Reading the Multiplier Distribution: What a 'Normal' Crash Game Looks Like

An honest crash game produces multipliers that follow a specific distribution, a truncated power-law with a house edge. Most rounds crash low; a small fraction reach high multipliers. This article explains the shape of that distribution, what it should look like in a large count of rounds, and how to spot a game whose distribution doesn't match what it should.

What shape should the multiplier distribution have?

In a fair crash game with house edge h, the probability that the crash multiplier is at least x is:

P(multiplier ≥ x) = (1 - h) / x for x ≥ 1

This is an inverse relationship: as x doubles, the probability halves. The result is a distribution that is heavily weighted toward low values and has a long right tail of rare high values.

For a game with 3% house edge (97% RTP), the cumulative probabilities are:

This table describes what "normal" looks like. If you play 1,000 rounds on a fair 97% RTP game, you should see approximately 40 rounds end at 1.00×, approximately 485 rounds reaching 2× or higher, approximately 97 rounds reaching 10× or higher, and approximately 10 rounds reaching 100× or higher.

These numbers are not guarantees. They are statistical expectations. In any specific 1,000-round sample, the actual counts will vary. But they should not vary wildly from these expectations, and the pattern, many low, few high, should be unmistakable.

Where does the power-law shape come from?

The shape is not arbitrary. It is a direct mathematical consequence of how crash points are generated.

In most crash game implementations, the crash point is derived from a uniform random variable (the hash output) through an inverse transformation. If U is uniformly distributed between 0 and 1, the crash point is:

multiplier = (1 - h) / U

When U is close to 1 (high hash value), the multiplier is close to 1, a low crash. When U is close to 0 (low hash value), the multiplier is very high, a rare big round. The uniform distribution of U maps to the inverse distribution of multipliers.

This is why the distribution looks the way it does:

• Most of the probability mass is at low multipliers because most of the uniform range (say, 0.5 to 1.0) maps to multipliers between 1× and 2×.
• High multipliers are rare but possible because a small slice of the uniform range (say, 0.001 to 0.01) maps to multipliers between 97× and 970×.
• The house edge shows up most visibly at the bottom. With the result rounded down to two decimals, every draw below 1.01× is shown as 1.00×, so the share of rounds that end at once is about h + (1 − h)/101: roughly 4% in a game designed at 97%, 2% at 99%.

The beauty of this construction is its simplicity: one formula, one parameter (the house edge), and the entire distribution falls out mathematically. There are no "cold streaks" programmed in, no "hot cycles," no "loosening" or "tightening." There is only the formula, which the design applies independently to each round's random input.

For a technical deep dive into how the random input is generated, see How Crash Game RNGs Work. For how the provably fair system ensures the formula is applied honestly, see our provably fair explainer.

What does a "normal" distribution look like on real data?

When you plot a histogram of 10,000+ crash multipliers from a fair game, it should show:

• A tall spike at 1.00× (rounds that end at once, about h + (1 − h)/101 of them)
• A steep decline from 1.00× to about 3.00× (this range contains the majority of all rounds)
• A long, thin tail extending to the right (occasional high multipliers)
• No gaps, clusters, or periodicities in the distribution

What you should NOT see in a fair distribution:

• A secondary peak at any multiplier above 1× (would suggest the formula has multiple modes)
• A sudden cutoff at a specific multiplier (would suggest a maximum multiplier cap below the theoretical max)
• Periodic clusters (e.g., a spike every 10× or 50×) that are not consistent with random variation
• A distribution that looks different before and after server seed rotations

The formal way to compare an observed distribution with the theoretical one is a goodness-of-fit test, such as chi-squared on binned counts or Kolmogorov-Smirnov on the whole curve. These tests quantify how likely the observed data would be if the game worked as stated.

On each game page, once a game passes 10,000 recorded rounds, the lab shows the distribution in the bins below 1.01x, 1.01x to 1.5x, 1.5x to 2x, 2x to 3x, 3x to 5x, 5x to 10x, 10x to 30x and 30x and above, together with a survival curve and the return at fixed cash-out targets. Each figure carries its sample size, its time and a 95% interval. Start from the games list, or see a single game such as Aviator or Spaceman.

By game: rounds that ended below 1.01x and rounds that reached 10x

Game	Rounds, as of	Below 1.01x (95% CI)	If the claim holds (below 1.01x)	Reached 10x (95% CI)	If the claim holds (10x)	Answers
Aviator	59,600 · 21 Oct 06:26 UTC	4.1% (4.0% to 4.3%)	4.0%	9.4% (9.2% to 9.7%)	9.7%	Answers
Big Bass Crash	Table paused	—No figure yet	—No figure yet	—No figure yet	—No figure yet	Answers
Crash X	69,367 · 21 Oct 06:28 UTC	6.3% (6.1% to 6.5%)	5.0%* (outside the measured 95% interval)	9.6% (9.4% to 9.8%)	9.6%	Answers
High Flyer	54,740 · 21 Oct 06:27 UTC	4.0% (3.8% to 4.2%)	4.0%	9.6% (9.4% to 9.9%)	9.7%	Answers
JetX	63,713 · 21 Oct 06:30 UTC	1.9% (1.8% to 2.0%)	—The provider states a range, so the standard formula gives no single figure	9.7% (9.4% to 9.9%)	—The provider states a range, so the standard formula gives no single figure	Answers
Lucky Jet	62,705 · 21 Oct 06:27 UTC	4.0% (3.9% to 4.2%)	—No provider claim, so no formula figure	9.7% (9.5% to 9.9%)	—No provider claim, so no formula figure	Answers
Space XY	67,307 · 21 Oct 06:29 UTC	2.1% (2.0% to 2.2%)	—The provider states a range, so the standard formula gives no single figure	9.8% (9.6% to 10.1%)	—The provider states a range, so the standard formula gives no single figure	Answers
Spaceman	Table paused	—No figure yet	—No figure yet	—No figure yet	—No figure yet	Answers

