Nim
Pick a heap, take as many stones as you like. Take the last stone to win.
You go first. Choose one heap, then how many stones to take. Changing the setup starts a new game.
The secret
Write the heap sizes in binary and compare each column. An even count of 1s in every column means a nim-sum of zero. From any nonzero position, one move can restore that balance.
Read more: Game Theory Reading.
About: Nim’s origins are uncertain; Charles Bouton published the complete winning rule in 1901.