Mathematicians have constructed a set of five dice that allows five players to determine a single winner with one simultaneous roll, eliminating the need for rerolls or tiebreakers.
Each die carries a distinct set of numbers chosen so that, when all five are rolled together, the highest face is always unique and every player has an exactly equal chance of producing it.
The discovery resolves a question that had remained open for about ten years: whether such a fair, single-roll mechanism exists for five participants.
Previous solutions were known for two, three and four players, but the five-player case resisted both exhaustive search and constructive proof until now.
The dice are not standard cubic dice; their faces bear carefully calculated integer values that create the required probability distribution.
Researchers verified the design by checking all possible joint outcomes, confirming that no two dice can tie for the highest value and that each die wins exactly one-fifth of the time.
The result is a pure existence proof; the dice have not been manufactured for commercial use.
The work contributes to the broader study of non-transitive dice and fair-division protocols in combinatorial mathematics.
Dice discovered that solve decade-long mathematical problem
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