On the biased n-in-a-row game

The biased version of the n-in-a-row game1 is rather boring. The player who can occupy more points per move has a winning strategy [J. Beck, Tic-Tac-Toe Theory, Cambridge University Press, Cambridge, 2006, to appear] for any n. In order to make this game more interesting József Beck suggested to limit this power by requiring that the points occupied in one step are 'close' to each other. We will study this distance restricted version together with other variants.