A group of grad students and I regularly meet up at conferences. Often, we spend our coffee breaks between talks playing various suggested generalisations of common pen-and-paper games to see if we can find an interesting one. This has lead to some quite interesting games in the past such as connect 4 with changing gravity, and tic-tac-toe on more general surfaces (such as a cylinder and Klein bottle). A group favourite, which was suggested a few months ago seems to be an interesting variant of Ultimate Tic-tac-toe.
For want of a better name let us call it Spillage-tic-tac-toe or Spillage for short.
Before stating the rules I shall ask my question.
Is the game Spillage a well-known variant of Ultimate Tic-tac-toe? If it is, is there a reference to the game being solved in the literature? If it is not, can any insight into winning strategies be offered?
I'll now attempt to give the rules of Spillage. I apologise for not including any images with the rules (which would help to illustrate certain game states) and if anyone feels like editing the question with such illustrations, you are encouraged to do so.
- Players: 2
- Board size: 9x9 - separated in to 9 smaller 3x3 'meta squares' similar to Ultimate ttt.
We will label the 9 smaller 3x3 meta boards in the obvious way with the numbers 1 - 9 (using bold to indicate a meta square) reading from top-left to bottom-right, and the individual 81 squares by subscripts n_m to denote the m-th square in the n-th meta square. So for instance the four corner squares would be labelled 1_1, 3_3, 7_7, 9_9.
As usual, player O and player X alternate placing their respective symbols, O's and X's, on the board, with X going first, until a player wins or all available squares have been played in without a win (resulting in a draw).
There is no restriction to where a player may place their O/X (this is the first major deviation from Ultimate ttt).
When a player creates a line of three consecutive identical symbols anywhere on the board, if the central symbol is in a meta square which has not yet been claimed, then that player claims the meta square which that central symbol lies in. Chains of more than three consecutive symbols are considered to be separate instances of three-symbol chains, each with their own central symbol.
For instance, if no meta squares have yet been claimed, and the squares 4_2, 1_9, 2_4 all have O's in them, then 1_9 is the central symbol of the chain and so O claims the meta square 1 . If O later plays 2_2, then (if 2 has not been claimed yet), 2_4 is a central symbol and so O will claim the meta square 2 as well.
Once a meta square has been claimed, it can not be claimed by the other player. A player wins, when they claim a chain of three consecutive meta squares as in the usual tic-tac-toe. So, for instance if player O later claims 3 in the above scenario before X can win, then O has won the game.