Monte Carlo Simulation Monte Carlo Simulation
A method of finding probabilities and averages by repeating a random experiment on a computer countless times. Slot providers and testing labs use billions of virtual spins to verify RTP and volatility.
| English | Monte Carlo Simulation |
|---|---|
| Classification | Math & Probability |
| English | Monte Carlo Simulation |
| Category | Math · Probability |
| Origin | 1940s, Stanislaw Ulam and John von Neumann |
| Name origin | Monte Carlo, the casino city in Monaco |
| Slot use | Verifying RTP, volatility, and max win |
| Typical scale | Hundreds of millions to billions of virtual spins |
Overview
A Monte Carlo simulation is a method that repeats a random process a very large number of times on a computer to find the average and distribution of the results. Even problems that are hard to calculate exactly with formulas can yield values close to the answer if repeated enough times.
The name comes from Monte Carlo, the casino town in Monaco. In 1940s US nuclear weapons research (the Manhattan Project), mathematicians Stanislaw Ulam and John von Neumann formalized this method, and because it is a calculation that relies on chance, they named it after the casino town.
How it’s used in slots
Modern slots have complex structures, such as tumbling, multipliers, and bonuses within bonuses, so it is hard to calculate every possible outcome by hand. So providers feed the game’s math model into a computer and run hundreds of millions to billions of virtual spins.
| What gets checked | Method |
|---|---|
| RTP | Sum of all wins ÷ sum of all bets |
| Hit frequency | Number of winning spins ÷ total number of spins |
| Bonus frequency | Number of bonus entries ÷ total number of spins |
| Standard deviation and volatility | How spread out the results of each spin are |
| Max win | How often the max win is reached and whether the cap kicks in |
Why run billions of spins
In high-volatility slots, part of the RTP comes from very rare big wins. For example, if a 10,000x win that hits once in 10 million spins contributes 0.1 percentage points to RTP, you need to observe that win enough times to measure RTP accurately. That’s why, with too few simulation runs, RTP comes out higher or lower than the real value (law of large numbers).
Verification by test labs
Independent test labs run their own simulations separately from the math documents submitted by the provider, to check that the published RTP matches the results of the actual program. They also test whether the RNG draws numbers evenly in a statistical sense. A game must pass this process before it can be registered with a regulator.
A small experiment to try yourself
The tables in the AI Slot wiki entries on variance and standard deviation and risk of ruin were also made with the Monte Carlo method. We ran two hypothetical 96% RTP games 20,000 times each and calculated how the probability of ruin and the probability of profit change with the number of spins. You can see in numbers that even with the same RTP, the shape of the results is completely different depending on volatility.
Uses outside slots
The Monte Carlo method is used very widely, from financial risk calculation, weather forecasting, and drug discovery to physics experiments and AI game play (the Monte Carlo tree search in Go programs). It is named after a casino, but today it is a basic tool across science and engineering.