Mini Match is a real-time social number game for iPhone. The host starts each independent round, players privately lock a positive integer, and the lowest number chosen exactly once wins.
Mini Match is based on the well-studied Lowest Unique Positive Integer (LUPI) game. Players independently and simultaneously choose a positive integer. Duplicate choices are eliminated, and the player with the lowest remaining unique number wins. If every choice is duplicated, nobody wins. A large-scale Swedish version of LUPI was offered under the name Limbo.
The puzzle is the tension between choosing low and staying unique: obvious low numbers attract collisions, while a high unique number can still be beaten. The papers below study randomized symmetric mixed-strategy equilibria rather than one always-best pick. Some large-population asymptotic models spread choices across a low range with an effective cutoff on the order of N / log(N). This is not a universal rule: the exact equilibrium depends on the number of players, allowed range, and assumptions of the model. In the unbounded, exactly-three-player formulation, the unique symmetric equilibrium has full support and a constant hazard rate.
LUPI has been studied theoretically, in laboratory experiments, and through data from the Swedish Limbo lottery:
- Testing Game Theory in the Field: Swedish LUPI Lottery Games — Robert Östling, Joseph Tao-yi Wang, Eileen Y. Chou, and Colin F. Camerer
- Equilibrium Solution to the Lowest Unique Positive Integer Game — Seung Ki Baek and Sebastian Bernhardsson
- Exact Asymptotics and Continuous Approximations for the Lowest Unique Positive Integer Game — Arvind Srinivasan and Burton Simon
- The Three-player Lowest Unique Number Game — Balázs Szentes
For approachable discussions, see Mathematics Stack Exchange, MathOverflow, and the r/GAMETHEORY community discussion.
- Private simultaneous picks; only each player's lock status is shared before the reveal
- Host-controlled rounds with a full result reveal after every player locks
- A hostless Daily Table with one private pick per UTC day and an aggregate result the next day
- A separate all-time Game Center leaderboard for Daily Table wins
- Invite-only Game Center multiplayer and shareable party codes
- Live lobby status, reconnectable sessions, and automatic host promotion
- Game Center profiles, profile photos, and achievements
- Sign in with Apple account linking and profile controls
- English, French, Spanish, and Italian localization with accessible SwiftUI controls