Clue Deduction Lab

The setup

• 21 cards: 6 suspects, 6 weapons, 9 rooms. One of each type goes in the envelope. The other 18 are dealt clockwise, so seats 1–2 get 5 cards and seats 3–4 get 4. Everyone knows these hand sizes.
• Pure deduction, no board. Every turn a player may suggest any suspect, weapon and room. Dice and walking to rooms are left out, so the turn counts here are the logical minimum for this strategy. A real board game takes longer.
• After a suggestion, players to the left answer in order. The first one holding any of the three cards shows exactly one, privately. If they hold several, they show a card they already showed that same player when possible, so they leak less.
• A player accuses only when their notebook proves all three envelope cards. They may accuse at the start of their turn or right after their own suggestion. A correct accusation ends the game.
• Standard questions: in each category still unsolved, name the envelope candidate the notebook knows least about. In a solved category, name a card from your own hand (or the solved card) so that slot cannot draw a response and the answer must come from the other two.
• Smart questions: the player builds 120 complete deals that fit everything in their notebook. For each of the 324 possible suggestions, it plays out every deal: who would show a card, and which one. It then asks the suggestion that leaves the least uncertainty about the envelope on average, so it hunts for the answer and learns about other hands only when that helps. It also reads opponents' suggestions: people rarely name cards from their own hand, so a deal where an opponent holds a card they asked about counts for less. This reading only steers which question to ask. It never puts a mark in the notebook.

Notebook marks

• ✓ this player holds the card (or, in the Envelope column, it is the answer).
• ✗ this player does not hold it.
• Small numbers are open clues. When P2 shows someone else a card for the suggestion on turn 9, every onlooker writes 9 in P2's column next to all three named cards. P2 holds at least one of them.
• Cell colour says how the mark was earned: plain ink for things seen directly, coloured for things deduced. Click any cell for the exact reason and the turn it was learned. A yellow frame marks what was learned this turn.

Rules of inference, by level

Each level keeps all the rules of the levels before it, and repeats them until nothing new follows.

1. BASIC One place per card. A ✓ anywhere crosses out the rest of that row. If every column but one is ✗, the last one is ✓.
   One answer per category. Once the envelope suspect is known, every other suspect is ✗ in the envelope. If all suspects but one are ✗ there, the last one is the answer.
   Direct marks. Your own hand, cards shown to you, and players who pass (✗ on all three cards).
2. COUNTING Hand sizes. If P3 holds 4 cards and four ✓ are known, the rest of the column is ✗. If only four cells in P3's column are not ✗, all four are ✓.
3. CLAUSES Numbered clues. Clue 9 says P2 holds Plum, Rope or Hall. When Plum and Rope get ✗ for P2, Hall becomes ✓. If any of the three is already ✓, the clue is explained and closed.
   Clues fill the hand. If P4 holds 4 cards, 2 are known, and two open clues share no cards, those clues must use up the last 2 slots. Every other unknown in P4's column is ✗.
4. PERFECT Exhaustive search. The notebook tries to build complete deals that agree with everything observed. If no consistent deal puts a card in some place, that cell is ✗. If every consistent deal puts it in the same place, that cell is ✓. This finds every fact that logically follows, including chains no simple rule names.

SMART uses the Perfect notebook and changes only how questions are chosen (see The setup).

What the numbers say