.

I'm going to start with 4 outs and go to 15 to give you a better idea of where you stand. I'll give a minimum and an ideal that I've used.

4 outs This is giving you 10.75. Minimum is 11, ideal 12
6 outs This is giving you 6.83. Minimum 7, ieal 10
8 outs 4,88. Minimum 5, ideal 8
9 outs 4,22, Minimum 5, ideal 7
10 outs 3.7, Minimum 4, ideal 6
12 outs 2.91, Minimum 3, ideal 4
15 outs 2.13, Minimum 3, ideal 4

Now as you can imagine, the more outs you have, the less you need to really make up because of the number of times that you will hit. Now the ideal that I've set from 6 outs to 12 are in decending order by 1, which is fairly easy to memorize, with 8 being 8.

Based on table image, what I know of my opponents tendencies, and the reads I have on them I will adjust it, but always keep in mind the minimum so that I always keep above break even. It's by no means completely accurate as far as calculating implied odds, but it's a hell of a lot faster and I know that the minimum is still a slight profit.

o rly?

Can you give a few hand examples?

Does this mean you'll always call if you have 10 outs and are getting 6:1 on the pot and his stack? Or are you still making the necessary considerations as to whether or not you'll likely extract enough money to make a call profitalbe?

I'm just a bit confused by the idea of 'minimum' and 'ideal' values, unless you're using these to make your decisions in certain spots.

Do you never call with 15 outs if you think you're getting a price of 2.5:1, since it is below your minimum?

The 2% per out per street approximation isn't too difficult to do and i'd say is probably at least as reliable as rounding approximations.

Gotta agree with loony. Post up some examples please!

hrm interesting. continue please.

I don't have any examples off hand. I play mostly live at the moment until I can get some money online.

As for calling with certain outs, for me that depends on a number of variables such as effective stack sizes, the opponent's range I put them on, and my past reads on them. There were times I've folded when I was getting 6:1 but knew I was beat and if I hit I wouldn't be paid off.

For me this is more what I take into account when I'm calculating outs. Say I have 10 outs, I will hit that 10 out of 37 times. Well for that play to break even I need to make 3.7*the bet. I just rounded that up to 4, but really try to push for 6 for more of a profit.

looney, I do agree with you that the 2% per out per street is likely just as easy and gets you to about the same spot as well.

Unless I have misinterpreted your chart, I don't think of implied odds in as fixed numbers or equations as you have seemed to have it laid out. The concept of implied odds is relatively simple, but the difficulty of applying implied odds isn't so much in the calculation in my opinion so much as it's in your ability to predict the future in terms of how your opponent will act. For example, if there's a $100 pot and you're on a flush draw with one card to come and villain bets $50. Your pot odds are 25% and your probability of hitting the flush are about 18%. So the question is: IF you hit your flush, will you make-up that extra 6% ($14) from the villain? Some villains won't put another penny in the pot once the flush comes. Some will give your their stack. Other villains will do everything in between.

So, the hallmark of good implied odds play in my opinion is your ability to predict future villain play if you hit your draw. Some of the main factors to consider are obviously your villain's tendencies, but maybe more important is the type of hand you're drawing to coupled with board texture. Drawing 4 cards to make a flush won't pay nearly as well as a well disguised 86s on a A752 rainbow board. There are more factors to consider like your image, position, stack sizes, and the usual suspects, but your ability to assess the situation in the future is the key. I've had some hands recently where I called without the right pot odds, but thought I had the right implied odds and then ended up hitting my card BUT not getting a penny more. To me, even though I won the pot, in the long run, I really lost and just got lucky. That is important: if you don't make up the difference, you really lose and anything you get past what you need to break-even is your profit.

I know a lot of players seem to think that it's acceptable to set mine with pocket pairs IF the villain has a full stack or deeper, but that isn't really the only factor to consider. Will the villain give you his stack OR enough of it when you hit to make up the 10 to 1 dog you are to make your set? Many players just assume that if the villain HAS the stack to pay you, he will. Again, that is not always the case. Maybe he won't. Also, off topic, if villain gets you to put in more than 10% of your stack pre-flop heads up with a small pocket pair versus his over pair, villain has already won because 10 times you'll lose at least 10% and only one time you MIGHT double up, which is break even best case.

I think I understand what you're saying, about not making only slightly +EV plays. I suppose we rarely want to draw to a hand when our implied odds are only just better than 0EV, since, while we expect to get paid, not doing so every now and again is going to make this -EV (and 0EV plays = variance, which makes me ).

Just to be pedantic: when you have 10 outs you expect to hit 10 in 47 times. Odds format isn't all that mathematically pleasing imo, but is certainly helpful if we consider pot equity vs hand equity in the same odds format.

I would usually just say: I have 10 outs at 2% each so i've got 20% equity. Then I say:

"how many 20s are left to make up 100%", and the answer is 80% / 20% = 4. So 4 times I lose, 1 time i win, which is 4:1. Then i compare pot:bet or (pot+stack):bet. I won't say, I win 1 in 5 times, except in retrospect.

