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Our test was essentially a "birthday paradox" simulation, with 8 people in total and 7 possible birthdays. Instead of checking whether two or more people share a birthday, we tested whether six or more people shared a birthday. Per a math/rand simulation with ten million iterations, that test has a 0.13% flake rate. That is low enough that we didn't immediately notice, but high enough to realistically cause problems at some point. My previous math in the test comment was clearly wrong. First, we recently lowered the range by 1, and `(1 / 7) ** 6` is three times higher as a probability. Second, that's the probability of 6 people to share the same birthday, without taking into account the extra two people in the total of 8. That clearly drives the chances up, per the birthday paradox. Double the number of people to 16, and look for 14 or more to share a birthday. The simulation returns a 0% chance at that point, so it's extremely unlikely to cause issues. Fixes #634. |
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