If each all-in is an independent event, the chance of winning several in a row is the single-all-in chance raised to the number of all-ins. A true coin flip five times is 1 in 32. The 53% column is the neighborhood of deuces against ace-king offsuit. The 57% column is a slightly better edge. Both of those edges are examples. The powers are exact for the percentages shown.
| All-ins in a row | True 50/50 flips | At 53% | At 57% |
|---|---|---|---|
| 1 | 50.0%, 1 in 2.0 | 53.0% | 57.0% |
| 2 | 25.0%, 1 in 4.0 | 28.1% | 32.5% |
| 3 | 12.5%, 1 in 8.0 | 14.9% | 18.5% |
| 5 | 3.1%, 1 in 32 | 4.2% | 6.0% |
| 7 | 0.8%, 1 in 128 | 1.2% | 2.0% |
| 10 | 0.1%, 1 in 1,024 | 0.2% | 0.4% |
Aces against callers, wins and equity.
Equity counts split pots at half. An outright win does not. Each row is a simulation of 100,000 deals against that many random calling hands.
| Callers | Aces win outright | Aces' equity, splits included |
|---|---|---|
| 1 | 85.0% | 85.3% |
| 2 | 73.1% | 73.3% |
| 3 | 63.8% | 64.0% |
| 4 | 55.4% | 55.7% |
| 5 | 48.8% | 49.1% |
| 6 | 43.4% | 43.7% |
| 7 | 38.1% | 38.4% |
| 8 | 34.6% | 34.8% |
| 9 | 30.9% | 31.1% |
One bubble.
Four players remain and three are paid, 50%, 30%, and 20%. The stacks are an example: 4,000, 3,000, 2,000, and 1,000. The 4,000 stack shoves. The 3,000 stack has to call off the rest of its chips. In chips, that call wants 50% equity. Under the Malmuth-Harville model, folding keeps 29.5% of the prize pool and winning the all-in brings 40.5%, so the call wants 72.9% equity. The model ignores the blinds still to be posted. Near the money, staying alive is worth more than the chips in the middle.
These counts are for study and post-session review. Where a row comes from a simulation, the caption names how many deals were run. Where a stack or a pot is made up, the caption says so. None of these figures is an instruction for a live pot.