xkcd is a very funny web comic. But I saved this particular episode not for the humour content, but as a really interesting example of information design and data visualization. It's an illustration for every optimal move to win (or at least draw) a game of Noughts and Crosses (or Tic-Tac-Toe, for the non-Commonwealth readers), anticipating every possible move of the opponent:
It takes a few moments to figure how to read it, but it's so rewarding. The red X's mark the optimal move - here, X moves first, and the optimal move is the top-left square. O may make any of 8 possible moves in response; drill down into one of the 8 largest "boxes" in the grid to find the smaller red X that anticpates that next move, and so on. As more moves are played without a win, you'll drill deeper and deeper into the chart until you get to the smallest sub-games (you'll need to view the larger version by then), many of which end in a draw (or tie).
It's a lovely, and unique, example of hierarchical information design, where the one layer serves as the framework to put the next layer down in context, all the while encapsulating the results from all 102 possible games. I counted that number by hand -- each small box represents a completed game in the chart -- so I might be off a couple. It's clearly smaller than the number of possible games when not playing optimally, and doesn't count the symmetry of X playing in any of the four corners. The chart for O is more complex (it's much harder to win when you don't get to go first) and is also included in the full chart linked below.
xkcd: Tic-Tac-Toe (via)
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