Your strategic position determines what information you hold and what decisions you face each round.
You know who all the Traitors are. Each night you choose a Faithful to murder, and at the Round Table you must vote and speak without giving yourself away. Survive to the end and the prize is yours.
Game theory concepts: coordination games, pooling equilibria, cheap talk, credible threats.
You don't know who the Traitors are. Watch what people say, how they vote and who gets murdered, update your beliefs, and persuade the castle to banish the right people.
Game theory concepts: Bayesian updating, signalling, information cascades, collective action.
8 players, 2 Traitors, numbers announced. No recruitment, no challenges. A starter or plenary.
12 players, 3 hidden Traitors, one recruitment, prediction challenges. Follows the teacher guide's lesson pathway.
14 players, 4 hidden Traitors, majority voting, high signal costs. For Year 13 or Oxbridge stretch.
Estimated time: —
Everyone starts at the base rate. Each speech, vote and murder carries a likelihood ratio, and Bayes' rule turns these into the probability that each player is a Traitor, given the castle's model of how each type behaves.
If Traitors can say exactly what Faithfuls say, speeches tell you nothing (pooling). Here, making wrong accusations costly makes Traitors accuse less, so the types partly separate. In theory, that only happens if the cost hits the two types differently.
Speaking up helps the group but makes you a murder target. With the game's illustrative payoffs, keeping quiet is a dominant strategy and everyone ends up worse off. Whether a real Round Table works like this depends on how big that murder risk is.
Once a few people accuse the same player, others may follow the crowd rather than their own evidence. Majorities are reliable only when judgements are independent, and cascades destroy that.
Plurality, majority and supermajority rules change who gets banished, how often nobody is, and how easily a coordinated minority can swing a split vote.
In a known final round, promises can't be enforced. A recruitment ultimatum ("join us or be murdered") works only if the threat is credible, and the payoffs decide whether accepting is rational.
Select a role above to begin
Posterior probability that each player is a Traitor, from Bayes' rule. Click a name to see the evidence.