ICM Poker: The Only Guide You Need

Updated on September 28, 2023

In poker ICM, short for 'Independent Chip Model', serves as a tool that assists players in understanding their equity based on chip counts. poker player at any stage of a poker tournament determine their current tournament equity This model assesses how much of the prize pool a player is entitled to at any given moment.

The evaluation hinges on the number of chips each player possesses in relation to the total chips in circulation and the tournament's payout structure.

This critical data can be leveraged to –

• Guide players in making crucial decisions during tournament hands, particularly during the later stages or final tables.
• Aid in calculating how the prize pool will be distributed if the players agree to a 'chop' before the tournament concludes.

ICM CHART – What Factors Are Considered?

THE FOUNDATIONS – Understanding ICM in Poker

The reason for using ICM in tournament poker The worth of each tournament chip fluctuates as players are eliminated and as the payout amounts grow. This dynamic is markedly different from cash games, where each chip consistently correlates to a fixed dollar value. cash games In cash games, if you double your stack, you also double your equity, stack size, and money. Conversely, in a tournament, you could double your chips on the first hand, yet your tournament equity hasn't changed.

To illustrate this with a straightforward scenario, imagine a 10-player Sit and Go (SNG) with standard payout ratios: 1st earns 50%, 2nd gets 30%, and 3rd takes home 20%. Every player starts with 1,000 tournament chips, equating to a total of 10,000 chips in play.

At the tournament's onset, ICM reveals that, with equal stacks among players, they each have an equal share of 10% tournament equity. (It’s important to note that ICM does not factor in skill, blind levels, etc.; it simply looks at chip counts in relation to total chips).

In the initial hand of this hypothetical tournament, Player 1 doubles up (sitting in the early position) while Player 10 is eliminated (who was in the small blind). At this point, Player 1 possesses 2,000 chips while the others maintain their 1,000 chip stacks. EV Now, Player 1 commands 20% of the chips available, but have they actually increased their tournament equity from the initial 10%? table position Given the different prize pool distribution, simply doubling their chip count won’t inherently double their expected value. If the tournament were winner-take-all, Player 1, with 20% of the total chips, would enjoy a 20% chance of claiming the full prize pool. Thus, their tournament equity would indeed be pegged at 20%.

However, since the tournament's prize pool is allocated to 2nd and 3rd places as well, no player can claim more than 50% of the overall equity in the tournament. They could possibly earn 30% or 20% of their tournament equity if they land in 2nd or 3rd place. This is precisely why ICM is utilized to calculate a more nuanced portrayal of a player's tournament equity. big blind Utilizing an ICM calculator shows that Player 1's current tournament equity stands at 18.44%. Consequently, while their stack growth did elevate their equity from 10% to 18.44%, they didn't achieve a complete doubling.

What accounts for this, and where did the remaining equity distribute?

No!

Why is this the case?

The eight remaining players collectively gained the extra tournament equity, accruing 0.19% equity from Player 10’s downfall, despite not engaging in any hand! This uptick in equity is rational, as there's now one fewer contender to overcome given the same chip total is in the game.

NOTE: The prize amounts designated for each placement in earnings (ITM) will also influence ICM and the calculation of tournament equities. If the setup were 1st-2nd-3rd with payouts of 65%-25%-10% of the total prize pool, Player 1's equity would respectively rise to exactly 19% in this same context!

This example aims to clarify why relying on ICM (rather than simply looking at chip piles) is crucial in comprehending the potential value of a player’s equity at varying stages in a tournament, measured against their current chip count.

BASIC ICM: Calculating ICM (Simplified)

To further emphasize why a chip stack doubling doesn't equate to doubling a player's tournament equity (and to deepen our grasp of the ICM concept in tournament poker), let’s explore this:

Consider two players remaining in a 6-man SNG, where each contestant commenced with 1,000 chips. The payout structure awards 70% to 1st place and 30% to 2nd. Player 1 holds a significant chip advantage with 5,900 chips, while Player 2 has only 100 chips. After one hand, Player 2 manages to double their stack, raising their count to 200 chips against Player 1's 5,800.

