progressICM on the bubble: four players, three paid
The classic bubble with one place to go.
This page works through a bubble with four players left and three paid places. The numbers are exact results of the ICM model (the probability of finishing first is proportional to the stack, then the same rule for the next place), not estimates.
The payouts
Share of the prize pool by finishing place:
| 1st | 2nd | 3rd |
|---|---|---|
| 50% | 30% | 20% |
Equity of every stack
Example stacks, total 10000 chips:
| Seat | Chips | Share of chips | ICM equity | Equity minus chip share (points) |
|---|---|---|---|---|
| 1 | 4000 | 40% | 33.6% | -6.4 |
| 2 | 3000 | 30% | 29.5% | -0.5 |
| 3 | 2000 | 20% | 23.6% | +3.6 |
| 4 | 1000 | 10% | 13.3% | +3.3 |
The biggest stack is worth 33.6% of the prize pool while holding 40% of the chips. The smallest stack is worth 13.3% and holds 10%.
Bubble factors
Bubble factor of the row player when all-in against the column player, for the first 4 seats:
| Hero \ Villain | Seat 1 | Seat 2 | Seat 3 | Seat 4 |
|---|---|---|---|---|
| Seat 1 (4000) | — | 1.71 | 1.31 | 1.13 |
| Seat 2 (3000) | 2.69 | — | 1.48 | 1.16 |
| Seat 3 (2000) | 2.35 | 2.17 | — | 1.18 |
| Seat 4 (1000) | 1.57 | 1.48 | 1.30 | — |
Across all pairs the highest bubble factor in this example is 2.69 (seat 2 with 3000 chips all-in against seat 1 with 4000), and the lowest is 1.13 (seat 1 against seat 4). A seat with bubble factor 2.69 needs about 73% equity to call an all-in that offers even odds.
What it means for your play
- Calls need more equity than pot odds. The highest bubble factor above is the price of the riskiest call.
- The chip leader can pressure medium stacks, since the cost for them to call is high.
- Short stacks are worth more than their chips and should avoid needless gambles unless the blinds force them.
- Change the payouts in the calculator to see how the same stacks are worth different amounts in different structures.
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progressGTO guides use our own solution book (v13, 8-max tournaments with ante, chip EV): an approximation of equilibrium with a modelled postflop, not an exact solution. Numbers are computed from the book and from the exact ICM model.
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