This is a fairly easy one (at least as this website goes) with a premise taken from the Reader's Digest Book of Puzzles & Brain Teasers.
The Riddler is devising yet another trap for Batman to prove that once and for all that he has the superior intellect. Once he has the Caped Crusader at his mercy, he will challenge him to a game, as follows:
Take a chessboard-like board of squares, eight squares by eight. The two players take turns laying down tokens. Each token must be placed down so that there is not one full square that represents the halfway point between the token being played and any token already on the board. For example:
If the Riddler took his turn first, playing where the $?$ is, then Batman could put his token down where the Batman symbol is depicted, as no one square is the halfway point between his token and the Riddler's. Batman could not put his token where the $X$ is, as the purple square above it is the halfway point between that square and the Riddler's token. (On his next turn, the Riddler couldn't play there either.)
When one player cannot play any more tokens that satisfy the rule, the game is over and the other player has won.
This being the Riddler, he wants to win every time he plays. So, the question is...
What's the winning strategy for this game?