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Alice and Bob take turns to place regular dominoes into a $7\times8$ board. The first player who cannot go loses.

Is there a winning strategy for either player?

Note that in this version the pips on the domino don't count for anything - it's just about placing the dominoes into the board.

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The player with the winning strategy is

Alice

Strategy

First she places a domino in the middle as follows: enter image description here
After that, whenever Bob places a domino she places hers in the position which is a $180^o$ rotation of the board from where Bob placed his. Given the symmetry she has set up, she will always be able to place a domino as long as he can.

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    $\begingroup$ That's pretty neat! I'd almost worked through all the possibilities of a non-symmetric game, which could be played if the board was initially set-up in a non-symmetric style, say for example randomly place 5 dominoes before the game starts. But that's a different question... $\endgroup$ – JonMark Perry Jul 8 at 9:02
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    $\begingroup$ Without that added wrinkle, this question devolves to a dup of coins on a table ... $\endgroup$ – Rubio Jul 8 at 12:40

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