What is an advantage worth?

Data: the survivoR project's tables (MIT licence), through Gamebot, my warehouse of Survivor statistics. The vote model predicts whom each castaway writes down at a tribal council, from the record up to that night: who has voted with whom, who has voted against whom, the voter's allies' last targets, immunity wins and idols held. It is gradient boosting, trained on 77 seasons from five countries and tested on US seasons it never saw. Votes are drawn for everyone at once, with a fitted setting for how tightly blocs vote together. The most votes go home, and an idol held by the main target cancels the votes against them as often as real idols did. Separate models pick immunity winners and the jury's votes, and castaways find idols at the rate of their era.

In the advantage test, each replay hands the advantage to one castaway picked at random. With no advantage, a castaway picked at random wins one season in n, where n is the number left, so the difference is the advantage's value. Each past season is replayed with models fitted without it. The browser runs the same code as the Python, and a test checks that both compute the same features and vote probabilities to fifteen decimal places. Split votes count as votes cast together. Before the merge, replays start at the first tribal on each season's last pre-merge tribes, because swaps aren't simulated. One boot per council, no quits or returns, and no reward challenges. A tie goes to a random pick, with no revote or rock draw. The simulator also can't tell who knows about an advantage. The data records who held one, not who had heard about it, so a known idol and a secret idol look the same to it. Code, the plan written before fitting, and every report are in the repository; the project page has the full write-up.