Has Player 2's tournament equity effectively doubled due to this increase in chips?

With just two players in play, both are assured at least 30% of the overall prize pool. This guarantees a baseline return for both players should they end up losing the tournament.

As a result, any player maintaining a chip stack is guaranteed to hold slightly over 30% equity in the tournament. Consequently, in this scenario, the two players are vying for the remaining 40% of the total prize pool. (The first place payout is 70%, but since both players have secured 30%, that narrows the contestable equity to 40%. The difference between 1st and 2nd is that 40%).

As long as Player 2 has any chips remaining, they possess a chance, albeit slim, of rallying for a win, giving them a fraction of the equity in that remaining 40%.

Thus, with only 100 chips, Player 2 would have a tournament equity of 30.67%. This figure is calculated by adding the secured base equity (30%) to their potential for claiming part of the remaining 40%, gauged by their chip count relative to the total chips in circulation:

No, it hasn't.

= 30% secured equity + ((100 chips / 6,000 total chips) * 40% remaining tournament)

Following their chip doubling from 100 to 200, we can utilize the same methodology to determine that Player 2's tournament equity escalates to 31.33% .

Clearly, they have not achieved a full doubling as was initially queried.

This illustration shows that increasing one's stack in a poker tournament does not result in a proportional increase in equity. It's vital to understand how to compute ICM to make informed strategic choices from hand to hand. (Refer to further sections in this article for more insight.)

Furthermore, it equips you with knowledge on how to fairly distribute winnings among players if a 'chop' negotiation occurs at the final table. However, unlike prior examples with fewer players, calculations become slightly more intricate with more participants involved.

= 0.3 + (0.0167 * 0.4)
= 0.3 + 0.0067
= 0.3067

= 30.67% tournament equity

How To Calculate ICM In Poker

As a practical illustration, let’s reference an actual situation from Day 9 of the 2019 tournament, with chip counts at hand, to execute manual ICM calculations for an estimated chop scenario with multiple players involved.

With three players remaining, six potential outcomes exist for how the tournament may conclude. chop We will enumerate these outcomes according to 1st, 2nd, and 3rd placements: heads-up In terms of our ICM calculations, let’s aim to identify the tournament equity for Hossein Ensan, the chip leader entering Day 9. In the previously mentioned table, it's clear that Ensan has two scenarios of finishing 1st, two chances of securing 2nd, and two opportunities for 3rd.

To convert these into comprehensible ICM tournament equity, we must evaluate the probability of him landing each of these placements (predicated on the current chip counts).

Holding 63.5% of the chips in play grants Ensan a strong 63.5% possibility of taking 1st place purely based on his chip count versus the total in play.

At this stage, we must assess the options separately to account for the chances of the other players potentially outperforming him. WSOP Main Event in Las Vegas:

• Hossein Ensan - 326,800,000 (63.5% chips in play)
• Dario Sammartino - 67,600,000 (13.1% chips in play)
• Alex Livingston - 120,400,000 (23.4% chips in play)

Total chips in play: 514,800,000

NOTE: While a chop For scenario number three, Livingston carries a 23.4% likelihood of finishing 1st. To ascertain what Ensan’s chances become of landing 2nd (if Livingston takes 1st), we compute it using the formula (Ensan's chips / combined chips of remaining players, Ensan's + Sammartino's).

This calculation results in an 82.9% chance for Ensan to come 2nd, provided Livingston finishes 1st.

Now, to find the overall likelihood for this scenario, we multiply the individual probabilities: 0.234 * 0.829 = 0.194, yielding a 19.4% probability of this combination taking place.

1. Ensan, Sammartino, Livingston
2. Ensan, Livingston, Sammartino
3. Livingston, Ensan, Sammartino
4. Sammartino, Ensan, Livingston
5. Livingston, Sammartino, Ensan
6. Sammartino, Livingston, Ensan

For the fourth scenario, we repeat the calculations, but now with Sammartino triumphing (assumed at a 13.1% chance). Utilizing the same mathematical principles, we find that this scenario carries a 9.6% potential occurrence based on the ICM model and current chip stacks.

