Crash,
priced as a heavy tail.
Crash looks like a guess: when do I cash out. The math is actually fixed. Every cashout target has the same expected value per dollar wagered. What changes is variance. What also changes is whether you survive long enough to see the average.
Crash, in 60 seconds
A multiplier starts at 1.00x and climbs continuously until it crashes. You bet before the round, optionally set an auto-cashout multiplier, and either pull the trigger before the crash (collect bet × multiplier) or miss it (lose the bet). One round, one decision.
The interesting part is the distribution: the multiplier does not climb forever with equal probability. It follows a heavy-tailed inverse curve, with a small hard-coded probability of an instant crash at 1.00x to bake in the house edge.
Where the 3% house edge lives
Most crash games use a variant of this formula (the Stake / BC.Game family is documented; others tune the instant-crash probability slightly):
Pseudocode
fraction = HMAC_SHA256-derived value in [0, 1)
if fraction < 0.03: // hard-coded instant crash, ~3%
crash = 1.00
else:
crash = floor( (0.99 / (1 - fraction)) × 100 ) / 100
The 0.99 numerator is what produces the 99% RTP. The 0.03 instant
crash probability produces the 3% effective house edge. Together
they yield the heavy-tailed distribution players observe.
Probability of reaching multiplier M (and cashing out at M):
P(crash ≥ M) = 0.99 / M (approximately, for M ≥ 1.01)Because P(reaching M) shrinks as 0.99/M, every cash-out target has the same expected value per dollar:
EV per $1 at cashout target M
EV = P(reach M) × (M − 1) + (1 − P(reach M)) × (−1)
= (0.99/M) × (M − 1) − (1 − 0.99/M)
= 0.99 − 0.99/M − 1 + 0.99/M
= -0.01
→ −1% per $1, before the instant-crash term
→ −3% all-in, with the 1.00x instant crash baked in
The result is invariant in M. Whether you target 1.5x or 100x,
the long-run cost is the same. Variance differs wildly.Same EV, different rides
The cash-out target you pick determines your win probability and your variance. EV is fixed; everything else is preference.
| Cashout target | P(win) | Net per $1 win | Felt-shape |
|---|---|---|---|
| 1.10x | ~90% | +$0.10 | Most rounds win small. Single bust streaks erase weeks of micro-wins. |
| 1.50x | ~66% | +$0.50 | Two-of-three winning. Comfortable rhythm; bust streaks are real but recoverable. |
| 2.00x | ~49% | +$1.00 | Coin-flip cadence. The "I always cash at 2x" baseline. Bust streaks of 5+ happen. |
| 5.00x | ~20% | +$4.00 | One in five. Bust runs of 10–15 standard. Variance product. |
| 10.00x | ~9.7% | +$9.00 | One in ten. Long droughts then big spikes. Only viable on small unit. |
| 50.00x | ~1.94% | +$49.00 | Lottery shape. Almost never wins; covers it when it does. |
| 100.00x | ~0.97% | +$99.00 | Pure tail bet. Hundreds of losses per win at any sustained pace. |
The non-obvious read: the 2x cashout has the highest dollar- return-per-spin paired with the highest hit-rate. The 100x cashout has the same EV but you need a bankroll to absorb ~100 losses to see one win.
What to actually do
Auto-cashout removes the chase. The biggest losing pattern in crash is "let it ride", because the math says nothing changes but adrenaline says otherwise. Auto-set, walk away.
A 10x target needs 100 bets in your bankroll, minimum, to avoid bust. A 2x target survives on 30. Match unit size to the cashout volatility, not the dollar value of one win.
Doubling after a 2x bust on the next round produces the same blowup pattern as Martingale roulette. The instant-crash term turns it lethal: a 5-loss streak at 2x targets is ~3.4% likely. Bankroll dies.
Crash is provably fair, that's the upside
Every multiplier is derived from a HMAC-SHA-256 of your client seed plus a per-round nonce, with the server seed published before the session. Once the seed rotates, you can replay every round you played and verify the multipliers match. See the provably-fair guide for the verification walkthrough.
What this proves: the operator did not retroactively lower a multiplier after you placed your bet. What it does not prove: that the published instant-crash probability is what they said it is. For that, you need a sample-size analysis on thousands of rounds, which is the same problem as auditing slot RTP.
