Understanding Aviator

Understanding Aviator: The Mathematics Behind the Crash Game

By Tlokotsi Potloane

Aviator is a crash betting game where a multiplier increases from 1.00x upward until it suddenly crashes. Your goal is to cash out before the crash.

Rule: Cash out before crash = win. Fail = lose bet.

Core Probability Model

$$ P(M \ge x) = \frac{1}{x} $$

This means the probability that the multiplier reaches at least x is 1/x.

Example Probabilities

Multiplier	Probability
1.5x	66.6%
2x	50%
3x	33%
10x	10%
100x	1%

Distribution Formula

$$ M = \frac{1}{U} $$

Where U is a random number between 0 and 1.

$$ P(M \ge x) = P\left(\frac{1}{U} \ge x\right) = P(U \le \frac{1}{x}) = \frac{1}{x} $$

Expected Value

$$ EV = P(win)(x - 1) + P(loss)(-1) $$

$$ EV = \frac{1}{x}(x - 1) - \left(1 - \frac{1}{x}\right) $$

$$ EV = 0 $$

Meaning: Fair game before house edge.

House Edge

$$ P(M \ge x) = \frac{0.99}{x} $$

$$ EV = -0.01 $$

Result: You lose about 1% per bet long-term.

Independence

$$ P(\text{next outcome} \mid \text{history}) = P(\text{next outcome}) $$

Each round is completely independent.

Bankroll Model

$$ B_{next} = \begin{cases} B(1 + f(x - 1)) & \text{win} \\\\ B(1 - f) & \text{loss} \end{cases} $$

$$ \lim_{n \to \infty} B_n = 0 $$

Conclusion: Long-term loss is inevitable.

Final Insight

Aviator is a probability-driven system. You cannot predict outcomes— you can only manage risk.