By totaling the probabilities of each outcome (19.4% plus 9.6%), we determine there exists approximately a 29% probability of Ensan placing 2nd.

Probability of Placing 1st - Options 1 + 2

The probability of Ensan finishing in 3rd amounts to 7.5% . We arrive at this figure by calculating a 4% chance of Scenario 5 happening (23.4% * (67.6 million / 394.4 million)) and a 3.5% chance tied to Scenario 6 (13.1% * (120.4 million / 447.2 million)).

Probability of Placing 2nd - Options 3 + 4

Learn how to utilize the Independent Chip Model (ICM) framework to enhance decision-making during poker tournaments by evaluating your current equity in the tournament.

The acronym ICM denotes 'Independent Chip Model', which serves as a tool for players.

It helps players identify the current share of the prize pool that is effectively theirs.

This calculation considers the number of chips each player currently holds in relation to the total chips available and the payout scheme.

Such insights can be employed to -

Guide players in making crucial decisions during a hand when they reach the later stages of a tournament, especially near the final table.

Probability for Placing 3rd - Options 5 + 6

Aid in determining how the prize money should be allocated if players decide to make a deal before the tournament concludes.

ICM CHART - What Aspects Are Considered?

Converting % into $ Using ICM

Structure of blinds and chip stacks measured in blinds.

UNDERSTANDING THE FUNDAMENTALS - How Does ICM Operate in Poker?

• 1st - $10,000,000
• 2nd - $6,000,000
• 3rd - $4,000,000

The worth of each chip in a tournament fluctuates as participants are eliminated and as the payouts increase. This contrasts sharply with cash games,

• EV of 1st = 0.635 x $10,000,000 = $6,350,000
• EV of 2nd = 0.290 x $6,000,000 = $1,740,000
• EV of 3rd = 0.075 x $4,000,000 = $300,000

where each chip has a fixed dollar value attached to it.

In a cash game, if you double your stack, you double your equity, stack size, and cash amount. Conversely, in a tournament, you might double your chips initially, but your tournament equity doesn't immediately reflect this.

For a clearer illustration, let's assume we have a 10-player Sit and Go (SNG) with a typical payout structure: 1st place receives 50%, 2nd gets 30%, and 3rd takes home 20%. Each player begins with 1,000 tournament chips, leading to a total of 10,000 chips in play.

Prior to the beginning of this tournament, ICM indicates that with uniform starting stacks, every player has a share of 10% in tournament equity.

(It's important to note that ICM doesn’t factor in player skills or blind levels; it only relates the number of chips a player possesses to the total chips in the game.)

ICM Formula for ICM Calculation

On the first hand of our theoretical tournament, Player 1 doubles their chips (sitting in the high position) while Player 10 is eliminated (sitting in the small blind). Now, Player 1 has 2,000 chips, while the others retain 1,000 each.

1. At this moment, Player 1 controls 20% of the total chips available, but have they truly doubled their tournament equity from the initial 10%?

2. Because of the prize pool distribution, simply doubling their chip count does not guarantee a doubling of equity. If it were a winner-takes-all format, with 20% of the chips in circulation, Player 1 would indeed have a 20% chance of securing the entire prize pool. Hence, their tournament equity would also be recorded at 20%.

• Chip Stack / Total Chip
• However, in this tournament structure, the prize pool is split among the 2nd and 3rd place finishers as well. Therefore, the maximum equity any player can achieve is 50% of the entire tournament's prize pool, with possibilities of walking away with 30% or 20% if finishing in 2nd or 3rd place, respectively. It is in these circumstances that ICM provides a more precise calculation of tournament equity.

3. Utilizing an ICM calculator reveals that Player 1's current tournament equity rests at 18.44%. This indicates that even though they've increased their chip count, their equity has only grown from 10% to 18.44% rather than fully doubling.

