One of the most common questions new poker players ask when they begin studying the game is, “What is ICM in Poker?” Independent Chip Modeling (ICM) is a mathematical way to determine each remaining player’s equity in a tournament in which one or more payouts are pending. Although the ICM concept is relatively new (it was introduced in the 21st Century), many live and online poker tournament “deals” have since been made subsequent to an ICM calculation for that event.
ICM calculations are a key element of Endgame Poker Strategy.
The concept and use of ICM can be extremely helpful in assisting remaining players in a tournament. But while the actual ICM poker calculation has proven its worth over the years and is frequently used by live and online tournament hosts/players alike, it does have two key weaknesses.
In this article, we’ll take a look at the poker ICM meaning, explain how it is calculated, show which variables are NOT considered when using any poker ICM calculator, and hopefully provide our readers with a clear understanding of how and when to use Independent Chip Modeling.
ICM Weaknesses and Missing Variables
To start, we should probably explain that an ICM calculation – in and of itself – is seldom the outright, absolute answer for how to appropriately divide total payouts among remaining players in a tournament.
This is because there are two major, missing variables in most ICM calculations:
- The current positioning of the blinds and/or antes
- The skill level of each remaining player
The only circumstance in which these two variables would be unnecessary or irrelevant would be a tournament situation in which ALL remaining players would automatically be committed to contributing ALL their remaining chips for ALL subsequent hands. In other words, when the forced ante levels (or Small Blind levels if the match is heads up) are equal to or greater than the total combined remaining chips that ALL players have.
For any other tournament situation, player skill level and the positioning of blinds/antes WOULD in fact be necessary variables to include in any true player equity calculation. And as explained above, ICM calculations do not take either of these two variables into account.
Simple Poker Tournament ICM Calculation (Single Payout)
So, with these clear caveats in mind, let’s take a look at the most simple example of an ICM poker calculation. One that only offers a single payout for first place; one that doesn’t offer ANY prize for second place and beyond.
Let’s use a hypothetical scenario in which there are three remaining players at a final table. Each player is competing for a sole first place prize. This means that the players who finish second and third in this hypothetical event are awarded zero.
A practical example of how this situation might arise is during a satellite qualifier event, where only first place wins an entry into a larger tournament.
For the sake of simplicity, let’s assume that the first place payout in our hypothetical example is exactly 10 units (or $10 if you prefer). And let’s say that the Blind Levels (although, as explained, this isn’t a variable that is considered in most ICM calculations) are 0.01/0.02 unites – or $0.01/$0.02 with no antes.
Player A: 5 chips or 250 Big Blinds
Player B: 3 chips or 150 Big Blinds
Player C: 2 chips or 100 Big Blinds
The three players who remain are all interested in negotiating a deal – or a “chop” – instead of playing the tournament out to its ultimate conclusion in which a sole player will walk away with 10 units.
The total amount of chips remaining equals ten. This means that:
Player A: 50% of all chips
Player B: 30% of all chips
Player C: 20% of all chips
Since there is only one, sole payout that each player can aspire to (the first place payout of 10 units), calculating each player’s equity at this precise moment is relatively simple compared to a payout structure in which more than one player is guaranteed to receive a prize.
A typical ICM calculation for the above scenario would award:
Player A: 50% of total first place payout equals 5 units (or $5)
Player B: 30% of total first place payout equals 3 units (or $3)
Player C: 20% of total first place payout equals 2 units (or $2)
Of course, this example does NOT delineate between each player’s skill level (or even the positioning of each player relative to the Blinds and/or Antes for the following hand).
And since the Blind Levels are 0.01/0.02 units going forward, there are a total of 500 Big Blinds still in play when considering the total combined amount of all players’ chip stacks.
This is why more highly skilled players (or any player who believes his/her skill is superior to that of the remaining opponents) commonly request MORE than their respective result of an ICM calculation during the tournament deal-making process.
Whether inferior players should concede to the demands of a more highly skilled player in these scenarios depends on how large the requested amount is relative to that player’s skill edge over the remaining opponents.
This will be an imperfect calculation, but it is one that all remaining players must decide upon if a deal is to be reached. Otherwise, the tournament will continue with no deal in place and reach its eventual conclusion with a sole winner (or each winner) being awarded the corresponding prize amount.
If the Blind Levels happen to be 10/20 units with a 10-unit ante, then player skill level does not matter. All players will be committed to being “all in” during any and all subsequent hands that are played. In this case, whichever player is fortunate enough to show down winning hands will be awarded first place prize money if the event is played out to its natural conclusion without a deal (ICM or otherwise).
A single payout is the easiest calculation to make in terms of Independent Chip Modeling.
