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Squid Games. Four players go in turn (while observing each other), move each their own piece (_ wazir) onto one square vertically or horizontally on the 5x5 board (watch the image below). If one player manages to reach the other side without stepping on one of the four (invisible and randomly placed) squids, the team wins. How is the best strategy for their co-operation? And the win rate?

Trying four rows at random has a ~95% win rate. I don't know whether there is a strategy that has a >99% win rate.

Squid Games

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    Welcome here. I think this question is better suited for Puzzling.CE or BoardAndCardsGames.CE because this challenge is not related to chess or chess-variants at all (but for the checkered board).
    – Evargalo
    Apr 15 at 8:39
  • 3
    I’m voting to close this question because this question is not really related to chess, and belongs to possibly puzzling.SE
    – DialFrost
    Apr 15 at 8:52

1 Answer 1

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Let's name the files from A to E and the rows from 1 to 5.

Each player will either go through the board and bring victory, or reveal the position of exactly one squid by their generous sacrifice.

Player 1 can try the path a3-b3-c3-d3-e3.

  • If they go through, hurray!
  • If they die on e3, they have revealed a safe path until d3: player 2 will try to exploit this by going a3-b3-c3-d3-d2-e2.
  • If they die on d3, they have revealed a safe path until c3: player 2 will try to exploit this by going a3-b3-c3-c2-d2-e2.
  • If they die on c3, they have revealed a safe path until b3: player 2 will try to exploit this by going a3-b3-b2-c2-d2-e2.
  • If they die on b3, they have only revealed one useless safe square a3, from where one can only try to go to a2 or a4, squares already accessible from the starting point. Player 2 should goind through either the row 2 or the row 4.
  • If they die on a3, it's just the same.

We can continue the strategy: if a safe path has been opened until the B-file at least, exploit it with the remaining options that avoid known squids. Otherwise, try to open a path on a new row.

Calculating exact probabilities might be boresome, but I think I will revert to computer simulation when I can find some time...

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