Alice is taking Artificial Intelligence from Professor Bob. To earn extra credit, Bob offers to play the following game. Alice and Bob both put all the coins they have on a table. Alice goes first, and can pick up either one or two coins. Bob goes second and can pick on either one or two coins. The process repeats until there are no coins left. Whoever picks up the last coin wins.

Email me your answers to the following questions.

1. Suppose that upon emptying their pockets, they discover that they have 5 coins. Draw a complete game tree, including actions and rewards (from Alice's perspective) for this game.
   
   
2. Does Alice have a winning strategy (i.e., can she force a win)? If so, what is this strategy?
   
   
3. (Extra credit) Suppose that the game is changed so that at the end, whoever wins gets to keep all the coins they picked up. (The remainder are paid in taxes.) The loser gets nothing. What is the maximum total win that Alice can force? What about Bob?