Weekly Tournament Discussion. ICM
A few weeks ago, C9 made a post with different situations involved and in one situation we had JJ against A6s and the question was if we wanted a call or a fold seeing as we were short stack and the blinds we really high in comparison to our stack. A lot of people (including myself har har har) assumed that we wanted a call but on further calculation by ICM, it showed that the more profitable play in the long run was a fold. A lot of people were confused by this and did not want to accept the math and that is why I thought it was a must to get a post like this going. Yea I know limping vs raising was the topic that won the poll but due to some shenanigans in that thread, it was decided that this would be a better topic to discuss.
A few things
1) Independent Chip Model or ICM is a way of showing how much your current equity is, in a tournament, based on the payout structure of the tournament and the stack sizes of the players left.
2) It is a way of assessing risk/ reward of 1 play against the other (eg, shoving from the SB with 5bb left or just folding).
3) It deals with long term and not just 1 game seeing as some one might run good/ bad for a couple games and equity takes some time to even out.
4) It relates more to SNG play and final table play but before you can really go on, you would need a good ICM calculator or a programm like SNG wizard. It would be extremely time consuming to do the calculations on your own and programms like sng wizard make it a lot easier. Also, because of its time consuming nature, you definitely cannot do it while in a game, it is generally used before and after as a study tool to help your game in future events seeing as if you play a decent amount of sngs, the same situations will tend to come up over and over again. So part of getting better at this is not just playing a lot of games but devoting your time to studying and doing analysis on your game. Poker does not come easy and studying is a must.
Now I could have written a long ass strategy post on this but I found this good article written by fox who probably summed it up a lot better than I could have.
I'll copy and paste that articles here if someone cannot access the site.
I am surprised at how rarely I see in depth hand discussions here on pocketfives. In the interest of starting a few more of those discussion I’m going to do an introduction to Independent Chip Modeling or ICM programs. Regardless of your skill level if you aren’t working with an ICM on occasion you probably should be. Before I get into the nitty gritty of working with these handy programs a quick caveat may be in order…
My last article caught some flack on the boards. Some of it was deserved, but some of it was also in relation to how basic the article was. Let me say first off that if you are a serious expert in using ICM calculations and evaluating chip equity in tournament situations then I would love to have you write an article on it. I don’t use this kind of stuff nearly often enough to be an expert with it, though I know I should. If anyone has tips or hints, or wants to write a more advanced article, I’m sure the P5’s community would learn a great deal from it, myself included.
An ICM is basically a tool for finding your equity in different tournament situations. Two excellent (and free) examples are my personal favorite here – ICM (a useful heads up database is also hosted on this site) and a much more widely used version here – another ICM. I honestly don’t know the math involved in writing these programs, though it wouldn’t be that hard to figure out and the writers of the two programs might share that information if you contact them. What I do know is that they work, and they are very valueable tools once you learn how to use them. I’m going to use my favorite ICM calculator in the examples if you want to follow along.
The basic premise goes something like this – You have a number of options and you have an estimate of your opponent’s reaction to each one, but you need to find out which is the most profitable. I’m finding that this stuff is easier to show with examples so we’ll start with a very simple one.
You are 3 handed in a SNG and on the small blind with K2o. The blinds are 500/1,000, the button has folded, and the stacks look like this this -
Button – 5,000
SB (Hero) – 10,000
BB – 5,000
You have been watching your opponents closely like you always do, and because of this you can estimate that if you move all-in the big blind will only call with a hand in the top 30% of his hands. We are working on the assumption that a smooth call or a raise smaller than all your chips in a bad idea. Whether those things are true or not is debateable, but for the sake of simplicity we are assuming them to be true.
Option A – Fold and give the BB your small blind. This one is easy, and it would leave the stacks looking like this -
Button – 5,000
SB (Hero) – 9,500
BB – 5,500
You can plug those numbers into the ICM and get equity numbers for each player that look like this -
Button – .3071
SB (Hero) – .3764
BB – .3165
Those numbers tell you the percentage of the prize pool each player can expect assuming equal skill and random distribution of the cards. Equal skill isn’t usually the case, but we’ll address that a little later.
Option B – Raise all-in and hope your opponent folds. If he folds you can easily calculate the equity in the ICM once again and come up with -
Button – .3099
SB (Hero) – .3902
BB – .2999
It’s interesting to note here that the button loses equity compared to when you fold even though his stack doesn’t change with either decision. This is because the more chips you have as the big stack the less chance he has to take first place and the jump between first and second is much larger than the jump between second and third.
Your opponent may also call you, and if your estimate is correct he will do so 30% of the time. If he calls you have two more calculations to do. First of all how often will he win? We could debate all day about what hte top 30% of hands are here, or what your opponent might think the top 30% of hands are, but for the sake of the example let’s take a reasonable estimate that you will win the hand about 30% of the time against the hands he will call you with. We have two possible results and we can calculate the equity for each of them in the ICM as well.
If we are called and win then the chip stacks look like this -
Button – 5,000
SB (Hero) – 15,000
BB – 0
and when we put those numbers into the ICM we get -
Button – .35
SB (Hero) – .45
The big blind has however taken his 20% of the prize pool and left the game, so he did not recieve 0 equity, which is why we are left with numbers that don’t add up to 100%
If we are called and lose the hand the numbers look like this -
Button – .3083
SB (Hero) – .3083
BB – .3833
So far all of these numbers just tell us how much equity we will have in various situations.Next we need to learn how to apply them to find out which move was correct given our assumptions about the situation, and how to do that. This article is running awfully long and I’m awfully tired, so let’s take a break here and come back to ICM calculations tomorrow. In the next few days I’ll not only tell you how you can use these numbers to learn how to make better decisions, but we’ll learn about the flaws in ICM modeling and how to adjust the numbers for things like skill levels and unique opponents.
