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Expected Value in Games: What the Average Outcome Tells You
Learn what expected value means, how to calculate it for simple game choices, and why the long-run average is a useful guide but never a prediction.
Applied Math
Expected Value and Variance
Averages, spread and what they say about repeated play.
Calculating Expected Damage in Tabletop Combat
Multiply hit chance by damage to compare attacks in tabletop combat, with worked d20 examples covering crits, multiple attacks and advantage.
Expected Value Traps: When the Average Misleads
See how skewed payouts, rare jackpots and ignored limits make the average outcome a poor description of what players actually experience.
High Variance Versus Low Variance Game Designs
Compare swingy and steady game designs: how variance shapes tension, skill expression and replay, and which kinds of players tend to enjoy each style.
Median Versus Mean in Game Outcomes
Why the typical result in a game can differ from the average. Mean and median explained with drop-rate and loot examples that include checked numbers.
Risk of Ruin Explained for Resource-Based Games
Understand the chance of running out of resources in games with random swings, and how stake size, spread and starting reserves shape that risk.
The Law of Large Numbers in Plain Language
A plain-language look at how long-run frequencies settle toward true probabilities, what that does and does not promise, and common misreadings.
Variance and Standard Deviation Explained Through Dice Rolls
Use dice and dice sums to see how variance and standard deviation measure spread around the average, with every step of the arithmetic shown.
Weighted Averages and Fair Prices for Game Items
Learn how to weight outcomes by probability to value a random reward such as a loot box or card pack, and how to compare that value with its price.
Why Short Sessions Rarely Match the Averages
Why a single evening of play can stray far from expected value: small samples, normal streaks and the numbers that show how much wandering is typical.
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