Katy's
Noughts and Crosses Game
To win my game of noughts and crosses you need to
have three X in a row before I get three O in a row. Click on the board
in the place you want to put your X
When the game ends, you can start a new one by clicking anywhere on the
board.
To make it more fun you can select any one of my four different levels
of difficulty – Good luck, I will be watching to see how you are doing!
The more you play the better you will get.
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Despite the apparent simplicity of noughts and crosses, it requires some
complex mathematics to determine the number of possible games. This is
further complicated by the definitions used when setting the conditions.
In theory, there are 19,683 possible board layouts (39 since each of the
nine spaces can be X, O or blank), and 362,880 (i.e. 9!) different
sequences for placing the X’s and O’s on the board; that is, without
taking into consideration winning combinations which would make many of
them unreachable in an actual game.
When winning combinations are considered, there are 255,168 possible
games. Assuming that “X” (That’s you) makes the first move every time:
131,184 finished games are won by ” X”
1,440 are won by “X” after 5 moves
47,952 are won by “X” after 7 moves
81,792 are won by “X” after 9 moves
77,904 finished games are won by “O”
5,328 are won by “O” after 6 moves
72,576 are won by “O” after 8 moves
46,080 finished games are drawn
Ignoring the sequence of X’s and O’s, and after eliminating symmetrical
outcomes (i.e. rotations and/or reflections of other outcomes), there
are only 138 unique outcomes. Assuming once again that “X” makes the
first move every time:
91 unique outcomes are won by “X”
21 won by “X” after 5 moves
58 won by “X” after 7 moves
12 won by “X” after 9 moves
44 unique outcomes are won by “O”
21 won by “O” after 6 moves
23 won by “O” after 8 moves
3 unique outcomes are drawn
Strategy
You can play perfect noughts and crosses if you choose the move with the
highest priority in the following.
Win: If you have two in a row, play the third to get
three in a row.
Block: If the opponent has two in a row, play the third
to block them.
Fork: Create an opportunity where you can win in two
ways.
Block Opponent's Fork.
Option 1: Create two in a
row to force the opponent into defending, as long as it doesn't result
in them creating a fork or winning.
For example, if "X" has a corner, "O" has the centre, and "X" has the
opposite corner as well, "O" must not play a corner in order to win.
(Playing a corner in this scenario creates a fork for "X" to win.)
Option 2: If there is a
configuration where the opponent can fork, block that fork.
Centre: Play the centre.
Opposite Corner: If the opponent is in the corner, play the opposite
corner.
Empty Corner: Play in a corner square.
Empty Side: Play in a middle square on any of the 4 sides.
The first player, you or "X," has 3 possible positions to mark during
the first turn. Superficially, it might seem that there are 9 possible
positions, corresponding to the 9 squares in the grid. However, by
rotating the board, you will find that in the first turn, every corner
mark is strategically equivalent to every other corner mark. The same is
true of every edge mark. For strategy purposes, there are therefore only
three possible first marks: corner, edge, or centre. Player “X” can win
or force a draw from any of these starting marks; however, playing the
corner gives the opponent the smallest choice of squares which must be
played to avoid losing.
The second player, me or "O," must respond to X's opening mark in such a
way as to avoid the forced win. Player ” O” must always respond to a
corner opening with a centre mark, and to a centre opening with a corner
mark. An edge opening must be answered either with a centre mark, a
corner mark next to the “X”, or an edge mark opposite the “X”. Any other
responses will allow “X” to force the win. Once the opening is
completed, O's task is to follow the above list of priorities in order
to force the draw, or else to gain a win if “X” makes a weak play.