Start here · Essential guide
Variance and Standard Deviation in Games of Chance
How variance and standard deviation measure the spread of results around the average, explained with simple coin and dice examples and checked arithmetic.
Design and Decisions
Variance and Bankroll Maths
Swings, streaks and why short runs differ from long-run averages.
Bankroll Maths as a Concept, Not a Strategy
A general explanation of how stake size relates to swings and expected loss, using checked examples and without suggesting any way to profit.
Confidence Intervals for Win Rates
How confidence intervals show how much a small sample of wins and losses really tells you about a true win rate, with worked and checked examples.
Gamblers Ruin: Why a Finite Bankroll Runs Out
The classic gambler's ruin problem explained with small worked examples: why a finite bankroll meets a negative expectation and eventually runs out on average.
Short Run Versus Long Run Results
Why outcomes over a few plays vary widely while averages settle only over many, shown with coin-flip arithmetic and clear limits on what long runs mean.
Streaks and Clusters in Random Sequences
Why genuinely random sequences contain more streaks and clusters than people expect, with checked coin-flip examples and a note on what streaks do not mean.
The Kelly Criterion as a Mathematical Idea
The Kelly criterion explained as theory: how it relates stake size to a known edge, why it gives zero when the edge is negative, and what it cannot do.
The Law of Large Numbers Explained
What the law of large numbers does and does not promise, with coin and dice examples, and why it is not the same as the gambler's fallacy.
The Normal Distribution and Bell Curves
Why sums of many random events form a bell curve, illustrated with dice and coins, with the one and two standard deviation rules of thumb and their limits.
Volatility in Games: High and Low Variance Design
How game volatility contrasts frequent small outcomes with rare large ones at the same average, using two simple illustrative games with checked arithmetic.
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