# ICM Calculations Part 1

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This is a part one of a three part series. For the rest, check out Fox's Blog.

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
BB- 0

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.

I'll see you at the final table,
Fox