ICM Basics: Chips Are Not Money

The Independent Chip Model Converts Tournament Chips Into Shares Of The Prize Pool, And It Shows That Chips Are Not Worth Their Face Value: With Half The Chips In Play And Three Players Left, A 50/30/20 Payout Gives The Chip Leader 38.39% Of The Prize Pool, Not 50%.

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Why Chips Are Not Money

In A Cash Game A Chip Is Worth Its Face Value, Because You Can Leave With It. In A Tournament You Cannot. You Are Paid By Where You Finish, And The Prize For Finishing First Is A Fixed Amount No Matter How Many Chips You Win It With. That Is Why Each Extra Chip Is Worth A Little Less Than The One Before It, And Each Chip You Lose Costs More Than A Chip You Win Is Worth.

The Independent Chip Model, Usually Called ICM, Puts A Number On That. It Estimates How Often Each Player Finishes In Each Paid Place From Their Share Of The Chips, And Multiplies Those Chances By The Payouts.

A Worked Example

Take Three Players With 5000, 3000, 2000 Chips And Payouts Of 50, 30, 20 Percent Of The Prize Pool. The Malmuth-Harville Version Of ICM Says Each Player Wins First Place In Proportion To Their Chips, So The Chip Leader Wins 50% Of The Time. Given Who Finished First, Each Remaining Player Finishes Second In Proportion To The Chips That Are Left, And So On.

Run Through Every Order And The Chip Leader's Equity Is 38.39% Of The Prize Pool, The Middle Stack's Is 32.75% And The Short Stack's Is 28.86%. The Leader Holds Half The Chips But Less Than Half The Money. The Short Stack Holds A Fifth Of The Chips And More Than A Fifth Of The Money, Because It Is Already Guaranteed A Share Of Third Place And Can Still Move Up.

ICM Equity, Three Players, 50/30/20 Payouts, Malmuth-Harville
PlayerChipsChip SharePrize Equity
Player 1500050%38.39%
Player 2300030%32.75%
Player 3200020%28.86%

What ICM Changes At The Table

Because Losing Chips Costs More Than Winning Them Gains, Calling An All In Needs More Equity Near The Money Than A Chip Count Alone Suggests. Players Who Cover Their Opponents Can Apply Pressure, Because The Short Stacks Have More To Lose By Calling. Short And Medium Stacks Should Avoid Marginal Confrontations With The Chip Leader.

ICM Has Limits. It Looks Only At Chip Counts And Payouts, Not At Position, Blinds, Skill Or Who Is About To Be Forced All In. It Is Most Accurate Close To The Money And At Final Tables, And Less Useful Early In A Tournament When The Payouts Are Far Away. Treat It As A Strong Guide To How Much A Chip Is Worth, Not As A Complete Strategy.

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