Risk premium and the bubble
Why a coin flip is not a coin flip when the payouts are close.
7 minute read
Risk 4,000 chips to win 4,000 chips and in chips you need 50% to break even. In prize money you need more, because the equity you lose by busting is larger than the equity you gain by doubling. The gap is the risk premium, and it is largest on the bubble, when the next finisher gets nothing.
ICM break-even equity
(equity if you fold − equity if you lose) ÷ (equity if you win − equity if you lose)
Compare with the chip break-even of 50%. The difference is the risk premium.
Stacks and prizes
4 left · 3 paid| Player | Chips | Chip share | Prize equity | Prize share |
|---|---|---|---|---|
| You | 25.0% | $250 | 25.0% | |
| P2 | 25.0% | $250 | 25.0% | |
| P3 | 25.0% | $250 | 25.0% | |
| P4 | 25.0% | $250 | 25.0% |
Payouts
Malmuth–Harville ICM: your chance of first is your chip share; later places follow from the remaining chips. It ignores blinds, position and skill — a model, not a prophecy.
Calling an all-in
Risking 4,000 chips to win 4,000 is a coin flip in chips. In prize money the downside costs more than the upside gains, so you need 65.2% hand equity before calling shows a profit.
Two practical consequences. The short stack, with little equity to protect, can call closer to chip odds. The medium stack, with the most to lose relative to what it can gain, should be the most cautious — and the big stack can shove into it knowing the call needs a premium hand.
Quick check
Why does the risk premium for calling shrink after the bubble bursts?
Show answer
Once everyone is in the money, busting costs only the difference between payout steps rather than the whole min-cash, so the equity lost by losing is closer to the equity gained by winning.