Part 5 · Lesson 23 of 25 · Free
Tournaments: chips aren't cash
Three players with 5,000, 3,000 and 2,000 chips share a 50/30/20 prize pool. The leader holds half the chips but only 38.4% of the money. In a tournament that pays several places, chips and money are not proportional: the chips you could win are worth less than the chips you could lose.
The hand
Three players left, three places paid. You have 5,000 chips, the Tight-aggressive player 3,000 and the Rock 2,000. The prizes are 50%, 30% and 20% of the pool.
Predict first
You hold half the chips. What share of the prize money are your chips worth?
- Exactly 50%
- More than 50%: the leader is the favorite
- Less than 50%
Show the answer
Answer: Less than 50%
The independent chip model gives you 38.4%. You can win at most 50% of the pool, and the others are sure of at least 20% each.
Working it out
ICM sets each player's chance of finishing first to his share of the chips, then repeats for the places left. Your chance of first is 5,000 ÷ 10,000 = 50%. Of second: if the 3,000 stack wins (30%), you take 5,000 of the remaining 7,000 chips; if the 2,000 stack wins (20%), 5,000 of 8,000: 0.3 × 5/7 + 0.2 × 5/8 = 33.9%. Third is the rest, 16.1%. Worth: 0.5 × 50 + 0.339 × 30 + 0.161 × 20 = 38.4% of the pool.
Early in a tournament chip value is close to linear and chip EV decisions are fine. The closer to the money and the bigger the pay jumps, the more ICM matters.
Formula
ICM: P(1st) = stack ÷ total chips, then the same for the remaining places; equity = Σ P(place) × prize. Required equity to call (ICM) = loss ÷ (loss + gain)
Check your understanding
Stacks of 6,000, 3,000 and 1,000 chips; prizes 50/30/20. What share of the prize pool is the 6,000 stack worth, in %?
Show the answer
Answer: 41.2%
First: 6,000 ÷ 10,000 = 60%. Second: 0.3 × 6/7 + 0.1 × 6/9 ≈ 32.4%. Worth: 0.6 × 50 + 0.324 × 30 + 0.076 × 20 ≈ 41.2%.
Losing an all-in would cost 1.5 times the prize equity that winning it adds. What equity does the call need, in %?
Show the answer
Answer: 60%
Required equity = loss ÷ (loss + gain) = 1.5 ÷ (1.5 + 1) = 60%.