Begin with a base rate, then run noisy tests one at a time and revise your belief, beware the false positives that trip up everyone's intuition.
Each case has a hidden cause with a known prior (base rate). Run diagnostic tests one by one, each with its own sensitivity and specificity, and update how strongly you believe the cause is present. Set your final belief and lock in. You're scored on how well-calibrated your stated probability is against the Bayes-correct posterior, not just which side you picked.
Prior Knowledge is a Bayesian-reasoning game about base rates, test accuracy and calibrated belief.
Running diagnostic tests with known sensitivity and specificity against a cause with a known prior is Bayesian updating, and it is built to provoke the base rate fallacy.
Running the tests one at a time, updating as you go, is the original structure.
The fallacy is reliable enough to be a public-health problem: for a rare condition, a positive result from a 99%-accurate test can still mean the cause is unlikely, because the false positives drawn from a large healthy population outnumber the true positives drawn from a tiny sick one. Sequencing the tests makes you watch the prior do that work.
Prior Knowledge is a Bayesian-reasoning game about base rates, test accuracy and calibrated belief. It's an original free browser game built for PlayPendium.