In part one I came up with some numbers for a few different outcomes from a specific hand. Now we’ll work with putting those numbers to work in helping us make decisions. As refresher, and to have everything on one page, I was looking at a SNG situation where our hero has K2o in the SB and the button had already folded. The chip stacks were -
Button – 5,000
SB (Hero) – 10,000
BB – 5,000
For reference I did in fact leave the default settings in the ICM, with payouts of 50%, 30% and 20%.
When our hero folds his SB here we found that we now have an equity of .3764 or about 37% of the prize pool. The question is whether that is the best play. Given the assumptions we made in the first article about the BB we came up with numbers for moving all-in and hoping that he folds.
Because we assumed our opponent would fold 70% of the time and our equity if he folds is .3902 we can multiply those numbers and get .3902 * .7 = .27314. We’ll save that number and add it to the numbers we get when he calls.
When he calls and we still win we get an equity of .45 and we need to know how often that will happen. With the estimates we came up with we think that will happen .3 (he calls 30% of the time) * .3 (we will win 30% of the time we are called) = .09. Then we find that .09 (how often this outcome will happen) * .45 (our equity when it does happen) = .0405
When he calls and we lose the hand our equity becomes .3083, and we think from our earlier assumptions that this will happen .3 (he calls 30% of the time) * .7 (he wins 70% of the time when he calls) = .21 So we get .21 * .3083 = .064743
Now we can compare the number we got when our hero folds (.3764) to the total of the numbers we got from when our hero raises all-in (.27314 + .0405 + .064743 = .378383). It looks like we have a winner! The equity when we raise all-in turns out to be higher than the equity when we fold the hand. K2o isn’t so bad after all.
What we did here was detemrine the frequency of an opponent’s actions according to our best guess, and find the value of each of those actions. Let’s do an even more simplified version of this so it is a little easier to understand.
Let’s say that we are in an even chip position with 5k each and we are down to 3 handed in a SNG. The river has just brought a brick, and our flush draw has missed, leaving us with a hand that has no chance of winning. The pot is 3,000 so we each have 3,500 left in our stacks. The pot is heads up, and we are first to act. Is it right to put all of our chips in on a big bluff? Let’s assume that our opponent will call us 40% of the time, and when he calls we will lose every time. We will also assume that if we check we can not win the hand.
Checking gives us an equity of .2333 which we find by simply entering in the stack sizes after we give up the hand into the ICM.
Raising all-in means we win the pot 60% of the time which gives us 6,500 in chips for an equity of .3649. It also means that we lose the pot 40% of the time for an equity of .2 because we will have gone out in third place and in this case third place receives 20% of the prize pool. When we add up the equity for pushing all-in we get
(.3649 * .6) + (.2 * .4) = (.21894) + (.08) = .29894
Aggression has won both battles. If our assumptions about our opponent are correct then we have determined that the all-in bluff is the best choice.
ICM calculations for more complex situations like a steal at a final table can get very complex, but they all follow
the same simple rules.
1. What are your choices?
2. How often will your opponent have each possible response?
3. What is your equity with each response, multiplied by the frequency of that response?
Add them up and you can find what the correct decision would have been.
Obviously ICM calculations are too time consuming to be doing in the heat of the moment, but using them later to find the correct play will teach you a lot about the game. ICM programs are not necessary to be a very good tournament player, but for even the best players they will yield some valuable information about the game and tournament situations. There are of course many things to be considered when using an ICM that I haven’t covered here, but I’ll be covering some of those things tomorrow. Things like like the size of the blinds in relation to the stacks, your skill level in relation to your opponents, and their playing styles, all change things quite a bit.
Eventually once I have all three or four articles written I’ll try to put them in some coherent order and maybe make one big useful article out of them.
In part 3 I’m going to give some of the reasons that ICM’s won’t always give you a perfect answer. There are a lot of factors that an ICM can’t understand, and they can have a big effect on your strategy in a tournament situation.
1. Your skill level compared to that of your opponents. If you are a much better playerthan your opponents then a number fo thigns change. Having a big stack is slightly less valuable, having a small stack gives you much more equity than the ICM might tell you, and gambling becomes a very bad thing in most situations.
Mike Matusow commenting on Phil Ivey’s play toward the end of the WSoP is a great example. He said Phil was playing too many big pots and that he didn’t need to take so many risks against these bad players. Mike was right, and Phil agreed that he should have played smaller pots and let his skill work gradually against the weak players rather than gambling so much even when he had a slight edge in the gamble.
As the strogner player you want to cut down variance and take the gamble out of things. See more hands go farther into the hand, and try to avoid getting all your chips in as a small favorite when you may have a chance to get them in as a big favorite later. On the other hand if you are facing competition that is very strong and you think you are actually at a disadvantage then you want to gamble more, increase your variance, and make it hard for the more skilled players to make their skill work for them.
2. How well you play various sized stacks. I personally play a short stack very well, while my big stack game might need a little work. This means that a big stack is even less valuable to me, and staying alive to fight with my short stack is more important.
3. How wild your opponents are. If your opponents are gambling like crazy and likely to move you up a couple of money spots very soon without any risk from you then it’s a better idea to play a little more conservatively.
4. Your “M”. If your stack is fairly deep compared to the blinds, then gambling it up is not often a good choice. If your M is low then go ahead and get your chips in there, you can’t do much with them until you double or triple up anyway.
There are an infinite number of considerations, but most of them have to do with how much you want to gamble right now. A good understanding of tournament play will help you use all the factors available and allow you to make wise decisions on how much gambling you want to do right now. Pay close attention to the tournament lobby and what the payouts are.
Just made it into the money in a huge tourney and you have a short stack? It’s gambling time, pick some hands and go with them.