Prior Odds Hunt

Prior Odds Hunt is a probability reasoning game built on Bayes' theorem — the rule that governs how rational belief updates when new evidence arrives. A glowing semicircular gauge fills the screen. It shows a probability: how likely something is, right now, given what you know. Evidence arrives one clue at a time. Before each reveal, you predict whether the clue will push the probability up or down. Then the numbers appear. The gauge sweeps to its new position. The calculation shows every step of the arithmetic. The key insight the game teaches is not the formula — it is the likelihood ratio. Every piece of evidence can be summarised as a single number: how much more likely is this clue if the hypothesis is true versus if it is false? A likelihood ratio of eight means the evidence is eight times more common in sick patients than healthy ones. A ratio of 0.46 means the absence of a symptom is actually evidence against the disease. Multiplying these ratios together, one at a time, is exactly what a Naive Bayes classifier does. Playing the game is running a Naive Bayes classifier by hand. Three scenarios teach three different lessons. A medical diagnosis starts at a two percent prior — a rare disease with a low base rate — and shows how strong evidence can revise a tiny probability upward dramatically, while weak evidence barely moves the gauge at all. A spam filter introduces the experience of watching a high probability collapse from a single strong disconfirming clue. An artefact authentication bounces probability up, down, up, down, and up across five clues, demonstrating that the final answer depends only on the evidence, not the order it arrived. After every reveal, the full calculation is shown: prior odds, multiplied by the likelihood ratio, equals new odds, converted back to probability. Reading this five times is enough to understand how machine learning classifiers work from first principles.