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In an SMBC comic published on 20 June 2022, Zach Weinersmith proposes the following variant of tic-tac-toe:

  • Play consists of a number of rounds
  • At the start of each round, each player rolls a d6 in secret
    • A player rolling 1 or 2 is set the goal of winning the round (which in this game means 'making a line of three')
    • A player rolling 3 or 4 is set the goal of drawing the round (neither player makes a line of three)
    • A player rolling 5 or 6 is set the goal of losing the round (never making a line of three)
  • Board and play are as regular tic-tac-toe, with starting player alternating between rounds; except that play continues until all nine squares are filled, no matter if a line of three is made
  • After the end of the play, a player who achieved their goal scores 1 point; a player who did not achieve their goal scores 0 points
  • First player to 5 points wins; if both players reach 5 points simultaneously, play continues, and the overall winner is whoever is first to take a lead

So, a player is trying to both achieve their goal (known) and to prevent opponent's goal (can only be inferred). Formally, they maximize: their score - opponent's score.

What does best play look like?

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  • 1
    Two corrections: 1."once the board is filled" - players play all 9 turns in a round. Only then they reveal their secret mission and calculate scores. 2. if both get to 5 points then then they play "golden goal" the next player to have higher score wins the game.
    – Cohensius
    Jun 22 at 12:08
  • Ah, I misinterpreted the tie-breaker, thanks. When we continue to fill the board, does the presence of both O lines and X lines count as a 'win' for both players, or only the first to be made?
    – AakashM
    Jun 22 at 12:13
  • 1
    We only exam wins/loses/draws when the round ends, after 9 turns. both players can win/lose/draw or more importantly: each player can get her goal or not. So the score at each round is one of the four options: (0,0), (0,1), (1,0), (1,1)
    – Cohensius
    Jun 22 at 12:32
  • @Cohensius I think I've got all that in now
    – AakashM
    Jun 22 at 12:39
  • 1
    see the twitter debate at: twitter.com/ZachWeiner/status/1538935850339377154
    – Cohensius
    Jun 22 at 12:57

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