The maths of treachery
Three small experiments behind the Burn Vote meter. Drag the sliders, flip the switches, and find out how much a single twitchy breakfast is really worth.
Bayes at breakfast
Start with how likely a guest is to be a Traitor before you know anything about them. Then add clues. Each clue multiplies the odds by its likelihood ratio: how much more often Traitors produce it than Faithfuls.
chance this guest is a Traitor
10,000 round tables
A stripped-down castle: every round table banishes the most-voted guest, every night the Traitors murder a Faithful. Each Faithful has a chance of voting for a real Traitor; otherwise they vote at random. How good do they need to be?
Faithful win rate
How long the games lasted
Faithful win rate by accuracy
Show the numbers as a table
The wisdom of the table
Two suspects, one is the Traitor. Each guest independently picks the right one with probability p. In 1785 the Marquis de Condorcet showed that if p is above 50%, a bigger table makes the majority more and more likely to be right — and if it's below 50%, a bigger table makes it worse.
chance the majority picks the Traitor
The catch, in real castles: votes aren't independent. Guests talk, herd, and get herded — sometimes by the Traitors themselves.