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- In a poker tournament, the Independent Chip Model (ICM) is a mathematical model that is used to more precisely calculate overall equity in a tournament. Due to chip stack values changing over time as the tournament progresses with the remaining players getting closer to the money, each player must take into account the rewards/risks of any play.
- Making decisions using the independent chip model and prize pool equity is useful for post-game analysis and helping you to gauge risk vs. Reward situations near the bubble. ICM is basically the theory behind the common concern of 'is it worth risking all my chips in this spot?'
- Independent Chip Model Poker
- Poker Independent Chip Model
- Poker Independent Chip Model Calculator
- Poker Independent Chip Models
- Poker Independent Chip Model Anchor Chart
One of those tools is the so-called Independent Chip Model or ICM poker. Essentially, it is an approach for converting tournament or SNG chip stacks to real money equity. It helps you make precise decisions, which bring positive expected value in the long run.
Calculating ICM
Although it would be nice if there were a simple equation to determine the cash value of a player's stack on the fly, the reality of ICM is that it includes an immense amount of calculations. That being the case, it is highly recommended that players looking to find their prize pool equity use ICM calculators.
Still, let's look at ICM with simplified numbers:
Consider four players are left at a $10 Sit & Go table that started with ten players and each player started with 1000 chips. The payouts are the standard $50, $30 and $20 for first, second and third, respectively. If each of the four players has 2,500 chips, their chip value in regards to ICM would be $25 each. However, that congruency among players is rarely the case, so let's distribute the chips a little less evenly, as such:
- Player 1 has 4,500
- Player 2 has 2,500
- Player 3 has 2,000
- Player 4 has 1,000
Upon entering these figures into an ICM calculator, we can see each player's cash equity:
- 4,500 chips are worth $35.44
- 2,500 chips are worth $27.09
- 2,000 chips are worth $23.85
- 1,000 chips are worth $13.61
What this means is that on average and assuming equal skill level, each of these players will make the amount of money that the ICM calculator has determined their stacks to be worth.
Using ICM to Make Moves
The majority of ICM-based decisions end up happening on the bubble since, at that point in the competition, players simply want to reach a payout. ICM figures combined with equity value (EV) estimates can help make smarter moves to more often reach the money.
If you are player three from the previous example and have 2,000 chips, pushing all in with any two cards against player four with 1,000 chips will still leave you with a chip stack that's actually worth something.
However, if you're against player one or two, risking your poker tournament ICM calculated value can be a bad decision, even in cases where you begin the hand as a 60 percent favorite with something like A♣T♣ or J♦J♠.
When ICM Trumps Positive EV Moves
Though many players treat +EV plays as the ultimate deciding factor, situations arise where ICM figures are more important. As discussed before, these happen specifically around the bubble.
Consider you have the aforementioned hand A♣T♣ and are against player one who's a wild player. If he or she makes a bet that puts you all-in at the bubble with your current hand, ICM determines that you should still fold even though 60 percent win rate means you have positive EV for that hand.
If you win the hand
The table ICM will look like this:
- 2,500 chips are worth $26.70
- 2,500 chips are worth $26.70
- You - 4,000 chips are worth $33.50
- 1,000 chips are worth $13.09
Also take note that since this play made the top three players closer in chip stacks, the equity value of player four dropped slightly from $13.61 to $13.09.
If you lose the hand
The table ICM will look like:
- 6,500 chips are worth $42.39
- 2,500 chips are worth $32.42
- 1,000 chips are worth $25.19
- You - 0 chips are worth $0
So, with your 60 percent favored hand, there are two outcomes from an ICM simulator. In the winning situation, your value has raised $9.65 to $33.50. In the losing situation, your value has dropped from $23.85 to zero. This means that calling the all in from the big stack is, though a +EV move, bad ICM poker strategy since you are risking $23.85 to earn $9.65.
