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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.


Spillage

  • 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.

Spillage tic-tac-toe

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.

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    As a side-note, I'm new to this particular SE (but not the SE-network), so if my question doesn't conform to any community guidelines, I apologise. – Dan Rust Nov 23 '13 at 4:32
  • Tic tac toe has roughly 3^9<20000 possible states. This game has roughly 3^81>1e38 possible states. These are both large overestimations, but I very much doubt this game is solved. For comparison, a similar estimate gives that the number of states for chess is 12^64>1e69. – KSFT Sep 11 '16 at 21:38
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    @KSFT Does noughts and crosses really have that many states? Surely you can consider states which are symmetries of other states to be the same. – TRiG Sep 16 '16 at 0:50
  • @TRiG No, all the games have far fewer legal states than that. It's just a very rough estimate. – KSFT Sep 16 '16 at 23:50
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BGG doesn't have any game with "Spillage" in the title. Looking at the Tic-Tac-Toe entry there is also no game that reimplements Tic-Tac-Toe which is the same as Spillage. There are a number of games which play some sort of meta-game of Tic-Tac-Toe in which there are nine 3x3 games being played and the object is to get 3 in a row on the meta-board. So all in all "Spillage" would seem to be as good a name as any.

I'd guess that the game is a first player win like the game Hex since having an extra position can't hurt.

Since it is a "new" game it won't have been solved. But writing a program to play would need a dept first approach with symmetry. The look ahead would seem to be fairly uncomplicated so I'd guess that a computer could either win or tie with a decent program.

Given that the human moves first I'm not sure that a human could out-play a computer on this. If such a winning strategy could be found for the first player then the game would just be a gigantic meta-Tic-Tac-Toe game of course.

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    You're right that it's either a first-player win or a draw, by strategy-stealing, but I don't see any compelling reason to believe that it's one over the other. – Steven Stadnicki Dec 12 '16 at 23:06

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