hachi from the block (hachibambatar) wrote in multitic,
hachi from the block

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further generalisations

in my experience, tic tac toe on 4x4 boards, row of 4 to win is not a playable game and in fact always ends with cat.

here is the most general definition of tic tac toe i can muster, which also includes connect 4 without gravity...

n dimensions, p players, l cells to an edge, w cells in a row or diagonal to win.

perhaps there is a topological method of looking at multidimensional tic tac toe. in n dimensions, how many cells border a given cell? (including along diagonals) obviously this is different on edges, different on walls, different in corners, and different in high dimensional analogues of such things.

i suggest using a bit of the language of go here, and refer to a cell's bordering cells as liberties.

clearly on a large board (length, not necessarily dimensions), the first player will always win if only 3 in a row are required to win.

i see you monitoring this, perhaps you should post...
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