When only the last one will do
  An unknown positive number of items arrive at independent uniformly distributed times in the interval [0,1] to a selector, whose task is to pick online the last one. We show that under the assumption of an adversary determining the number of items, there exists a game-theoretical equilibrium, in other words the selector and the adversary both possess optimal strategies. The probability of success of the selector with the optimal strategy is estimated numerically to 0.352917000207196. 
Johan W\"astlund
cs.GT math.PR