On lattice world i start from some point.
At each time-step i claim $n$ neighboring points as ordered randomly. So at $t=1$, i claim $3$ points,
$t=2; 2$ points,
$t=3; 6$ points and so on.
At any time instant, the convex hull of the points chosen should have maximum convexity. One strategy is to choose points closest to the initial point. Could it be proved that this is the best strategy?
Basically the best strategy should lead to circular expansion. So question is does this strategy ensure circular expansion?