In this blocking game for 2 is there a clear strategy for the first player, the second player or neither?
You have a 5 x 5 grid of squares. The players take turns laying dominoes so as to cover a pair of adjacent squares. The last to be able to do so is the winner. (As readers can confirm, if 1 or 5 isolated squares remain at the end, the second player has won; if 3 or 7, the first.)
All I've been able to establish is that, if they play haphazardly, there is a greater probability of a win for the first player.
Paul Stephenson
Since this is an impartial game with a normal play, every position has a Sprague-Grundy value. If it is 0, it is a win for the previous player. Otherwise, it is a win for the next player.
Indeed, this game is called cram. The Sprague-Grundy value of the 5x5 board is 0. Thus, the second player will always have a winning strategy.