If I were to do things properly, maybe if i'm only getting 4:1 on the pot and need to know my equity more exactly. Then I say:

"47 cards in the deck, the probability I win is 10/47 ('10 in 47') so what is the fraction of wins/losses: it's 10/(47-10) = 10/37 = 1/3.7 because of the 47 cards that come, I don't lose on 10 of them".

A wins to losses ratio of 1/3.7 is a probability of 1/4.7 is a % equity of (1/4.7)*100 = 21.28%. Also we might say,

"I'm a 1:3.7 favourite or a 3.7:1 underdog".

Jason, I definitely agree. I think I may have written it a bit vague or confusing. The way I view implied odds, like you, is the futurity of the actions subsequently to the one you're making. Obviously there are several factors to take into account but you also have to think what your opponent may do in the future. If your card(s) hit, do it also hit their range. Can we expect them to fire out a second or even third barrel based on the cards to come?

I think in your example that you gave in your first paragraph goes in line with what I'm saying. The actual variable to multiply is something like 4.38:

(4.38*50)-200=19 so it gets you in the ball park of the 14. That just to break even. I rounded to 5 which would give you a slight profit. You do have to consider out of the 8 times that you would hit you would need to make that up to turn a long term profit; however, that is dependent on effective stack sizes and whether the op will bet again when you hit, or c/f to your bet.

The example of using a 100 is a little easier to figure out without taking into account of the minimum and ideal. I developed this for more of odd numbered pots that you're in say the pot is 78 and facing a bet of 32 as the round numbers make it a bit quicker. However, I am still very new to the game so any criticism would be greatly appreciated, but based on the small sample of games I've played this has helped figure out certain spots I was in, while taking into account the other variables such as effective stack size and reads on the opponents.

Loony, I see what you're saying. I am new to the game, but I thought of this in a kind of attempt at looking at certain spots as a more long term +EV play. Granted we need to take into account lots of things, but when it comes to whether I should call, raise, or fold, it can be beneficial to make plays that are more +EV in the long term as far as the br is concerned. I think a lot of us take for granted that fact. Making a slightly +EV play can be beneficial in that hand, in a vacuum, but looking in the long term, getting that slightly +EV play to be a little bit more can help pad the br or your stack those several times that you make a similar play but don't hit and lose.

I don't think my post was probably that useful actually. I essentially ended up talking about terminology.

As for implied odds (since I didn't say a single thing), I tend not to like using formulae in-play (or much at all). If my equity to win is 4.38:1, the pot is $200 and it's costing me $50 to call... then i say: "I'm getting 4:1 on the pot, so I need to win at least 0.38*$50 on later streets."

The problem I have with using the Erpel formula above is that, when you multiply the $50 by 4.38, you are essentially adding $50 to $50 to $50 to $50, then you have to multiply 0.38 by $50 and then add it on. Then we subtract the pot. Whereas, only one step in this process is used if we first make an observation (our immediate odds on the pot and how far off they are what we need) that need not be stored in memory.

This is just me and the way i deal with numbers though so might not be that useful, but i'd have thought it a more natural way to work out amount needed to extract.

Yeah, that's one of the reasons I had a problem with it too and just decided to round up a little to make it slightly faster and show more of a profit than break even. I like your way of doing it as well. Maybe I just tried to over-simplify it for myself to make things quicker, but perhaps over-complicated it in the end.

With .38*50, I'd just round that up to .4 and just make up 20 over the next streets.

With .38*50, I'd just round that up to .4 and just make up 20 over the next streets.

Are you playing draws with the intention of making up a certain amount on later streets? I don't mean to pick, this just sounds a bit odd to me. When you make the call you're expecting to make the money on later streets based on your strategy for later streets. Like, i've done it myself, thought "OK i just need to make a few extra $ and this set mine worked out ok."

Basically, if i'm calling in position, i expect him to bet or check/call down. Out of position, things are going to be a little tougher unless my hand is pretty well disguised.

I'd be rounding the 0.38 to 0.4 yeah, but in truth, i'm rarely gonna know my equity to 2 decimal places.

Maybe I just tried to over-simplify it for myself to make things quicker, but perhaps over-complicated it in the end.

Just whatever makes you feel most comfortable. I don't like learning things to memory and I dont like using formulae (more to remember) so it doesn't work for me. What I would say is not to get too caught up on place accuracy. Your 'minimums' are a good idea in that they are nice easy numbers to work with, but so I suppose are the %s we deduce in a 2% per out per street approximation. I'd just play around with things, see what you are best at.

Well I've played with a few different things, but using this has allowed me to quickly compute it and more or less have more time to focus my attention to other important things. To me, this seems more in correlation to effective stacks to kind of see if certain plays may or may not be worthwhile because I won't get paid off well enough when I hit.