• What caused this, and where did the rest of the equity disappear?
• The remaining eight players gained additional equity totaling 0.19% thanks to Player 10's elimination, and they did not even need to play a hand to benefit! This increase in equity is logical, considering there is now one less competitor contending for the same total chips.
• NOTE: The amounts awarded for each position in the prize pool influence the ICM and the calculations of tournament equities. If the payouts had been structured at 65%-25%-10% for the top three finishers, Player 1's equity would have surged to exactly 19% under the same circumstances!
• This scenario serves to emphasize the importance of using ICM, rather than merely comparing chip stacks, to assess how a player’s tournament equity stands at various points during the competition, depending on their chip count.

4. FURTHER ICM FUNDAMENTALS: Simplified ICM Calculations

• To further clarify why simply doubling one’s chip stack doesn’t equate to doubling tournament equity, let’s consider this situation:
• Add them together.
• Imagine two players remaining in a 6-man Sit and Go, where each began with 1,000 chips and the payout structure is set at 70% for 1st and 30% for 2nd. Player 1 has an overwhelming lead with 5,900 chips, while Player 2 holds a scant 100 chips. After one hand, Player 2 successfully doubles their chips, resulting in stack sizes of 5,800 and 200.

ICM Software for ICM Calculations

Does Player 2's tournament equity truly double with this increase?

With only two players left, both players are guaranteed at least 30% of the prize pool. This percentage indicates the lowest payout either player can receive if they end up losing the tournament.

Given this, any players still holding chips must possess equity exceeding 30% in the tournament. In this case, both players would vie for the remaining 40% of the prize pool. (While 1st place holds 70%, since both players have secured at least 30%, the remaining equity to contest amounts to 40%.)

As long as Player 2 still possesses chips, there's a minor possibility they could rally to a victory. Hence, they are competing for some portion of the remaining 40% equity. database management software Thus, with a mere 100 chips, Player 2 has tournament equity estimated at 30.67%. This figure is determined by adding their guaranteed share of 30% plus their prospective chance (calculated based on their relative chip count) of acquiring a portion of that remaining 40% equity:https://www.icmizer.com/icmcalculator/ = Guaranteed 30% equity + ((100 chips/6,000 total chips) * 40% remaining tournament)

Once Player 2’s chip stack climbs from 100 to 200, this same logic leads us to find that their tournament equity rises to 31.33% .

However, it hasn't doubled, as was initially questioned.

Clearly, increasing one's stack in a poker tournament does not equate to doubling one’s equity. Mastering ICM calculation is essential for making informed tactical choices from hand to hand. (For more insights, refer to the latter sections of this article.)

Moreover, it's crucial for understanding the distribution of prizes if a potential deal arises at the final table. However, unlike previously discussed scenarios with a smaller number of players, the calculations become increasingly complex when more players are factored in.

To manually assess ICM with more than three players left in a tournament, we begin by taking a player’s chip count in relation to the total chips available and using this to gauge their chances of finishing at each potential position in the tournament.

Next, we match these probabilities with the monetary rewards corresponding to each finishing position and sum the results together.

Let’s consider a real-world example using player chip counts from Day 9 during a three-player scenario at the 2019 championship; even if this wasn’t a realistic situation in that tournament, the calculations below will serve to explain how to manually work through ICM for cooperative distributions involving multiple players.

1. With three players remaining, there are six different outcomes for how the tournament could finish.

2. Here are those possibilities listed according to 1st, 2nd, and 3rd place:

To facilitate our conversion into ICM tournament equity, we need to estimate Ensure's chances of securing each position based on the current distribution of chips.

With Ensan currently holding 63.5% of the total chips in play, he has a 63.5% probability of achieving 1st place, based solely on his chip count in relation to the total in play. MTT For this section, we will calculate options independently to account for the likelihood of the other two players finishing ahead of him.

The bubble For option 3, Livingston has a 23.4% chance of coming in 1st. To find out the probability that Ensan secures 2nd place (if Livingston is first), we divide the number of Ensan's chips by the total of the other two players' chips.

This computation results in 326,800,000 / (326,800,000 + 67,600,000) = 82.9%, indicating an 82.9% chance of Ensan finishing second, assuming Livingston is in first.

ICM Catastrophe: A Hand Example

Adding the probabilities of the different scenarios (19.4% and 9.6%) gives us a 29% chance of Ensan finishing in 2nd place.

