Deal Making with ICM by Andre Coimbra
After many hours of poker you finally made the final table of that tournament you have been playing for months. You are tired but excited, happy for making it so far but thirsty for more and suddenly someone at the table starts talking about making a deal. Someone else asks to see the numbers and you are curious, so you say "Let's do it!". At this point the tournament host arrives and shows the ICM numbers. What now?

This is not about playing flops, turns and rivers, and it's not about bluffing when you feel weakness or getting value from your strong hands. What is this ICM thing? How should you approach the deal process and get the most value? These are all valid questions that everyone will have to face at some point. I will try to make you understand how the process works so that you get the most out of it!

ICM stands for Independent Chip Model and tries to give a money value to the poker chips at a tournament. While this value is not 100% accurate, it is superior to assuming a linear value of the chips.

Before using ICM, people used to assume your share of the prize pool could be calculated by dividing your stack by the total amount of chips in the tournament and multiply that number by the remaining prizes.

To explain the different models let's use the example of a High Roller with a \$1 Million prize pool that only pays the top 2 players and has 3 players left in the tournament

Stacks:
Stack 1: 500K chips
Stack 2: 450K chips
Stack 3: 50K chips

Payouts:
1st: \$700K
2nd: \$300K
3rd: \$0

The linear model

In this tournament if we use the linear model the equities would be the following:

Player 1: \$500K ( (500K/1M) * \$1M)
Player 2: \$450K ( (450K/1M) * \$1M)
Player 3: \$50K   ( (  50K/1M) * \$1M)

Instead of agreeing on a deal, they keep playing and you know that the poker gods can be cruel sometimes, so they give Player 2 pocket aces while Player 1 is trying to bully him at the final table. Unfortunately for Player 2, his aces get cracked by pocket fours.

While Player 2 is leaving the computer crying, Player 3 is jumping on his chair and calling all his friends and family, because suddenly he is winning at least \$300K since he is guaranteed 2nd place!

We assumed that his equity was \$50K and he just guaranteed himself at least \$300K. If we use the linear model that I was referring to, we can see that it doesn't make any sense since he still has just 5% of the chips but is guaranteed 30% of the prize pool.

The chip-chop model

A quick fix to this problem would be to start by giving all the remaining players the last guaranteed prize and then distribute the remaining prizes according to their share of the chips. This is the chip-chop model.

After the big bad beat at the final table, where the remaining stacks are 950K and 50K, would be to give \$300K to each player first since they are guaranteed 2nd prize and then give 95% of the remaining \$400K to the first player and 5% of the remaining \$400K to the 2nd player. This means that the Chip Chop model would give \$680K to Player 1 and \$320K to Player 2.

Usually at a final table the players are already in the money, so the chip-chop will guarantee the next payout to everyone as well as their chip share of the remaining pie. However, if a player has most of the chips, sometimes something absurd can happen: the chip leader can get more than the 1st prize in a tournament! I know this sounds crazy, but trust me, I've seen it happen many times! I honestly don't know how the other players can agree to that, but these things have happened in the past…

Another problem is that it doesn't take into account the possibility of some all-in action between big stacks, where the small stacks move up a pay jump and their equity is increased immensely. A perfect example of this is when pocket aces got cracked by the chip-leader's 4-4.

The ICM model

A different way to calculate things is to attribute the 1st prize to the chance of a player winning the tournament, the 2nd prize to the chance of the same player getting 2nd, the 3rd prize to the chance of that player getting 3rd and so on. Add all of these equities together and you get the tournament equity. This is how you calculate ICM.

This is the model currently used by default when requesting a deal in PokerStars. Players will always be able to request other ways to share the prizes, but the first proposal will be based on ICM. ICM assumes that the chance of getting first equals your percentage of the total chips available in the tournament, and so on through the positions remaining.

It gets very complicated with many players involved and computers usually take care of the complex equations. Even though ICM is the best model of the ones mentioned above, it tends to overvalue small stacks and doesn't take into consideration the skill level of the players at the table. ICM also has no way of calculating what will happen in the upcoming hands, such as a big stack bullying other medium and short stacks at the table. ICM is a good system for working out deals, but it's not perfect.

Deal tips

When you're the big stack…
If I have a big stack at the final table I will usually ask for a chip-chop, since it values big stacks more and in extreme cases might even lead to winning more than the 1st prize. If people won't accept a chip-chop and want an ICM deal instead, I will usually ask more than what the ICM deal gives, since it tends to overvalue small stacks a bit.

When you're a medium stack…
ICM and chip-chop both tends to be of similar value for medium stacks. If this is a final table where there is a big stack bullying everyone and you are bleeding chips slowly, you probably want to take a deal and might even be correct to give up a bit of equity. This is especially true if you feel like you don't have a decent edge on the field, since ICM doesn't take this into consideration.

When you're the small stack…

Conclusions

A conclusion we can draw from the previous ICM example is that it's extremely expensive for big stacks to lose all their chips against other big stacks. When Player 2 lost all his chips against Player 1, his equity dropped from \$456,900K all the way down to \$0. In some extreme cases, usually in satellites, there are even some situations where it is correct to fold aces pre-flop versus an all-in. Winning 80% of the time is nice, but the cost of losing 20% might be too big in some rare situations.

In general, if there are meaningful pay jumps coming up and smaller stacks that will often bust before you, you should avoid potentially fatal confrontations. Just be patient and collect those nice pay jumps instead.

If there is only one smaller stack, you usually shouldn't worry too much about ICM and just try to accumulate chips to get into a better position. When there are two or more small stacks, it becomes more complicated because having one of the other smaller stacks bust might be worth a lot of money to you. In some extreme situations, you might even fold down to one or two big blinds because the money you make from the pay jump is worth more than a potential double-up in terms of tournament equity. Understanding all of these dynamics is key to playing a proper final table game. Ignoring them might lead to more wins, but will definitely cost you money in the long run!

Final table negotiations are an arena where you want to get at least your fair share of the prize pool and, if possible, a part of the other players' equity. In the past I've always wanted to make a deal because the good final tables usually come after many hours of play and I can't stay focused for that long. I would never say this to the other players of course!

If I was the chip leader I would put pressure on them with my chips, make them fear me and have an advantage for the deal-making game. Be polite, but don't be afraid to ask for anything that you think there is a chance the other players will give you. If you can sell yourself well at the final table deal, not only you will make more money on the long run, you will make it with less variance as well!

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