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Independent Chip Model

ICM (Independent Chip Modeling) is a very valuable resource in a tournament player's poker tool kit. The math behind ICM can be called complicated, at best, but the basic concept is pretty simple. Basically it is a way of finding your real equity based on your stack size as it relates to the total prize pool. It is really only accurate when you are down to 5 or less players.

A major problem with using chips to determine pot odds in a tournament is that tournament chips do not have a set value. If you have 70% of the chips in play they are not worth 70% of the total prize pool. For example say you are in a SNG where 3 are paid in the standard format of 50%, 30% and 20% for 1,2 and 3 place finishes. If you have 70% of the chips in play you are pretty much guaranteed to win the tournament but you will only win 50% of the prize pool.

Lets take an example final table. The stacks are as follows:
5000
3500
3000
2000
1500

Using an ICM calculator (http://tomfmason.net/sandbox/poker/icm) we can determine each player's ICM equity for their chips. This assumes that 3 places are paid and in the standard 50%, 30% and 20% payout.

5000 -> 0.2898
3500 -> 0.2330
3000 -> 0.2330
2000 -> 0.1509
1500 -> 0.1171

You might be asking your self "Ok what does that mean?".. Well, it is really pretty simple. Lets say that this tournament was a 10 man $5 + $0.50 buy in SNG with a total prize pool of $50. The chip leader's expected value for his current chip stack would be 50 * 0.2898. Basically this means that over a period of time in the exact same situation you could expect to win $14.49 or ruffly 29% of the total prize pool.

Lets say that the blinds and antes are pretty steep - 250/500 75 ante. Meaning you are putting in 1125 every round. This means that everyone is pretty short stacked and we are likely to see a lot of all-ins preflop. Now lets take an example hand. Say we are the chip leader with A9s and the short stack pushes preflop. He could be playing just about any two cards. Using pokerstove I gave the short stack a range of about 50%. Meaning he could push with about half of the possible starting hands.

Before you read any further answer this.. Would you call?










Our equities looks like this:
A9s: 58.819%
50% range: 41.181%

Ok, so now we have two options in this situation - call or fold. If we fold our icm equity will stay the same or 0.2898. (I am going to assume the blinds are going to fold) If we call and win the icm equity would look like this:

7450 -> 0.3712
3450 -> 0.2644
2675 -> 0.2280
1425 -> 0.1363


Now we will look at the icm equity for calling and losing the hand.

3450 -> 0.2266
3450 -> 0.2266
2675 ->0.1875
1425 ->0.1091
4000 -> 0.2502


Now that we have our icm equities for winning and losing we can determine our real EV. Remember that we said that our opp could have pushed with a range of about 50% of the possible starting hands. So, our A9s would win about 58% of the time and would lose about 41% of the time against that range.

(0.58*0.3712) + (0.41*0.2266) = 0.3082

Ok, you may be asking your self what does this mean and how can I use it. Well, lets look at the difference between calling and folding. If we fold our ICM equity would stay the same or about 28.9% and if we call, on average, our ICM equity would be 30%. In terms of the actual dollar amount we see:

50 * (0.3082 - 0.2898) = 0.92 or about a 92 cents difference on average.

That 92 cents difference dosn't seem like much but it is about 18% of our buy in. Not that this is a big deal in the short term but it could add up to a lot over a period of time.

This is a lot of semi complicated math to be using in a live hand. I don't generally do this with a live hand but I almost always look at every hand of a final table after the fact. By doing this I am able to look at similar situations and take my action based on the previous results. If you follow this method at your final tables you should see an increase in your overall ROI. Which means more money for you.

Here are some useful links regarding ICM:

http://www.pokerplayernewspaper.com/viewarticle.php?id=2329
http://www.sitandgoplanet.com/sitandgo/sng_bubble/Introduction_to%20ICM.html
http://www.chillin411.com/node/7
http://www.holdemresources.net/hr/sngs/icm.html
http://archives1.twoplustwo.com/showflat.php?Cat=0&Number=10393737&an=0&page=0