Full Tilt Poker gives MTT & SNG players the option to chop heads up according to ICM. |
ICM Calculators
Chimp v1.0 (Desktop Program)
ICMIZER (Web-Based App)
ICM Nash Calculator (Web-Based App, Detailed Explanations on Push/Fold Scenarios)
Many high profile poker players started out their career by playing single table tournaments, more commonly known as sit-n-go's. Samer Khuri, more commonly known in the online sit-n-go world as 'Braminc,' moved up the ranks in the online sit-n-go world and was one of the best players in the high-stakes six and nine-man sit-n-go's on Full Tilt Poker.
After Black Friday, Khuri left the U.S. for Lebanon, where he has continued his sit-n-go career on PokerStars.
Khuri netted hundreds of thousands of dollars by understanding the nuances of these single table tournaments. He recently sat down with Card Player to talk about the Independent Chip Model (ICM) and the role that it plays in forming a solid sit-n-go strategy.
Independent Chip Model Poker
Steve Schult: Can you explain what ICM is?
Samer Khuri: It stands for independent chip model and it is a way of assigning a value of chips at any stage in a tournament. The reason this is even necessary is because chips are not directly related to a dollar value during the course of a tournament the same way they are in a cash game. Because the formula is so complicated for calculating the value of your chips, some genius math guys created the independent chip model and some calculators that we can use to calculate the actual dollar value of our chip stack. It's a way for measuring the value of our stack.
The term is overused in a sense. People will say things like 'ICM doesn't say to do that.' I think what people really mean to say is that it's not a good shove or fold because of the value of your stack before and after based on what ICM would tell you. The daily usage of the term has gotten a little more generous if you will.
SS: How does ICM and different payout structures affect how you should be playing in the early stages of a sit-n-go and in the late stages?
SK: In general, it is going to mean that you have to play tighter than you would in a winner-take-all or a cash game format. That would be the first thing to note because when you get into more details it gets pretty complicated. Different payout structures have different results on what your strategy should be. If you are playing a very top-heavy payout structure, with the most top-heavy being a winner-take-all format, then you are going to be allowed to play very aggressively in order to have optimal strategy. Likewise, any tournament with a structure that comes close to that, such as a six-max sit-n-go with 70 percent of the prize pool going to first place, then generally a more aggressive strategy will be the best choice.
Conversely, a more flat payout structure where first place gets paid a much less percentage of the prize pool and second, third, fourth, and sometimes even fifth and sixth place getting some of the prize pool, then ICM will play a much bigger part of your strategy and will result in you playing much tighter in a lot of situations. In general, the presence of ICM will instruct you to play pretty tightly both early and later in the tournament. Now, later in the tournament, if your opponents are playing too tight or if they know they are supposed to be playing tight, you can actually play a little loose so it does become a little complicated and the details become more dependent upon the players you are playing against. In general, it is going to force you to play a tight early game and then a tight or loose late game depending on opponents.
SS: How would you respond to those who say that sit-n-goes are solved. If you are able to make adjustments based on your opponents, wouldn't that lead to the game not being solved?
Poker Independent Chip Model
SK: I think in the highest ICM games, the games are closest to being solved. What I mean by highest ICM games are the flattest payout structures, like the double-or-nothings. All you have to do in that tournament is play ridiculously tight and make a few steals when you have a few opportunities just to stay alive into the final five. There is a little room for creativity, but in that tournament there really is no real room.
In a game like a six-max sit-n-go, where it's 70 percent for 1st and 30 percent for 2nd. That is a game that is much less solved and there is much more room for creativity and different strategies that can also be winning strategies. There is no one set winning strategy in those games.
There is also a lot of stuff in between from top-heavy to flat. A nine-man sit-n-go which is kind of the most typically thought of format because it's maybe the oldest one. It is a little more on the higher ICM side of things. It's a little bit tighter and closer to the double-or-nothings although still not even close to as tight as the double-or-nothing. It is probably the second or third tightest structure and is a little bit more into the solved area.
The thing about being solved is that I think it is just being used as an oversimplification. It's an exaggeration but it's not completely untrue. If you have all educated one of the most solved games it's going to be either unbeatable or beatable for a very small win rate. The thing is though is that it just never happens.
SS: Can you explain the 'ICM Tax' that you hear about so often in sit-n-go strategy?
