Two players start with a pile of stones.
1st player takes any number of stones from the pile, but not all of them.
Then the players alternate, taking up to twice as many stones
as their opponent just took.
The player taking the last stone (or stones) is the winner.

Question: If you and your friend start with 100 stones, what is the smallest amount of stones you should take on your 1st turn, and how will you proceed to win the game?