The concluding probability of Ensan taking 3rd place computes to 7.5% . We determine this by identifying a 4% chance of Option 5 happening (23.4% * (67.6 million / 394.4 million)) and a 3.5% chance of Option 6 occurring (13.1% * (120.4 million / 447.2 million)).

• John Racener - 36,450,000 (17% of chips remaining)
• Discover the ways to leverage the concept of ICM (Independent Chip Model) in order to enhance your decision-making in poker tournaments by assessing your current equity in the competition.
• Joseph Cheong - 95,050,000 (43% of chips remaining)

ICM, which stands for 'Independent Chip Model', serves as a valuable tool. 3bet to 6.75 million with Q♣Q♦. Cheong 4bet to 14.25 million. Duhamel 5bet to 22.75 million.

It quantifies the portion of the prize pool that should fairly belong to each player based on their current standings.

These calculations hinge on the number of chips a player holds in comparison to the overall chip count on the table and the distribution of the prizes.

• This knowledge can be instrumental in helping players – Aces Make informed choices during hands, particularly as they approach the later stages of a tournament or when nearing the final table. Pocket Aces Aid in determining how the prize pool is allocated if the players decide to make an agreement or 'chop' before the tournament concludes.
• ICM CHART - Key Considerations all-in The scale of the blinds / Size of stacks measured in blinds

THE FUNDAMENTALS - Understanding ICM's Role in Poker shove The worth of each tournament chip fluctuates as players are eliminated and as payout levels increase. This dynamic is markedly different from cash games,

where each chip has a stable value equivalent to a certain dollar amount. hand ranges In cash games, doubling your chips directly doubles your equity, your stack, and the amount of money you have. Conversely, in a tournament, you might double your stack right from the first hand but that doesn't necessarily double your equity in the tournament.

For the results of the hand, Duhamel called with his Queens – and they held. He had a commanding chip lead after that, with 176 million vs. Racener's 36 million and Cheong's 7 million.

To illustrate this with a simple scenario, let’s imagine a 10-player Sit and Go (SNG) with standard payouts: the first place earns 50%, the second 30%, and the third 20%. Each player starts with 1,000 tournament chips, resulting in a total of 10,000 chips in play.

At the outset of this tournament, ICM indicates that since all players start with equal stacks, they each hold an

equity of 10% in this 10-player tournament. (Keep in mind that ICM does not factor in player skill, blind levels, etc. It strictly looks at the number of chips relative to the total in play.)

• Calculate your pot odds In the very first hand of this hypothetical situation, Player 1 manages to double their stack (positioned in the
• ) while Player 10 is eliminated (having been in the small blind). Now, Player 1 possesses 2,000 chips, while all other players retain their initial 1,000-chip stack.
• Now Player 1 controls 20% of the chips in play, but has that translated to doubling their tournament equity from its original 10% ?

Due to the different prize pool structure, simply doubling chip counts does not automatically correlate with doubling expected value (EV). If it were a winner-take-all scenario, having 20% of the chips would give Player 1 a 20% chance of claiming the entire prize pool; therefore, their tournament equity would indeed stand at 20%.

However, since this tournament's prize pool is shared by the second and third placements as well, the maximum any player can achieve is 50% equity in the tournament – which accounts for 50% of the whole prize pool. Additionally, they might earn 30% or 20% equity by placing second or third. This is why ICM plays a crucial role in accurately evaluating one's tournament equity.

1. If we utilize an ICM Calculator, we find that Player 1's actual tournament equity is around 18.44%. Hence, although doubling their chips notably increased their equity from 10% to 18.44%, it did not truly reach a double.
2. What accounts for this, and where did the remaining equity go?

The equity that remained was redistributed among the other eight players, each receiving an additional 0.19% equity due to Player 10's elimination, even without participating in any hand! This rise in equity is justifiable because there's now one less opponent competing with the same chip count.

22+,A2+,K2s+,K4o+,Q2s+,Q9o+,J5s+,J9o+,T7s+,T9o,97s+,76s,65s,54s

NOTE: The payout structure for each finishing position (in the money) will also impact ICM and the computation of tournament equities. If the payouts were structured as 65%-25%-10% for 1st, 2nd, and 3rd respectively, Player 1's equity would have escalated to precisely 19% in this scenario!

