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):
There are 3 win conditions (paraphrasing from link below) :
- usual tic-tac-toe format: the same sized pieces in a row [horizontal, vertical, diagonal]
- 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]
- 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:
$\endgroup$ 31 Answer
$\begingroup$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. Unless you play by the revised rules where it is necessary to play with two colors instead of just one
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