What makes a crash game feel fair: the math behind a 1% edge

A crash game is the simplest product in your lobby and the easiest one to accuse of cheating. A line goes up, a rocket explodes, somebody's 40× auto cash-out didn't trigger, and the chat calls it rigged. The math is almost never the problem. What players see of the math usually is.

This is a practical walk through the one formula behind a 1% crash game, what it means for your hold, what "provably fair" proves (and what it doesn't), and the UI decisions that make an honest game also feel honest.

The whole game is one formula

In the standard crash design, the chance that the multiplier reaches a value x before it crashes is:

P(reach x) = 0.99 / x

That's it. The 0.99 is the house edge. bustabit, one of the longest-running crash games, puts it plainly in its provably fair write-up: the 99 in its formula is the house edge, encoded directly. Its house edge page gives the operator's view: on a 1 BTC wager it expects to earn 0.01 BTC.

Now the neat part. If a player bets 1 and cashes out at x, they win x with probability 0.99 / x. Expected return: x × 0.99 / x = 0.99. The x cancels. Every target, from 1.01× to 1,000×, returns 99% in the long run.

So there is no "good" target and no strategy that beats the edge. A player who cashes out at 1.5× wins 66% of the time and grinds slowly; a player who waits for 100× wins about 1 round in 100 and lives on hope. Same 99%. bustabit's mechanics page lists the same win chances: 49.5% at 2×, 9.9% at 10×, 0.99% at 100×.

Where the edge actually lives

Here is the version we run in Rocket Chip, our play-money demo, and essentially the formula bustabit publishes:

crash = max(1, floor(99 / (1 − X)) / 100), with X uniform in [0, 1)

Two details matter.

• The edge is spread over every multiplier. The 99 shaves every possible crash point by 1%, which is why the expected return is the same at every target.
• The instant bust is a side effect, not the edge. With this formula, about 1.98% of rounds end at 1.00×, before anyone can cash out (the chance of reaching 1.01× is 0.99 / 1.01 ≈ 98.02%). People often say the 1% "is" the instant bust. It isn't, and older crash games that bolted on a separate "1 in 101 instant bust" rule did the maths differently. Know which one your provider ships.

If you want a different edge, the general form is P(reach x) = (1 − e) / x. For reference, Spribe lists Aviator's RTP as 97%, a 3% edge.

Look at how small the visible difference is. A player can't feel the gap between 49.5% and 48.5% at 2×. Your P&L can: a 3% edge triples theoretical gross win on the same turnover.

Why "fair" is a feeling: streaks and the history bar

Here is what an honest 1% game looks like from the player's chair, using the same formula:

• The median crash point is 1.98×. Half of all rounds end below it.
• About 17.5% of rounds crash below 1.20×.
• Five rounds in a row below 2× happen with probability 0.505⁵ ≈ 3.3%. In a busy room that is every half hour or so.
• In any 30 rounds, there is about a 4.4% chance of seeing no 10× at all.
• On the other hand, the chance of at least one 100× in 100 rounds is about 63%.

None of that is suspicious, and all of it will be called suspicious. The fix is not to change the math. The fix is to show enough history that a cold streak looks like what it is: noise.

• Show at least the last 20–50 results in the history bar, colour-banded (for example, under 2×, 2–10×, over 10×), and link each one to its verification data.
• Never filter the history. Hiding low results to make the bar look hot is the fastest way to lose the players who check.
• The live bets feed must be real. Our play-money demo fills it with simulated players so you can see the layout; in a real lobby, a feed of invented winners is deception, not design.

Caps change liability, not the edge

Every real crash game has a maximum: a top multiplier, a maximum profit per bet, or a maximum total payout per round. Operators sometimes worry that a cap "breaks" the RTP. For cash-out targets below the cap, it doesn't: the chance of reaching x and the payout at x are unchanged, so the return stays 99%. What the cap removes is the far tail, which is exactly what your risk team wants removed.

Two rules make caps feel fair:

1. Put the cap in the rules and on the bet panel, with what happens when it is hit (the round ends and every open bet is paid at the cap, or bets are paid up to the max profit).
2. Apply it in the open. If a shared round hits the room's total payout cap, say so on screen. "The rocket exploded at 1,204×" and "we stopped paying" are not the same event.

Provably fair: what it proves, and what it doesn't

The provably fair model is elegant. As bustabit describes it, the operator generates a long chain of SHA-256 hashes (bustabit's has 100 million), publishes the last one before any game is played, then plays the chain in reverse. Each game's crash point comes from an HMAC-SHA256 of that game's hash, salted with the hash of a Bitcoin block that had not been mined when the chain was committed, so the operator couldn't pick a lucky chain. Anyone can recompute results with the open-source verifier.

Single-player originals such as dice and mines use a seed pair instead. In Stake's model, the server seed is hashed with SHA-256 and shown before play, the player can set their own client seed, a nonce increases by 1 on each bet, and the real server seed is revealed when the player rotates the pair.

What this proves: the result was fixed before the bet and nobody changed it afterwards. What it doesn't prove:

• that the game pays what it shows, or that withdrawals work;
• that the software, RNG and rules meet a regulator's technical standards. In regulated markets that is the job of accredited labs and standards like GLI-19, which also asks operators to compare theoretical and actual RTP;
• that the experience is responsible. That part is still on you.

Latency and the "I clicked at 2.00×" problem

Most crash complaints are about timing, not odds. The player clicked at 2.00×, the server received the click at 2.04×… or after the crash. Rules that prevent the argument:

• The server is the clock. The cash-out multiplier is the server's value when the request arrives. Show it in the confirmation, to two decimals.
• Auto cash-out runs on the server and pays exactly at the target. Make it the default teaching tool for new players (Rocket Chip has one per bet).
• Don't extrapolate on the client and round up. If the client curve runs ahead of the server, the player will screenshot a number you never paid.
• Write down the disconnect rule. For example: open bets with an auto cash-out are settled at the target; bets without one are settled at the crash.

A fairness checklist for your crash game

The short version: a 1% crash game is fair by construction. Whether players believe it depends on whether you show the formula, the history and the server's numbers. Show all three, and the chat will find something else to complain about. Probably the music.

Want to see it working? Play Rocket Chip (play money), compare it with Hyper Dice where the player sets the odds directly, or browse all the Scatterhaus Originals.

18+Gambling content for business readers. Every demo we link to runs on play money. If gambling stops being fun, free confidential help is available: BeGambleAware (UK), 1-800-GAMBLER (US), Gambling Therapy (worldwide).