Proof by Contradiction

TBD

Designer(s): e_is_cool, elara Match Type: MM (for 11 players)
Featured in: The Genius: Contractual Obligation

Main Match 3: Proof by Contradiction

IMAGE SUMMARY




Note: The second condition should read "Players lose 1 point for each time a clue of theirs was false for an opponent's final board."



STRUCTURE

In this MM, players will be placing colored tokens in their own personal 4 by 4 board, while providing clues. Each player is required to satisfy their own clues, but will aim to satisfy as few of their opponent's clues as possible.


Each player’s board is private; each player’s clues are public.


✏️ There are 6 colored tokens: Red (Triangle), Orange (Circle), Yellow (Star), Green (Plus), Blue (Droplet), Purple (Hexagon)


Players will be placing 5 out of the 6 colored tokens throughout the game.


In Round 1 and 2, a player will submit one clue and lock in the positions of two colors.

In Round 3, a player will lock in the position of one color.


CLUES

There are 4 clue formats, and a player cannot submit multiple clues of the same format. Additionally, a player cannot copy a clue that any player has used in a previous round. The 4 clue formats are listed below.


  • [COLOR] is on either [LINE] or [LINE].
  • The number of orthogonal steps between [COLOR] and [COLOR] is either [TWO INTEGERS], and both colors exist.
  • [COLOR] and [COLOR] exist and [do/do not] share a row or column.
  • The total number of colors on either [LINE] or [LINE] is [ONE INTEGER].

[COLOR] = A specific color

[LINE] = A specific row or column

[ONE INTEGER] = An integer between 0 and 5 inclusive

[TWO INTEGERS] = Two consecutive integers between 1 and 6 inclusive


INFO

During Round 1 and 2, you may query exactly two cells that are not in the same row or column. If you do so, you will learn the total count of each color among those two cells at the end of the round.


✏️ That is, for every color, you will know the number of players (including yourself) that have placed that color in either cell.


SCORING

  • Players gain 1 point for each opponent clue that is false for their final board.
  • Players lose 1 point for each time a clue of theirs was false for an opponent's final board.
  • For each color on a player's final board, that player loses 1 point for each other player's board where it is in the same position.

ENDGAME

✏️ Players are ranked based on the points they have, with ties first broken by more opponent clues that are false, then by MM2 performance.


Players are ranked by the number of points they have.

  • The highest ranked player earns a 4/4 ToL.
  • The second highest ranked player earns a 3/4 ToL.
  • The third highest ranked player earns a 2/4 ToL.
  • The fourth highest ranked player earns a 1/4 ToL.
  • The fifth highest ranked player earns a 0/4 ToL.
  • The highest ranked player that used both clue formats first place did not use earns a 4/4 ToL, replacing their current one if they have any.

Everyone with a negative point count (that doesn’t have a ToL) is an EC. If this amount is less than 3, additional players become an EC, starting from the player with the lowest rank.


CONTRACTS


There is one optional contract; you may choose whether or not to accept it.

Target Pact

Objective: Select another player; make sure they don't accept this contract, and that no one else selects this player (with this contract).

Bounty: 1 Shard


Please pick exactly one of these contracts to accept.


Contract of Boundaries

Objective: Don't place any colors in the center 4 cells or the corner 4 cells.

Bounty: 1 Shard


Contract of Iridescence

Objective: Be told in a query that each color appears at least once.

Bounty: 1 Shard


Contract of Evasion

Objective: Have none of your tokens be in the same position (with the same color) on another player's board.

Bounty: 2 Shards


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Amendment: The second scoring condition should read as follows:

  • Players lose 1 point for each time a clue of theirs was false for an opponent's final board.

Rephrasing the first two scoring conditions, if Player A's board is false for Player B's rule, then Player A steals one point from Player B; if it is true, then nothing happens.


Amendment: The image of the contracts is out of date; Contract of Boundaries has the wrong text (it should say "the center 4 cells or the corner 4 cells", as the written text does).


Amendment: You may violate your own rules at any point. However, if you violate either of your own rules at the end of Round 3, you will receive a -1000 point penalty, receive a Mark of Elimination, and be unable to complete any contracts.

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