Let's say you are offered a million dollars if you can win at least two consecutive games in a three- game chess match against a pair of adversaries, reigning world champion Vladimir Kramnik and an amateur player. You are also given the following option: You can choose to play either amateur-Kramnik-amateur or Kramnik-amateur-Kramnik.
It might seem obvious that you should avoid playing Kramnik as much as possible, but in fact your chance of winning the purse is greater in the latter lineup, where you play him twice. The reason is that you can't win two consecutive games without winning the second one, so you're better off facing the weaker opponent in the middle and giving yourself two shots to topple the grandmaster. In fact, the better Kramnik is relative to the amateur, the stronger the incentive to play him two times.