/pol/ is mostly Americans, so a straight random post gives you the United States over and over. These control how the flags get picked. Saved to a cookie, since this version stores nothing in your browser.
The same country never appears twice in a row regardless of this setting.
Fewer flags is an easier guess: 4 gives you a 25% shot at random, 12 gives you 8%. Points are scored against those odds, so an easy grid is worth less.