# Tactical Domino Placement Game

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.

The player with the winning strategy is

Alice

Strategy

First she places a domino in the middle as follows:
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.

• 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...
– JMP
Jul 8 '19 at 9:02
• Without that added wrinkle, this question devolves to a dup of coins on a table ...
– Rubio
Jul 8 '19 at 12:40