Problem

Alice has two queues, S and T, which can store integers. Bob gives Alice 50 odd integers and 50 even integers and insists that she stores all 100 integers in S and T. They then play a game where Bob picks S or T at random and then applies the round-robin scheduler, described in the chapter, to the chosen queue a random number of times. If the number left out of the queue at the end of this game is odd, Bob wins. Otherwise, Alice wins. How can Alice allocate integers to queues to optimize her chances of winning? What is her chance of winning?