Abstract
In this paper, games of the following general kind are studied: Two players move alternately by selecting unselected integer coordinate points in the plane. On each move, the first player selects exactly
r points and the second player selects exactly one point. The first player wins if he can select
p points on a line having none of his opponent's points before his opponent selects
q points on a line having none of his own. If this latter eventuality occurs first, the second player wins. It is shown that if
p ⩾
c(
r)
q, then the second player can always win.