Crash Simulator
Two linked models on one page. The first computes the exact probability that a crash round reaches any given multiplier, and shows algebraically why every cash-out target carries the same negative expectation. The second runs a seeded Monte Carlo backtest so martingale, paroli and flat betting can be compared on identical terms. Every calculation runs client-side — no wagers placed, no data sent anywhere.
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What Are the Odds of Reaching x?
A Stake-style crash round draws a 32-bit integer and converts it withcrash = max(1, (2^32 / (int + 1)) × (1 − e)). That formula has a clean survival function: the probability a round reaches at least x is(1 − e) / x.
| Cash out at | Reaches it | Busts first | 1 in | EV / $1 |
|---|
The last column is the whole argument. It is constant across every row. Reaching for 100× is not a higher-variance route to a better payout than grinding 1.5× — it is the same expected loss per dollar staked, distributed into rarer, larger outcomes. Your cash-out target sets the variance of the session and nothing about its expectation.
◆ Probability of reaching the target
Emerald bar = rounds that reach the multiplier. Ruby remainder = rounds that bust first.
Where the edge is applied: when the drawn integer falls in the top of its range, the formula clamps to 1.00× — an instant bust before any target can fire. That clamp is the entire house edge; everything else in the distribution is an unmodified 1/x curve.
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Strategy Backtest
A Monte Carlo run over the same distribution. Each session starts fresh from your bankroll input, and the summary statistics aggregate the full batch. The generator is seeded, so identical seed-plus-input pairs reproduce identical output — change the seed to draw a new sample from the same distribution.
◆ Session Settings
Reached in roughly 49.5% of rounds.
After this many consecutive doublings the bet resets to base — the same function a table maximum serves. Eight doublings puts the final bet at 256× the base.
Banks the streak and returns to the base bet after this many consecutive wins.
Any 32-bit integer. The same seed and inputs return the identical result set, every time.
◆ Results
Equity curve — last session
One session from the batch, plotted round by round. The dashed line marks your starting bankroll.
Round resolution: the formula above draws a crash point, and the outcome is binary — the round returnsstake × (target − 1) when that point reaches the target, and forfeits the stake when it does not. Two boundary rules keep the simulation honest at the tail: a bankroll too small to fund the scheduled bet stakes whatever remains, and anything below one cent is treated as ruin, terminating the session.
No system in this backtest removes the edge
No betting pattern alters the −e expected value of a single crash bet. Martingale, paroli, D'Alembert, Fibonacci, "wait for a drought", scripted auto-bet with a clever stop condition — every one of these is a sum of individually negative-expectation bets, and summing negative expectations cannot produce a positive one. What a pattern changes is variance: how often a session ends in profit, how deep the worst session runs, and how fast a bad stretch closes the session out. That variance is the only thing this backtest measures. A profitable run here is a lucky seed, not a discovered edge. Wager only what you can afford to lose, and read ourresponsible gambling pageif any of this starts reading like a plan instead of a game.
◆ Where the model comes from
The crash distribution used here is Stake's published one, sourced from the Bitcointalk pre-commitment post that seeded the crash chain: a 32-bit integer is read from the round's hash and converted withmax(1, (2^32 / (int + 1)) × (1 − e)), then floored to two decimals. Ourprovably fair verifierapplies this exact function to recompute real Stake crash rounds against their published game hashes, and this page reuses that arithmetic without modification.
Two limits are worth stating directly. First, other operators' crash implementations can diverge — house edge, instant-bust handling and even the shape of the distribution vary by site, so these odds describe Stake's game and close clones of it, not crash games generally. Second, the simulator draws crash points from a seeded pseudo-random generator sampling that same distribution rather than replaying real hash chains. It models the odds; it does not archive past rounds.
Last updated: August 2026.
Keep reading
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Crash Odds, Quantified
Can any cash-out target beat the house edge?
No target changes the sign of the expectation. Cashing out at multiplier x wins with probability (1 − e) / x and pays x times the stake, so the round's expected value works out to x × (1 − e) / x − 1 = −e regardless of x — the multiplier cancels algebraically. A 1.5× habit and a 100× habit both surrender exactly 1% of every dollar wagered on average; only the shape of the outcome distribution differs.
Why does a 1.5× target and a 100× target land on the exact same expectation?
Because the underlying distribution is constructed so they must. Payout and hit probability are reciprocals of one another, both scaled by (1 − e). A 1.5× cash-out clears roughly 66% of rounds at 1.5× payout; a 100× cash-out clears about 0.99% of rounds at 100× payout. Multiply either pair together and the answer is 0.99 either way — that reciprocal relationship is the mechanical definition of a constant house edge.
Does a martingale progression change the maths?
It trades a frequent small loss for an infrequent catastrophic one. Doubling after every loss means an n-round losing streak costs 2^n − 1 base units, so required bankroll grows exponentially against a bankroll that grows linearly at best. The backtest below typically shows martingale finishing more sessions in profit than flat betting — and busting far more of the rest. That asymmetry is the entire mechanism: it compresses the loss into the tail rather than removing it. A table cap turns the tail into a guaranteed bust.
How likely is a long losing streak at a 2× cash-out target?
At a 1% house edge, a 2× target misses roughly 50.5% of rounds. Ten consecutive misses is 0.505^10 ≈ 1 in 1,090 — routine across a 5,000-round session. Fifteen consecutive misses is roughly 1 in 34,000, which still shows up reliably at volume. Progression systems fail specifically because these streaks are scheduled events at scale, not improbable outliers.
Is the model behind this simulator taken from a real operator?
The distribution reproduced here is the one Stake published when its crash chain was seeded: crash = max(1, (2^32 / (int + 1)) × (1 − e)), with int read as a 32-bit integer. It is the identical formula our provably fair verifier applies to real Stake crash rounds. Cloudbet, BC.Game and Wolf.bet may run different house edges or different instant-bust mechanics, so treat this as a model of Stake's specific implementation rather than crash games in general. Checked August 2026.
What does the seed field control, and why is it editable?
Reproducibility. The backtest draws from a seeded mulberry32 generator rather than browser entropy, so a given seed plus a given set of inputs always returns the identical bankroll path, bust rate and drawdown. Changing the seed pulls a different sample from the same underlying distribution — a useful check, since a strategy that only performs well on one seed has been fitted to noise, not evaluated.
Does a simulation actually demonstrate that a strategy is bad?
It demonstrates the shape of the risk; the proof itself is algebraic. Every cash-out target above carries the identical negative expectation, and summing negative-expectation bets in any order or sizing pattern cannot produce a positive sum. The Monte Carlo backtest exists to make the variance concrete — drawdown depth, bust frequency, and the gap between a median outcome and a mean outcome that the algebra alone doesn't show.