SK: Using the phrase ICM tax is kind of a user-friendly way of describing what ICM is. It's not the most accurate way to look at something, but in general it goes back to the same principle of what ICM is and the fact that your chips are not directly related to the dollar value of your stack size and the way that fluctuates. Consider a situation where somebody is going all in and you have to call. ICM tax basically says that doubling up your stack is worth less than losing your whole stack.
If you lose your whole stack you lose 100 percent of your dollar value. If you double your stack, you do not gain 100 percent of your value. You usually a little bit less or a lot less depending on chip stacks and payout structures. So you will never be gaining a full 100 percent while you will always be risking a full 100 percent. You are paying a little bit extra to double up but you are still risking everything. So winning chips isn't as important as keeping chips in a lot of spots.
SS: Can you talk about how ICM tax affects bubble play?
SK: Whenever you are encountering ICM tax, you are going to need better than average odds to call off your stack. Sometimes on the bubble, you will need 70-75 percent edge to turn a profit. If you are second in chips and facing the chip leader going all in, you can know that he is going all-in with every single hand in the world, including 2-3 off suit, you need a hand that has 70 percent or more equity against his range. A hand like A-K or A-Q don't cover the ICM tax and usually in spots like this the bottom of our calling range will be either pocket tens or pocket jacks, which will have enough equity against an any two card range to make up for that ICM tax.
SS: Can you elaborate on a situation you have encountered where ICM tax really handcuffs you on the bubble?
SK: I've been in this situation hundreds of times where you are on the bubble of a nine-man tournament, so there are four players left. One player has around 1,000 chips, another player has like 2,500, and the big stack has like 5,500 and you are in the big blind with 4,500 and are dealt A-K suited. The blinds are 200/400, so you have about 11 big blinds and it folds around to the small blind who is the big stack at the table and he shoves all in. This player is somebody you know and you know he plays aggressively and you know he is shoving any two cards or very close to it.
Even if he is shoving any two cards, including 2-3 off suit, then you have to fold.
If you look it up in an ICM calculator, you will find that by making the call, you will be losing 1.77 percent of your prize pool equity. What that means is that if you measure your prize pool equity, which is the average amount of dollars you will win, at the beginning of the hand, and you measure after you have called, you will see that you actually have much lower prize pool equity. That isn't 1.77 percent less than your starting equity. That will be 1.77 percent less than the total prize pool in play.
Poker Independent Chip Model Calculator
Calculating ICM
Although it would be nice if there were a simple equation to determine the cash value of a player's stack on the fly, the reality of ICM is that it includes an immense amount of calculations. That being the case, it is highly recommended that players looking to find their prize pool equity use ICM calculators.
Still, let's look at ICM with simplified numbers:
Consider four players are left at a $10 Sit & Go table that started with ten players and each player started with 1000 chips. The payouts are the standard $50, $30 and $20 for first, second and third, respectively. If each of the four players has 2,500 chips, their chip value in regards to ICM would be $25 each. However, that congruency among players is rarely the case, so let's distribute the chips a little less evenly, as such:
- Player 1 has 4,500
- Player 2 has 2,500
- Player 3 has 2,000
- Player 4 has 1,000
Upon entering these figures into an ICM calculator, we can see each player's cash equity:
- 4,500 chips are worth $35.44
- 2,500 chips are worth $27.09
- 2,000 chips are worth $23.85
- 1,000 chips are worth $13.61
What this means is that on average and assuming equal skill level, each of these players will make the amount of money that the ICM calculator has determined their stacks to be worth.
Using ICM to Make Moves
The majority of ICM-based decisions end up happening on the bubble since, at that point in the competition, players simply want to reach a payout. ICM figures combined with equity value (EV) estimates can help make smarter moves to more often reach the money.
If you are player three from the previous example and have 2,000 chips, pushing all in with any two cards against player four with 1,000 chips will still leave you with a chip stack that's actually worth something.
However, if you're against player one or two, risking your poker tournament ICM calculated value can be a bad decision, even in cases where you begin the hand as a 60 percent favorite with something like A♣T♣ or J♦J♠.
When ICM Trumps Positive EV Moves
Though many players treat +EV plays as the ultimate deciding factor, situations arise where ICM figures are more important. As discussed before, these happen specifically around the bubble.
