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Comment by monochromatic | Hacker News Reader

> So we (or, more precisely, FiveThirtyEight’s lead lifestyle writer Walt Hickey) ran a simulation that flipped a weighted coin with a 97.9 percent chance of landing on a Jennings win. Every time it did, we “flipped the coin” again. We did 1 million of these simulations.

This is just a binomial distribution. Did they seriously estimate the answer instead of solving it analytically?

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Given that we stop after the first failure technically this should be a negative binomial distribution (http://en.wikipedia.org/wiki/Negative_binomial_distribution) with p = 0.979 and r = 1. The mean is p / (1-p) = 46.62. Also there is a p ^ 75 = 0.204 chance that someone of same skill will achieve a better score.

The waiting time distribution is actually the geometric distribution (with expectation 1/p = 1/0.021 = 47.6, so about what they got).

There's the didactic argument where they did it analytically but explained the intuition of the analysis mechanically. There's also the oversimplification argument where they actually did some kind of much larger sampling from a trained decision tree but then boiled the mechanism down to something easily understood by casual readers more interested in "Jeopardy!" than statistics.

I'm not certain about 538s target demographic these days.

I'm gonna guess that they did solve it analytically, but for the sake of exposition and readers that might not know what a binomial distribution, they bring up the coin-flip as an illustrative example.

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