Live and home games
Home game payouts: winner takes all or top three
Solved Hand5 min read
Before a home tournament starts, someone has to decide who gets paid. Winner takes all is simple. Paying the top three spreads the money out. The choice also changes what everyone's chips are worth, and how they should play once the field gets small. We can compare the payouts by keeping the four final stacks the same.
01The game
Ten players each pay $20, so the prize pool is $200. Everyone starts with 1,500 chips, 15,000 in all. Four players are left with these stacks: 6,000, 4,000, 3,000 and 2,000.
To put a dollar value on each stack, you need the payout table. The usual way to work it out is : it estimates each player's chance of finishing in each place from the chips alone, then adds up the prizes they would win.
| Player | Stack | Share of the chips | value | Chip chop − ICM | |
|---|---|---|---|---|---|
| 1 | 6,000 | 40.0% | 66.53 | 80.00 | +13.47 |
| 2 | 4,000 | 26.7% | 54.48 | 53.33 | −1.15 |
| 3 | 3,000 | 20.0% | 45.74 | 40.00 | −5.74 |
| 4 | 2,000 | 13.3% | 33.25 | 26.67 | −6.59 |
| Total | 200.00 | 200.00 | |||
02Three payout tables, one set of stacks
| Stack | Winner takes all ($200) | Top two ($130, $70) | Top three ($100, $60, $40) |
|---|---|---|---|
| 6,000 | $80.00 | $73.49 | $66.53 |
| 4,000 | $53.33 | $54.65 | $54.48 |
| 3,000 | $40.00 | $42.58 | $45.74 |
| 2,000 | $26.67 | $29.28 | $33.25 |
Under winner takes all, each stack is worth exactly its share of the chips. The 6,000 stack holds 40% of the chips and is worth 40% of $200, $80. Only first place pays, so every chip counts the same.
Paying more places shifts some of the prize equity from the big stacks to the small ones. Going from winner takes all to the top three, the 6,000 stack loses $13.47 of value and the 2,000 stack gains $6.59. The short stack now gets paid if it outlasts one player, and the big stack can no longer turn its lead straight into the whole pool.
03How the table changes the play
Under ICM with winner-takes-all payouts, prize equity is proportional to chips. That removes the model's payout risk premium, though tournament conditions such as rising blinds and skill differences still differ from a cash game.
Once more places pay, a chip you lose costs more than a chip you win. Busting fourth pays nothing, and surviving into third pays $40. So the short stack can be right to fold hands it would play with chips alone, and the big stack can push the others around, because they cannot afford to call. The gap is the , and it grows as the payouts get flatter.
Paying more places also means more players still have a prize to play for when the field gets small.
04If the game has to stop
Sometimes the night runs late and the players left want to split the pool and go home. ICM gives one way to split it that respects the payouts you agreed. Under the top-three table, ICM estimates the four stacks at $66.53, $54.48, $45.74 and $33.25, and those add up to the $200 pool.
The simplest alternative is a : split the money by share of chips. That gives the winner-takes-all column, $80 to the big stack and $26.67 to the short one. If the game paid three places, a chip chop pays the big stack more than its stack is worth and the short stack less. An uses the model's estimate of each stack's prize equity under the payouts you agreed. Every player must agree to a deal; ICM ignores skill and the next blinds.
Try itThe ICM calculatorAny stacks, any payouts: each stack's share of the prize pool.Try itThe rules of hold'em, step by stepHand rankings, the blinds, the order of play and the legal bets, for anyone new at the table.Sources
- Independent Chip Model, Wikipedia
- Poker tournament, Wikipedia
Solved Hand is a study tool with no real money. Nothing here is gambling or financial advice; see the disclaimer and how the charts and grades are made. If gambling is causing you harm, here is where to get help.