ICM Calculations for Multiple Tournament Payouts/Placements
Most non-satellite poker tournaments will award prizes for at least two or more final table participants – and this is where ICM calculations become more involved (meaning they include more variables or potential outcomes).
Let’s use the above hypothetical example to make a poker ICM calculation. But now, let’s assume that:
- 1st Place Payout: 5 units
- 2nd Place Payout: 3 units
- 3rd Place Payout: 2 units
For the sake of this example, let’s say that the Blinds are 0.01/0.02 and that:
Player A: 5 chips
Player B: 3 chips
Player C: 2 chips
First, let’s tackle the obvious.
Player C obviously has greater than 2 units of overall equity. This is because Player C is already guaranteed a minimum payout of 2 units if Player C finishes in 3rd Place. The same can be said for Player A, who obviously has less than 5 units of equity (because the best Player A can aspire to is a first place finish that pays out 5 units).
By default, Player C will refuse any ICM deal – regardless of opponents’ skill levels – that awards less than 2 units of equity to Player C. In fact, Player C’s equity in this scenario is obviously greater than 2 units.
So, would you be surprised to learn that the ICM Calculators that are commonly use in this scenario would assign the following equity to the three remaining players?
Player A: 5 chips = 50% of chips in play = $3.8393 in ICM equity
Player B: 3 chips = 30% of chips in play = $3.2750 in ICM equity
Player C: 2 chips = 20% of chips in play = $2.8857 in ICM equity
The question we have now is… how did we arrive at these equities? What calculation did we use?
The answer is a multi-step formula.
ICM in Poker: Formula for Multiple Payouts
First, let’s calculate each player’s equity for winning a first place prize of 7 units (while keeping in mind that no ICM calculation will take players’ skill levels into account). In this scenario:
- 1st Place: 7 units
- 2nd Place: 3 units
- 3rd Place: 0 units
Player A has 5 chips, or 50% of all chips in play. The first place payout is 7 units.
So 50% times 7 equals 3.5 units (or $3.50).
Player B has 3 chips, or 30% of all chips in play. The first place payout is 7 units.
So 30% times 7 equals 2.1 units (or $2.10).
Player C has 2 chips, or 20% of all chips in play. The first place payout is 7 units.
So 20% times 7 equals 1.4 units (or $1.40).
We now know each remaining player’s chip-based equity for the first place prize of 7 units.
Now, we need to calculate each player’s chip-based equity for the second place prize of 3 units. This is where it gets a bit tricky, because you’ll need to consider each player’s chance at achieving first place within your second place equity calculation.
Player A has a 50% chance of winning first place. So assuming that happens:
Player B has 3/(3+2) chance at obtaining the second place prize (or 60%). Therefore Player B has 60% times 3 units total equity in second place, or $1.80.
Player C has 2/(3+2) chance at obtaining the second place prize (or 40%). Therefore Player C has 40% times 3 units total equity in second place, or $1.20.
(now repeat for Player B’s chances of winning first place)
Player B has a 30% chance of winning first place. So assuming that happens:
Player A has 5/(5+2) chance at obtaining the second place prize (or 71.43%). Therefore Player A has 71.43% times 3 units total equity in second place, or $2.143.
Player C has 2/(5+2) chance at obtaining the second place prize (or 28.57%). Therefore Player C has 28.57% times 3 units total equity in second place, or $0.857.
(now repeat for Player C’s chances of winning first place)
Player C has a 20% chance of winning first place. So assuming that happens:
Player A has 5/(5+3) chance at obtaining second place (or 62.5%). Therefore Player A has 62.5% times 3 units total equity in second place, or $1.875.
Player B has 3/(5+3) chance at obtaining the second place prize (or 37.5%). Therefore Player B has 37.5% times 3 units total equity in second place, or $1.125.
Still here?
Once we have these calculations, we can then multiply all second place equities by their corresponding percentage-based chances of occurring.
Player A: (30% of 2.143) plus (20% of 1.875) equals 1.018
Player B: (50% of 1.80) plus (20% of 1.125) equals 1.125
Player C: (50% of 1.20) plus (30% of 0.857) equals 0.857
Now, for the final step, add these total second place equity numbers to each player’s first place equity to arrive at the total ICM equity.
Player A: 1.018 + 3.5 = 4.51 or $4.51
Player B: 1.125 + 2.1 = 3.225 or $3.23
Player C: 0.857 + 1.4 = 2.257 or $2.26
Use ICM Calculators for Quicker Results
There’s really no substitute for a Poker ICM calculator. You can find these via a quick Google search online and they will save you a lot of time – especially if you happen to find yourself at a tournament final table and need to input a lot of payouts/possibilities.
Best of luck at the tables. We hope this article has helped you understand how Independent Chip Modeling in poker works.
