Editing 832: Tic-Tac-Toe

{{comic
| number    = 832
| date      = December 10, 2010
| title     = Tic-Tac-Toe
| image     = Tic_tac_toe.png
| titletext = The only winning move is to play, perfectly, waiting for your opponent to make a mistake.
}}

==Explanation==
Each map shows every possible combination of moves which will result in that side winning or tying. It assumes that X moves first, which is why the map for O has more possible move combinations and, therefore, more subdivisions.

In what follows we will use numpad notation, i.e.:
 7|8|9
 -+-+- 
 4|5|6
 -+-+- 
 1|2|3

Note that only optimal moves are shown. This means that X only begins with X7, and all grids and subgrids in Map for X have an X in position 7. For example, you can't find a grid beginning with X2, because X2 is not an optimal move. 

In map for O you can find grids beginnig with X2. Since the optimal answer is O5, you won't find X2, O8, for example.

;Example 1
The largest red X in Map for X is X7. This means that O must go to cell 7 in  Map for O. The largest red O in this subgrid is the center cell O5. Therefore X must magnify cell 5 in the map for X and look for a big red X, which is X3, i.e. in the cell (6, 4) in a 9&times;9 grid. This can be repeated until one of the players wins or there is a tie.

;Example 2
Download http://xkcd.com/832_large/ and edit it. Delete the upper part. Now you have a picture sized 2040&times;2150 pixels, with title MAP FOR O.

Assume X used the center cell, X5. You as O must magnify the center cell in the 3&times;3 map for O. Better still, select that cell and delete everything else. Now you have a picture sized 670&times;670 pixels, with a big red O7 and a big black X5. You must move O7 this time.

Assume X moves X9. You select cell 9, which is 220&times;220 pixels. Look for the biggest red O, which is O1. You can see you blocked a winning move.
 O| |X
 -+-+-
  |X| 
 -+-+-
 O| |

Now X, naively, plays X3 and you select that cell in your editor, which is 73&times;73 pixels wide and looks like this
 O| |X
 -+-+-
 O|X| 
 -+-+-
 O| |X
The O in cell 4 is red, which is your winning move.

;Title text
The title text is a reference to the 1983 movie ''{{w|WarGames}}''. In that movie, by playing Tic-Tac-Toe the AI realizes that some games cannot be won when all the players play flawlessly, and subsequently concludes that the only way to win at the nuclear warfare "game" is not to play.

==Errors==
In Map for X, the grid for X7, O9, X1, O4, X3 (i.e. go to Map for X, select cell 9, and then select cell 4) shows the same picture for O5 and O6. Those pictures belong to O6. The correct pictures should be:
 X| |O    X| |O
 -+-+-    -+-+-
 O|O|     O| |O
 -+-+-    -+-+-
 X|X|X    X|X|X

In Map for X, the grid for X7, O1, X9, O8, X3  (i.e. go to Map for X, select cell 1, and then select cell 8) shows the same picture for O2 and O5. Those pictures belong to O2. The correct pictures should be:
 X|O|X
 -+-+-
  |O|X
 -+-+-
 O| |X
 =====
 X|O|X
 -+-+-
  | |X
 -+-+-
 O|O|X

In Map for O, the grid for X8, O5, X2, O6 (i.e. go to Map for O, select cell 8, and then select cell 2) shows the same picture for X1 and X3. Those pictures belong to X3. The correct pictures should be:
  |X|    \   /    |X| 
 -+-+-    \ /    -+-+-
 O|O|O     X     O|O|O
 -+-+-    / \    -+-+-
 X| |X   /   \    |X|X

In Map for O, the grid for X2, O5, X8, O4 (i.e. go to Map for O, select cell 2, and then select cell 8) shows the same picture for X7 and X9. Those pictures belong to X7. The correct pictures should be:
 X|X|    \   /    |X|X 
 -+-+-    \ /    -+-+-
 O|O|O     X     O|O|O
 -+-+-    / \    -+-+-
  |X|    /   \    |X|

==See also==
http://xkcd.com/832_large/

==Transcript==
:[The comic comprises two large square maps, each divided into nine sections, some of which are further subdivided in the same way. The subdivisions continue down for up to five levels, and the lower map has more tiny diagrams than the upper. The smallest divisions at every scale are completed tic-tac-toe games. At the smallest divisions some of the moves are too small to see.]

:Complete map of optimal Tic-Tac-Toe moves

:Your move is given by the position of the largest red symbol on the grid. When your opponent picks a move, zoom in on the region of the grid where they went. Repeat.

:Map for X:
:[The first square map.]

:Map for O:
:[The second square map.]

{{comic discussion}}
[[Category:Logic]]
[[Category:Comics with color]]