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The game "Otrio" is sort of a 3D version of tic-tac-toe (2 space dimensions and 1 size). You play as 1 color on a 3x3 board, and you control 9 pieces (3 small, 3 medium, 3 large circles): Otrio board and pieces

There are 3 win conditions (paraphrasing from link below) :

  1. usual tic-tac-toe format: the same sized pieces in a row [horizontal, vertical, diagonal]
  2. three pieces in a row [horizontal,vertical,diagonal] in either ascending or descending size order [e.g. small, medium, then large going from top left to bottom left]
  3. three concentric pieces in the same space [i.e. in the same space you have your small, medium, big]

Even though this is more complicated than tic-tac-toe it seems like the game tree is not so expansive and it should be fairly easily solvable with e.g. alpha-beta pruning? So then what is the optimal strategy if you are in a 2 player game, or if you are in the full 3-4 player game?

See this link for more: http://www.marblesthebrainstore.com/otrio.htm

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    $\begingroup$ This seems to be 3x3x3 tic tac toe, where the third dimension is "ring size". $\endgroup$ – Mark S. Dec 25 '16 at 2:58
  • $\begingroup$ Wikipedia on 3D tic-tac-toe: "The 3x3x3 version of the game cannot end in a draw, and is easily won by the first player." No winning strategy is provided in the article, but I assume it is in one of the several references in that section. $\endgroup$ – Rahul Dec 25 '16 at 3:11
  • $\begingroup$ Yes, and beyond the regular 2 player 3d version of tic-tac-toe, this one has 3 or 4 player gameplay options, so that should change strategy in interesting ways... $\endgroup$ – sambajetson Dec 25 '16 at 3:15
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If you are playing a two player game, there is a guarantee win for the first player,it is not really a formula, just play the medium circle in the middle, then on the side, when he blocks you, place a larger circle on the same square as the mid-sized wall piece, that way you are set up for either a descending order, or three circles on top of each other. https://barronwasteland.wordpress.com/2015/12/28/solving-otrio/ Unless you play by the revised rules where it is necessary to play with two colors instead of just one

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