I lay out twenty sticks on the table and we play a “pick up the sticks game.” You can pick 1, 2, 3, or 4 sticks during your turn, and the loser is the person who is left with the last stick laying on the table. If I let you pick up sticks first, devise a strategy to win every time.
Suppose you can choose the number of sticks that will be lying on the table at the start of the game. If your opponent goes first, then how many sticks do you want at the start if you want to win every time?
How would the strategy change if you could pick only 1, 2, or 3 sticks during your turn?