Consider you have the aforementioned hand A♣T♣ and are against player one who's a wild player. If he or she makes a bet that puts you all-in at the bubble with your current hand, ICM determines that you should still fold even though 60 percent win rate means you have positive EV for that hand.
If you win the hand
The table ICM will look like this:
- 2,500 chips are worth $26.70
- 2,500 chips are worth $26.70
- You - 4,000 chips are worth $33.50
- 1,000 chips are worth $13.09
Also take note that since this play made the top three players closer in chip stacks, the equity value of player four dropped slightly from $13.61 to $13.09.
If you lose the hand
The table ICM will look like:
- 6,500 chips are worth $42.39
- 2,500 chips are worth $32.42
- 1,000 chips are worth $25.19
- You - 0 chips are worth $0
So, with your 60 percent favored hand, there are two outcomes from an ICM simulator. In the winning situation, your value has raised $9.65 to $33.50. In the losing situation, your value has dropped from $23.85 to zero. This means that calling the all in from the big stack is, though a +EV move, bad ICM poker strategy since you are risking $23.85 to earn $9.65.
Full Tilt Poker gives MTT & SNG players the option to chop heads up according to ICM. |
ICM Calculators
Chimp v1.0 (Desktop Program)
ICMIZER (Web-Based App)
ICM Nash Calculator (Web-Based App, Detailed Explanations on Push/Fold Scenarios)
Many high profile poker players started out their career by playing single table tournaments, more commonly known as sit-n-go's. Samer Khuri, more commonly known in the online sit-n-go world as 'Braminc,' moved up the ranks in the online sit-n-go world and was one of the best players in the high-stakes six and nine-man sit-n-go's on Full Tilt Poker.
After Black Friday, Khuri left the U.S. for Lebanon, where he has continued his sit-n-go career on PokerStars.
Khuri netted hundreds of thousands of dollars by understanding the nuances of these single table tournaments. He recently sat down with Card Player to talk about the Independent Chip Model (ICM) and the role that it plays in forming a solid sit-n-go strategy.
Independent Chip Model Poker
Steve Schult: Can you explain what ICM is?
Samer Khuri: It stands for independent chip model and it is a way of assigning a value of chips at any stage in a tournament. The reason this is even necessary is because chips are not directly related to a dollar value during the course of a tournament the same way they are in a cash game. Because the formula is so complicated for calculating the value of your chips, some genius math guys created the independent chip model and some calculators that we can use to calculate the actual dollar value of our chip stack. It's a way for measuring the value of our stack.
The term is overused in a sense. People will say things like 'ICM doesn't say to do that.' I think what people really mean to say is that it's not a good shove or fold because of the value of your stack before and after based on what ICM would tell you. The daily usage of the term has gotten a little more generous if you will.
SS: How does ICM and different payout structures affect how you should be playing in the early stages of a sit-n-go and in the late stages?
SK: In general, it is going to mean that you have to play tighter than you would in a winner-take-all or a cash game format. That would be the first thing to note because when you get into more details it gets pretty complicated. Different payout structures have different results on what your strategy should be. If you are playing a very top-heavy payout structure, with the most top-heavy being a winner-take-all format, then you are going to be allowed to play very aggressively in order to have optimal strategy. Likewise, any tournament with a structure that comes close to that, such as a six-max sit-n-go with 70 percent of the prize pool going to first place, then generally a more aggressive strategy will be the best choice.
Conversely, a more flat payout structure where first place gets paid a much less percentage of the prize pool and second, third, fourth, and sometimes even fifth and sixth place getting some of the prize pool, then ICM will play a much bigger part of your strategy and will result in you playing much tighter in a lot of situations. In general, the presence of ICM will instruct you to play pretty tightly both early and later in the tournament. Now, later in the tournament, if your opponents are playing too tight or if they know they are supposed to be playing tight, you can actually play a little loose so it does become a little complicated and the details become more dependent upon the players you are playing against. In general, it is going to force you to play a tight early game and then a tight or loose late game depending on opponents.
SS: How would you respond to those who say that sit-n-goes are solved. If you are able to make adjustments based on your opponents, wouldn't that lead to the game not being solved?
