RULES OF ENGAGEMENT

The duel

Each duel pairs you against one opponent on the same problem. The fastest correct answer wins. Both wrong? Draw. Both right within a second? Draw.

Opponents

By default we pair you against a stored attempt by a real player at your rating. When no real ghost is available, we drop in a calibrated AI opponent whose accuracy and speed are sampled from a profile matched to your level.

Glicko-2

Your rating starts at 1500 with high uncertainty (RD=350). It moves quickly during your first few duels and stabilizes as the system learns your level. Beat opponents above you and you gain a lot; lose to opponents below you and you drop fast.

Tiers

Problems

Competition-math style — algebra, number theory, combinatorics, probability, geometry, series. Problems are drafted by Claude Haiku and validated by Claude Sonnet before they go live. Answers are numeric or simple expressions (e.g. 42, 3/4, -1). Whitespace and dollar signs are stripped before comparison.

Identity

You're anonymous. We set one HTTP cookie containing a random UUID — that's your "player." No email, no password, no signup. Clear cookies and you become someone new.

Fair play

Rate-limited per cookie. Solve times are measured and validated on the server, so a doctored stopwatch won't win you a tiebreak. Each duel scores exactly once. Bail on a problem you don't like and it's recorded as a forfeit, not a free re-roll — so the only way to genuinely climb is to beat real ghosts at your level.

The leaderboard

Ranked by your confidence-adjusted rating — Glicko-2's lower bound (rating − 2·RD) — so a brand-new account can't leap to the top off one lucky win. Play a handful of duels and your uncertainty (RD) shrinks; until then you're marked provisional (*).