# ICM formula

• Basic
Joined: 13.05.2009
Hi, I found ICM formula: Assuming you are player k in a tournament consisting of k players, the general expression for your probability of finishing in nth place is the following: http://www.pokerhelper.com/articles/independent-chip-modeling-part-1-derivation-and-sample-analysis/ its last formula on page. I think formula is not corect. Because Sum is depend on inside index i. (its hard to read if its m_i = 1 under Sum)? And if i = 1 than we ask what probability is that player1 finish on 1st place on condition that player0 finish on 0.place?

So i want to know correct formula.(if that formula is wrong..)
• 3 replies
• Bronze
Joined: 17.06.2010
The formula there seems ok, although the notation is ambiguous so it may be hard to determine its meaning.

Suppose there are opponents with stacks of size 2, 3, 5, 10, 20, and your stack is of size 15. According to the ICM, the chance you finish 4th, so that the first 3 players have stacks of size 20, 2, and 5, respectively, is

(20/T)*(2/(T-20))*(5/(T-22))*(15/(T-27))

where T is the total number of chips in play 2+3+5+10+20+15 = 55.

To determine your chance to finish 4th according to the ICM, you would sum over all of the possible permutations of the first 3 players. There would be 5*4*3 = 120 choices for first, second, and third. For each of these, you get a product like this, and you add up the 120 probabilities.

You do not need to do ICM calculations while playing. For most purposes when you are not playing, you can just use an ICM calculator which has already been written, such as the one built into SNG Wizard or my program ICM Explorer. Actually, the one in ICM Explorer uses a different algorithm which is faster so that it can calculate the probability of finishing 10th without doing 10*9*8*7...*2 = 3628800 calculations. The algorithm in ICM Explorer only needs a few hundred calculations instead.
• Bronze
Joined: 20.01.2008
Hi!

Could you tell to us that different algorithm of ICM, please?

Thank you,
morcos
• Bronze
Joined: 17.06.2010
I'd prefer not to give all of the details here. They aren't relevant for playing poker, only for writing a program like mine. If you are really curious, though, you can read some discussion of algorithms for evaluating the ICM equities in the Project Euler forums.