Poker Independent Chip Model
SK: I think in the highest ICM games, the games are closest to being solved. What I mean by highest ICM games are the flattest payout structures, like the double-or-nothings. All you have to do in that tournament is play ridiculously tight and make a few steals when you have a few opportunities just to stay alive into the final five. There is a little room for creativity, but in that tournament there really is no real room.
In a game like a six-max sit-n-go, where it's 70 percent for 1st and 30 percent for 2nd. That is a game that is much less solved and there is much more room for creativity and different strategies that can also be winning strategies. There is no one set winning strategy in those games.
There is also a lot of stuff in between from top-heavy to flat. A nine-man sit-n-go which is kind of the most typically thought of format because it's maybe the oldest one. It is a little more on the higher ICM side of things. It's a little bit tighter and closer to the double-or-nothings although still not even close to as tight as the double-or-nothing. It is probably the second or third tightest structure and is a little bit more into the solved area.
The thing about being solved is that I think it is just being used as an oversimplification. It's an exaggeration but it's not completely untrue. If you have all educated one of the most solved games it's going to be either unbeatable or beatable for a very small win rate. The thing is though is that it just never happens.
SS: Can you explain the 'ICM Tax' that you hear about so often in sit-n-go strategy?
SK: Using the phrase ICM tax is kind of a user-friendly way of describing what ICM is. It's not the most accurate way to look at something, but in general it goes back to the same principle of what ICM is and the fact that your chips are not directly related to the dollar value of your stack size and the way that fluctuates. Consider a situation where somebody is going all in and you have to call. ICM tax basically says that doubling up your stack is worth less than losing your whole stack.
If you lose your whole stack you lose 100 percent of your dollar value. If you double your stack, you do not gain 100 percent of your value. You usually a little bit less or a lot less depending on chip stacks and payout structures. So you will never be gaining a full 100 percent while you will always be risking a full 100 percent. You are paying a little bit extra to double up but you are still risking everything. So winning chips isn't as important as keeping chips in a lot of spots.
SS: Can you talk about how ICM tax affects bubble play?
SK: Whenever you are encountering ICM tax, you are going to need better than average odds to call off your stack. Sometimes on the bubble, you will need 70-75 percent edge to turn a profit. If you are second in chips and facing the chip leader going all in, you can know that he is going all-in with every single hand in the world, including 2-3 off suit, you need a hand that has 70 percent or more equity against his range. A hand like A-K or A-Q don't cover the ICM tax and usually in spots like this the bottom of our calling range will be either pocket tens or pocket jacks, which will have enough equity against an any two card range to make up for that ICM tax.
SS: Can you elaborate on a situation you have encountered where ICM tax really handcuffs you on the bubble?
SK: I've been in this situation hundreds of times where you are on the bubble of a nine-man tournament, so there are four players left. One player has around 1,000 chips, another player has like 2,500, and the big stack has like 5,500 and you are in the big blind with 4,500 and are dealt A-K suited. The blinds are 200/400, so you have about 11 big blinds and it folds around to the small blind who is the big stack at the table and he shoves all in. This player is somebody you know and you know he plays aggressively and you know he is shoving any two cards or very close to it.
Even if he is shoving any two cards, including 2-3 off suit, then you have to fold.
If you look it up in an ICM calculator, you will find that by making the call, you will be losing 1.77 percent of your prize pool equity. What that means is that if you measure your prize pool equity, which is the average amount of dollars you will win, at the beginning of the hand, and you measure after you have called, you will see that you actually have much lower prize pool equity. That isn't 1.77 percent less than your starting equity. That will be 1.77 percent less than the total prize pool in play.
Poker Independent Chip Model Calculator
Normally in ICM studies, anything above .1 percent is a clear call or shove and anything where you are losing .1 percent is a clear fold. We are talking about decimal points here, so when something is 1.77 percent, it's not even close or even debatable.
Poker Independent Chip Models
Khuri is currently an instructor at CardRunners and Pokerstrategy.com, as well as offering private coaching from his own site, www.Sngexperts.com.
Poker Independent Chip Model Anchor Chart
