Independent Chip Model
In poker, the Independent Chip Model (ICM) is a mathematical model used to approximately calculate a player's overall equity in a tournament. The model uses stack sizes alone to determine how often a player will finish in each position (1st, 2nd, etc.). A player's probability of finishing in each position is then multiplied by the prize amount for that position and those numbers are added together to determine the player's overall equity.[1][2]
The ICM is also known as the Malmuth-Harville method.[3] In 1973 David Harville published a method to calculate the probability for a horse to finish 1st, 2nd, etc. in a horse race.[4] In 1987 Mason Malmuth adapted Harville's method to calculate the probability for a tournament player to finish 1st, 2nd, etc.[5].
The term ICM is often misunderstood to mean a simulator that helps a player make decisions in a tournament. Such simulators often make use of the Independent Chip Model but are not strictly speaking ICM calculators. A true ICM calculator will have the chip counts of all players, as well as the payout structure of the tournament, as input and each player's equity as output.[6]
The ICM can be applied to answer specific questions, such as:[7][8]
- The range of hands that a player can move all in with, considering the action so far and the stack sizes of the other players still in the hand
- The range of hands that a player can call another player's all in with, and recommends either calling or moving all in over the top, considering all the stacks still in the hand
- When discussing a deal, how much money each player should get
References
- ^ Fast, Erik (2012-03-20). "Poker Strategy -- Introduction To Independent Chip Model With Yevgeniy Timoshenko and David Sands". cardplayer.com. Retrieved 12 September 2019.
- ^ "ICM Poker Introduction: What Is The Independent Chip Model?". Upswing Poker. Retrieved 12 September 2019.
- ^ Bill Chen and Jerrod Ankenman (2006). The Mathematics of Poker. ConJelCo LLC. pp. 333, chapter 27, A Survey of Equity Formulas.
- ^ Harville, David (1973). "Assigning Probabilities to the Outcomes of Multi-Entry Competitions". Journal of the American Statistical Association. Vol. 68, No. 342 (June 1973): 312–316 – via JSTOR.
{{cite journal}}:|volume=has extra text (help) - ^ Malmuth, Mason (1987). Theory and Other Topics. Two Plus Two Publishing. pp. 233, Settling Up in Tournaments: Part III.
- ^ Walker, Greg. "What Is The Independent Chip Model?". thepokerbank.com. Retrieved 12 September 2019.
- ^ Selbrede, Steve (2019-08-27). "Weighing Different Deal-Making Methods at a Final Table". PokerNews. Retrieved 12 September 2019.
- ^ Card Player News Team (2014-12-28). "Explain Poker Like I'm Five: Independent Chip Model (ICM)". cardplayer.com. Retrieved 12 September 2019.
Further reading
- Harrington, Dan; Robertie, Bill (2014). Harrington On Modern Tournament Poker. Two Plus Two Publishing LLC. ISBN 1-880685-56-6. Harrington discusses the ICM on pages 108-122.
- Collin Moshman (July 2007). Sit 'n Go Strategy: Expert Advice for Beating One-Table Poker Tournaments. Two Plus Two Publishing LLC. pp. 122–. ISBN 978-1-880685-39-6.
- Jonathan Grotenstein; Storms Reback (15 January 2013). Ship It Holla Ballas!: How a Bunch of 19-Year-Old College Dropouts Used the Internet to Become Poker's Loudest, Craziest, and Richest Crew. St. Martin's Press. pp. 17–. ISBN 978-1-250-00665-3.