BoardSolve
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Deduction

Cluedo (Clue)

SAT solver + Monte-Carlo marginals.

3–6 players2 solversHeuristic
SAT SolverMonte-CarloImport stateReplayBest moveProbabilities
Players
Pick how many people are at the table, then enter their seating order clockwise. Mark which seat is you.
Player count
Hand
Character
Hand
Character
Hand
Character
Hand
Character

The defaults split the 18 dealt cards as evenly as possible. Assign each player their suspect token so the assistant can drag tokens when their character is called.

Your hand
Tap each card you were dealt — need 5, selected 0.
suspects
weapons
rooms
First turn
Whose turn is it right now? You can change later.
Pick exactly 5 cards in your hand to continue.

Deep dive

How BoardSolve plays Cluedo (Clue)

Clue (Cluedo) is an imperfect-information deduction game: each suggestion either teaches you a fact (a card you have just seen) or a disjunctive clue (the responder owns at least one of three named cards). BoardSolve turns the whole game log into a Boolean satisfiability problem and samples the solution set.

Logical layer

Each (player, card) pair becomes a Boolean variable: true iff that player holds the card. Every observation adds clauses: handful sizes are cardinality constraints, a shown card is a unit clause, a 'pass' is a conjunction of three negative literals, and a 'someone showed a card' is a ternary disjunction.

A DPLL-style SAT engine unit-propagates and detects forced cards — both for the envelope and for individual hands — yielding the certain deductions you see highlighted in the UI.

Probabilistic layer

Beyond the certain facts, BoardSolve runs Monte-Carlo sampling over models consistent with the clause set. Per-card marginals are reported as probabilities, and the suggestion picker scores trios by expected posterior reduction of the envelope tuples and by the Shannon entropy of the responder's reply.

References & further reading

  1. van Ditmarsch, H. (2002) . ILLC, University of AmsterdamEpistemic-logic formalisation of Cluedo that BoardSolve's variable encoding mirrors.
  2. Davis, M., Logemann, G. & Loveland, D. (1962) . Communications of the ACM 5(7), 394–397The DPLL procedure underlying BoardSolve's unit-propagation deductions.
  3. Russell, S. & Norvig, P. (2020) . PearsonPropositional logic + probabilistic reasoning chapters; basis of the two-layer (logic + sampling) architecture.
  4. MacKay, D. J. C. (2003) . Cambridge University PressReference for the Monte-Carlo marginalisation and entropy-based question scoring.