Consider a game with two players and two piles of coins. One player chooses a pile and removes one to three coins. Then the other player does the same. The game ends when both piles are empty. The...

Consider a game with two players and two piles of coins. One player chooses a pile and removes
one to three coins. Then the other player does the same. The game ends when both piles are
empty. The loser is the first player that cannot make a move.
Use strong induction to show for all integers n ≥1, if both piles have n coins, then the player
who goes second can always win.
To start this, perform a belief phase until you can have a player remove 3 coins. What do you
notice the second player does to get back to a smaller value of n?