Chip chop and ICM — deals when few are left

What happens when the last players want to split and stop, why a plain chip chop favours the big stack, and how ICM works it out — with an example you can check yourself.

It is one in the morning, three players are left, and the blinds are so big that the next hand may as well decide everything. Someone asks: “Shall we split?” It is a sensible question, and the answer should be decided in advance — both whether you do it, and how.

Why deals are normal

Late in a tournament the stacks are short compared to the blinds, and what decides it is largely who gets dealt cards. A deal trades a random ending for a fair split, and everyone gets home. In home games it is common, and nothing to be embarrassed about.

What is not fine is negotiating the how for twenty minutes. Have one method you always use.

The example we use

Three players left. What remains to be split is three prizes: 1,500, 900 and 600 — 3,000 in total. The stacks are:

PlayerChipsShare
A60,00060%
B25,00025%
C15,00015%

Chip chop

The simplest method: split everything that remains by share of chips.

PlayerChip chop
A1,800
B750
C450

Easy to calculate, and wrong. A gets more than first prize, which is the most anyone can win by playing it out. And C gets less than third prize, which is the least C can finish with. A plain chip chop overvalues the big stack, every time.

ICM

ICM — the Independent Chip Model — works out what each stack is worth in prize money, not in chips. The idea is that chips are worth less the more of them you have, because prizes do not grow as fast as stacks: the player holding 60% of the chips does not have a 60% chance of finishing in each position.

The model uses chip share as the probability of winning, then works out the probability of second and third from the remaining stacks. Multiplied by the prizes, that gives:

PlayerICMChip chop
A1,2301,800
B950750
C820450

Everyone now sits between the lowest and highest prize, and the differences reflect how likely each of them actually is to win. That is why ICM is the standard for deals in tournaments.

The arithmetic is tedious by hand with three players and impossible with five. There are free ICM calculators online, and some tournament tools have it built in.

The simple compromise

If you do not want a calculator at the table, there is a middle ground that is easy to compute: everyone locks in the lowest prize, and the rest is split by chip chop.

Three players get 600 each — 1,800. The remaining 1,200 is split 60/25/15:

PlayerLocked + chip chop
A600 + 720 = 1,320
B600 + 300 = 900
C600 + 180 = 780

Not as precise as ICM, but close enough, and everyone understands where the number came from.

Rules for deals

  1. Decide in advance whether deals are allowed, and which method you use. Then there is no negotiation when it happens.
  2. Everyone has to agree. One player who wants to play it out means you play it out.
  3. Write it down. Note what each player got, and that it was a deal. If you keep a leaderboard, everyone in the deal counts as a shared placement — see Points systems and leagues.
  4. No deal during a hand. Between hands, with the clock stopped.

In DealMeIn

The tournament room has Prize distribution & deals with both chip chop and ICM computed from the recorded stacks. You can adjust the amounts by hand before confirming, and the deal is recorded as a shared placement in the result. See Run the tournament.