> 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.<p>This is just a binomial distribution. Did they seriously estimate the answer instead of solving it analytically?
> <i>Here’s how we figured this out. We assumed that Jennings headed into Final Jeopardy with at most one other player in contention to win. Then we assumed that in order for Jennings to lose, this sequence of events has to happen: The game must not be locked up, Jennings must get the Final Jeopardy question wrong, and the other contender must get it right. We used his stats across all 75 of his games, not just his 74 wins, to better reflect his overall skills. The probability he doesn’t have the game locked up is 13.3 percent, the probability he gets Final Jeopardy wrong is 32 percent, and the probability the other contender gets it right is 49 percent. When we combine these probabilities, we see that Jennings only has about a 2.1 percent chance of losing.</i><p>This is incorrect and overstates his dominance because (1) it assumes Jennings will be ahead, something that won't always happen against Rutter/Jennings/Collins/Chu/Craig level players and (2) the lock up and opponent knowing Final Jeopardy conditions are not independent.<p>Pretty sloppy basic probability by 538 and make me think I'm not missing much by not subscribing (they didn't offer full RSS last I checked).
I'm convinced that not only do we stand on the shoulders of giants, but we live among giants. What Ken Jennings accomplished is remarkable by any interpretation. How he did so probably even he can't explain.