The math behind Bustament's crash curve, and a tool to verify it yourself.
Bustament takes nothing from the crash curve. Every multiplier pays exactly what it should. We make money from tournament buy-in fees, and only from those.
P(crash >= m) = P(h >= 2^52 (1 - 1/m)) = 1/m
Cashing out at m wins mx with probability exactly 1/m, so expected value is 1.00 at every multiplier.
Most crash sites use 99 in that numerator instead of 100. That single digit is their 1% house edge. Bustament uses 100.
| Cash out at | Chance of reaching it | Expected value |
|---|---|---|
| 1.5x | 66.67% | 1.00 |
| 2x | 50.00% | 1.00 |
| 3x | 33.33% | 1.00 |
| 5x | 20.00% | 1.00 |
| 10x | 10.00% | 1.00 |
| 100x | 1.00% | 1.00 |
Rounds crash at exactly 1.00x about 1% of the time. This is not a forced or rigged bust — it's a natural consequence of the same formula above: whenever the raw computed value lands in [1.00, 1.01), the round crashes immediately. No special case, no separate rule.
Before a tournament's first round, we generate a random terminal seed and hash it forward through a long chain. We publish SHA-256(seed[0]) — the committed hash — before anyone plays a single round.
Each round uses the next seed in the chain, shown to players as its hash before betting opens. After the round ends, the seed itself is revealed and the crash point can be recomputed from it.
When the tournament completes, the terminal seed is published. Anyone can hash it forward the required number of times to derive every round's seed and confirm every crash point that ever ran.