Academy Contents
Monte Carlo Simulation
Understanding how computer simulations model gambling outcomes. Learn how Monte Carlo methods estimate probabilities and risks.
Key Formula
Simulation Result = Average of N Random TrialsWhat is Monte Carlo Simulation?
Monte Carlo simulation uses repeated random sampling to model probabilistic outcomes. By running thousands or millions of simulated gambling sessions, we can estimate the distribution of possible results, from best case to worst case scenarios.
Key Points
- Uses random sampling to model outcomes
- Runs thousands of virtual sessions
- Estimates probability distributions
- Named after Monte Carlo casino
How Monte Carlo Works
The simulation uses a random number generator to determine each bet outcome according to the game probabilities. It tracks bankroll changes over the session and records the final result. Repeating this thousands of times builds a statistical picture.
Key Points
- Generate random outcomes using game probabilities
- Track bankroll through entire session
- Record final result of each session
- Analyze distribution of all results
Accuracy and Convergence
As the number of simulations increases, the results converge toward the theoretical expected value. This is the Law of Large Numbers in action. More simulations yield more accurate estimates.
Key Points
- More simulations = more accurate
- Results converge to theoretical EV
- 1000+ simulations for reasonable accuracy
- 10000+ for high confidence intervals
Applications in Gambling Analysis
Monte Carlo simulation helps answer questions that are difficult to solve mathematically, such as the probability of reaching a win goal, the distribution of session outcomes, and risk of ruin with complex betting patterns.
Key Points
- Estimate risk of ruin distributions
- Model complex betting systems
- Calculate percentile outcomes
- Validate theoretical calculations
Try It Yourself
Apply what you've learned with these interactive tools:
Continue Learning
Learn how expected value (EV) determines the long-term outcome of gambling decisions and why negative EV is unavoidable in casino games.
Understanding how variance affects short-term results. Learn why even games with the same house edge can have very different risk profiles.
Understanding the probability of losing your entire bankroll before achieving your goal. Critical for bankroll management.
18+ Only. Gambling involves risk. Please gamble responsibly. Learn more →