Monty and Waldo play a game with `N` closed boxes. Monty hides a
dollar in one box; the others are empty. Monty opens the empty boxes
one by one. When there are only two boxes left Waldo opens either box;
he wins if it contains the dollar. Prior to each of the `N-2` box
openings Waldo chooses one box and locks it, preventing Monty from opening
it next. That box is then unlocked and cannot be so locked twice in a row.

What are the optimal strategies for Monty and Waldo and what is the
fair price for Waldo to pay to play the game?