What does an abnormal distribution look like?

An abnormal distribution is one where the observed data deviates from the theoretical prediction in a statistically significant way. There are several patterns that indicate potential problems:

Excess instant crashes. If a game is stated at 99% but clearly more rounds end at 1.00× than the formula allows (about 2%), the game is retaining more than stated. This is the simplest form of parameter fraud: the operator increases the instant-crash rate beyond the declared value.

Deficit in mid-range multipliers. If the distribution shows fewer 5×-20× outcomes than expected, the game may be using a modified formula that compresses the mid-range. This shifts value from players (who often target mid-range cash-outs) to the house without visibly affecting the extreme tails.

Truncated tail. If the distribution shows a sharp drop-off at a specific multiplier (say, 500×), the game may be implementing a hidden maximum multiplier that is not disclosed. This steals probability mass from the tail and redistributes it, effectively lowering the RTP.

Time-dependent distribution. If the distribution looks different during high-traffic periods versus low-traffic periods, or before and after seed rotations, the game may be adjusting parameters dynamically. In a fair game, the distribution should be stationary. It should look the same regardless of when you measure it.

Each of these patterns is detectable through statistical testing, but each requires different tests and different sample sizes. Evidence Tiers explains how sample size sets what can be detected.

How does RTP interact with the distribution shape?

RTP and the distribution are two views of the same mathematical object.

A game's RTP is the expected value of a $1 bet across all possible outcomes. The distribution tells you the probability of each possible outcome. The RTP is the integral of the distribution, the probability-weighted average of all multipliers.

Changing the RTP changes the distribution in a specific way: a lower RTP compresses the distribution toward lower values. Concretely:

• A game designed at 99% ends about 2% of rounds at 1.00× and reaches 10× about 9.9% of the time.
• A game designed at 97% ends about 4% of rounds at 1.00× and reaches 10× about 9.7% of the time.
• A game designed at 90% ends about 11% of rounds at 1.00× and reaches 10× about 9.0% of the time.

The differences are small in percentage terms but add up over hundreds of rounds. In relative terms the change is the same at every multiplier, because every chance of reaching a multiplier scales with the RTP. Where it shows most is at the bottom: the share of rounds that end at once grows several times over as the RTP falls.

This is why RTP matters even for players who target low cash-out multipliers (say, 1.5×). A lower RTP does not just reduce the rare big wins, it increases the frequency of instant crashes that eat your bet before you can act. An 11% instant-crash share against 2% is the difference between losing about two bets per hundred rounds at once and losing about eleven.

How are distribution anomalies detected?

Three standard statistical tests each catch a different type of anomaly:

Chi-squared goodness-of-fit. We divide the multiplier range into bins (1.00-1.50, 1.50-2.00, 2.00-3.00, etc.) and compare the observed count in each bin to the expected count. The chi-squared statistic quantifies the total discrepancy. A large chi-squared value (low p-value) indicates the observed distribution is unlikely to have come from the theoretical one.

Kolmogorov-Smirnov (KS) test. We compare the entire cumulative distribution function, not just binned counts, against the theoretical CDF. The KS test is sensitive to deviations at any point in the distribution, including the tails. It is particularly good at detecting shifts (the distribution is offset from where it should be) and compressions (the distribution is narrower than it should be).

Runs test on binned residuals. After computing the difference between observed and expected in each bin, we test whether the positive and negative residuals are randomly distributed or whether they cluster. Clustering suggests a systematic deviation (e.g., the game consistently under-delivers in the 5×-10× range) rather than random noise.

Together these tests cover the common failure shapes. A game that passes all three on a large sample is producing a distribution consistent with its stated design. A game that fails one deserves a closer look on fresh rounds, because one failing test in many can also be chance.

Sample size sets the sensitivity. A few thousand rounds can reveal a gross deviation; hundreds of thousands are needed to see a gap of a fraction of a point. See the methodology for how the lab computes its figures.

Does the distribution help predict the next round?

No. The distribution describes how a game behaves over many rounds: how often it ends low, how often it reaches 10x. It says nothing about which round will be which. History describes behaviour. It does not predict the next round. Tools that claim to read the next result from recent ones are covered in the predictor bots check, and the idea that certain hours or sequences pay better in patterns and hot hours.