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Monte Carlo Simulation for Game Odds: A Starter Guide
Learn how Monte Carlo simulation estimates game odds by running many random trials, with a dice example, accuracy notes and the limits of the method.
Math Toolkit
Simulation and Modeling
Testing odds with simulations, spreadsheets and simple models.
Expected Duration: How Long Does a Game Last?
See how per-turn probabilities translate into an average game length, with dice examples, the 1/p rule, stage-by-stage totals and why averages hide spread.
How Many Trials Make a Simulation Reliable?
Learn how the number of simulation trials sets the precision of an estimate, with the square-root rule, sample-size examples and the trouble with rare events.
Markov Chains and Board Game Movement
A plain introduction to Markov chains as a model for board game progress: states, transition probabilities, a small worked track and what the model can predict.
Random Walks and the Gamblers Ruin Intuition
Understand random walks as a model of cumulative luck, why swings grow with the square root of time, and what gambler's ruin says about limited funds.
Simulating Dice Rolls in a Spreadsheet
Set up a two-dice experiment in a spreadsheet with RANDBETWEEN and COUNTIF, build a frequency table, and compare results with the exact probabilities.
Testing a Strategy Against Random Opponents
How to set up fair simulated comparisons between simple game strategies: shared random draws, clear metrics, random baselines, and honest error ranges.
Writing a Simple Probability Simulator in Python
A short educational Python script outline for simulating dice rolls and card draws, with a reusable estimate function, a seed and exact answers to check.
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