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This is a Gomoku like game, played by two players with Go pieces (black and white stones) on an infinite (in all four directions) Go board.

Rules

  1. Four in a row: players alternate turns placing a stone of their color on an empty intersection. Black plays first. The winner is the first player to form an unbroken chain of four stones horizontally, vertically, or diagonally.
  2. Sticky: except for black's first stone, every stone must be placed adjacent to one of your opponent's.

Question: can black force a win?

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  • $\begingroup$ Does "adjacent" include diagonally adjacent? $\endgroup$
    – Benjamin Wang
    Commented Oct 28, 2021 at 10:39
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    $\begingroup$ @BenjaminWang Sure. Every intersection has eight adjacent neighbors. $\endgroup$
    – Eric
    Commented Oct 28, 2021 at 10:41
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    $\begingroup$ This is actually much tricker than I thought. Getting 3-in-a-row is rarely an immediate threat because the blank space is usually not adjacent to the opponent and so not immediately playable. $\endgroup$
    – Jaap Scherphuis
    Commented Oct 28, 2021 at 13:02
  • $\begingroup$ The only possible endgame I think is to create two 3-in-a-rows with one move, where the move itself and the two fourths are pairwise adjacent (forming a small triangle). Obviously the problem is how to force such a position in the first place... $\endgroup$
    – Bubbler
    Commented Oct 29, 2021 at 4:31
  • $\begingroup$ Looks like a funny game to play with family or friends, but I suspect that a systematic study would simply be an exhaustive search, probably computer-aided. Maybe @Eric can clarify whether there is a clever approach to be expected. $\endgroup$
    – WhatsUp
    Commented Oct 29, 2021 at 8:12

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