The game of tic-tac-toe, also spelled ticktacktoe and also known as 3-in-a-row or "naughts and crosses," is a game in which players alternate placing pieces
(typically Xs for the first player and Os for the second) on a 
board. The first player to get three pieces in a row
(vertically, horizontally, or diagonally) is the winner. For the usual 
board, a draw can always be
obtained, making it a futile game.
Wolfram (2022) analyzes 
and 
tic-tac-toe as multicomputational
processes, including through the use of branchial
graphs.
A generalized 
-in-a-row
on an 
board can also be considered, as can a generalization to a three-dimensional "board."
The game consisting of getting five (or more) in a row on a board variously considered
to be of size 
or 
is known as go-moku. The specific
case of 
tic-tac-toe is known as qubic.
For 2-in-a-row on any board larger than 
, the first player has a trivial win. In "revenge"
tic-tac-toe (in which 
-in-a-row
wins, but loses if the opponent can make 
-in-a-row on the next move), even 2-in-a-row is non-trivial.
For instance, 
on a 
board is won for the first player if he starts in the second or fourth square, but
not if he starts elsewhere.
In 3-in-a-row, the first player wins for any board at least 
. The first player also wins on a 
board with an augmented corner square, with three distinct
winning first moves (Gardner 1978).
If the board is at least 
,
the first player can win for 
(the 
board is a draw). The game is believed to be a draw
for 
, is undecided for 
, believed to be a proven win for 
, and has been proved as a win for 
by means of variation trees (Ma).
For 
, a draw can always be obtained on
a 
board, but the first player can
win if the board is at least 
. The cases 
and 7 have not yet been fully analyzed for an 
board, although draws can always be forced for 
and 9.
In higher dimensions, for any 
-in-a-row, there exists a dimension 
board (
) with a winning strategy for the first
player (Hales and Jewett 1963). The Hales-Jewett theorem, a central result in Ramsey theory, even allows for more than two players,
a dimension 
will still exist that gives a first player win. For 
and 
, the first player can always win (Gardner 1979),
thus establishing 
for 
and 
. For 
, Golomb has proven 
with a Hales-Jewett pairing strategy (Ma 2005). Values
of 
for other 
are unknown, and the Hales-Jewett theorem does not help, as
it is existential and not constructive.
