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Respond to the question: Pure strategies in a tictactoe game?

11/01/2007 05:43 AM by va_zotov; Pure strategies in a tic-tac-toe game.
Hello, I have a very simple and dumb question about multistage games (but not enough simple for me). I'm reading Guillermo Owen's "Game theory" text book and at the page 87 he gives such an example:
Suppose tic-tac-toe game.
Step 1: Player I has 9 choises. Player II - 8 replies for any choise of I.
Step 2: Player I has 7 choises for any reply of II.
Then, Owen concludes, that at the spep 2 I has 9*7^8 pure strategies (disregarding all symetries).
My result is 9*8*7 pure strategies. I have already spent 4 hours tring to figure out the idea behind Owen's result and have understood nothing. May be somebody can help me? [Manage messages]