The SBMC comic shared rules for a new version of tic-tac-toe today — I'm trying to figure out if there's a mental-poker/zero trustless version which could be played between two untrusting players (without the "monitor").
- Is there a way we can know this is not possible?
- Is there a way that this is possible?
The complex bit: the two players are playing on their own private tic-tac-toe boards (three each), and the fact that a square is already occupied by your opponent is only exposed after you play in that square.
I'm trying to learn more about how to approach problems like this, so any "working" would be useful too!
The rules
(From SMBC)
Setup
Requires 3 people: 2 players and 1 "monitor"
Each player has three private tic-tac-toe boards, which their opponent cannot see, but the monitor can. They are labeled A, B, and C.
There are also 3 public tic-tac-toe boards which everyone can see. These are also labeled A, B, and C.
Gameplay
Players take turns writing one symbol in one square on their private board. Squares that are occupied on a private board are also occupied on the corresponding public board.
Once a player draws a symbol on their private board, the monitor checks to see if their opponent has already occupied that square by writing a symbol on their private board.
If the square is already occupied, the player who tried to occupy it a second time loses their turn. The symbol in that occupied square is then drawn in the corresponding square of the public board.
Scoring
Whenever a player gets three in a row on a board, up-down, left-right, or diagonal, they get a point. The winning board is not publicly revealed, but players may no longer play on it.
Winning
Whoever has the most points when no more moves are possible wins.