This example serves to underscore the importance of ICM, as it illustrates why relying solely on the differences in chip stacks of players is insufficient for calculating how a player's equity may change at any point during a tournament.

ADDITIONAL ICM PRINCIPLES: Simplified ICM Calculation

To further demonstrate why merely doubling one’s chip stack doesn’t result in a doubled tournament equity (while also clarifying ICM in tournament poker), consider the following:

In a 6-player SNG with each player starting with 1,000 chips and a payout format of 70% for the winner and 30% for second place, Player 1 enjoys a significant chip advantage with 5,900 chips compared to Player 2’s 100 chips. After one round, Player 2 doubles their stack, bringing the amounts to 5,800 and 200 respectively.

% Chance of Win/Loss/Tie Now, did Player 2's tournament equity effectively double after this increase?

With only two players left, each is guaranteed at least 30% of the total prize pool. This 30% represents the minimum each player can expect to take home if they lose the tournament.

Consequently, any player still holding chips will have an equity exceeding 30% in the tournament. The two remaining competitors will vie for the additional 40% left in the prize pool. (While first place garners 70%, since each player is locked at a minimum of 30%, that leaves 40% of the tournament equity up for grabs. The contrast between 70% for 1st and 30% for 2nd accounts for the remaining equity).

As long as Player 2 has chips in play, they maintain a slim possibility of mounting a comeback and capturing a portion of the remaining equity amount.

By adding all of these results together, we can see that our tournament EV, based on ICM, if we called here would be 18.47% + 0.79% + 0% = 19.25% .

Thus, with only 100 chips, Player 2’s tournament equity is calculated at 30.67%. This figure comes from adding their base assured equity (30%) to their chances of winning a piece of that remaining 40%, which is based on their stack relative to the total chip count:

• BB (Hero): 4075
• SB: 4,275
• BTN (Villain): ,5175,
• CO: 4,475

= 30% guaranteed equity + ((100 chips/6,000 total chips) * 40% remaining tournament)

After Player 2 increases their chip stack to 200, we can again apply the same formula to ascertain that their tournament equity now rises to 31.33% . muck .\"

But, evidently, this doesn’t amount to a full doubling of their equity, as initially suggested.

Additionally, this knowledge proves useful for determining how to fairly divide amounts in a 'chop' situation at the final table. However, when more players join the fray, the calculations become more intricate.

The manual calculation of ICM in scenarios with multiple players (three or more) entails assessing the number of chips each player holds in relation to the entire pool, which then helps us deduce their odds of achieving various placements in the tournament.

Following this, we must align those probabilities with the relevant cash prizes for each positioning and aggregate the results.

To demonstrate this with an actual instance, we can derive the ICM calculations based on players and chip counts from the beginning of Day 9 (three-handed play) during the 2019 event. Although the exact outcomes never materialized in this tournament, the subsequent calculations serve to illustrate how manual ICM assessments work for scenarios involving multiple players in a chop.

When three players are remaining, the tournament could end in six different ways. ICMizer These potential outcomes can be listed as follows, indicating 1st, 2nd, and 3rd placements:

For the purpose of our ICM calculations, we’ll focus on determining the ICM equity for Hossein Ensan, the chip leader on Day 9. You'll note that in the above table, Ensan has two potential scenarios for taking 1st, two for 2nd, and two for 3rd.

ICM Summary

In this segment, we’ll calculate each option separately to factor in the probabilities of the other two players placing ahead of him.

For option 3, Livingston holds a 23.4% chance of landing in 1st. To estimate the possibility for Ensan to place 2nd (assuming Livingston ends up 1st), we must calculate (Ensan's chips / combined chips of the remaining players – in this case, Ensan's and Sammartino's stacks).

This calculation yields 326,800,000 / (326,800,000 + 67,600,000) = 82.9%, indicating there’s an 82.9% chance of Ensan finishing in 2nd if Livingston takes 1st.

Originally Published on October 24, 2019