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To explore this space I created an Exercism exercise called dnd-character.
First @AnAccountForReportingBugs suggested testing the mean/std.dev. via sampling, but that didn't persuade the crowd (myself included). There were two concerns: performance, and probability of false negatives. -- "Our unit tests should be 'too fast to notice'" -- "With which frequency will this test randomly fail?" -- "[...] I'd be happy to be proved wrong by a 100% reliable test that executes in <100ms." after which they rightfully responded,
Then @jippiee suggested testing the probability distribution, and actually delivered a PR to the Java track. First, it cached the correct probability distribution, but provided a program that generates it. I tried to nudge the PR along, and this prompted @jippiee to submit a couple of graphs, one after the other:
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