Welcome to the world of Dr. Nim. Dr. Nim is a simplified version of an ancient game called "Nim". Dr. Nim is so-named in honor of the 1960s game of the same name, a mechanical game which always played a winning strategy. No programs, just marbles and odd-shaped levers. It was quite amazing.
Dr. Nim (and for that matter, Nim itself) is a game of removals. The rules are simple:
Simple, eh? Shall we play a game.....?
Did you really think you'd get away without a footnote?
 Of course, ESR, Inc's Dr. Nim "toy" was a digital computer with a program built into the shape of the levers, the number of the levers, and even the tracks in which the marbles roll down. Nothing says a computer has to be electronic (ask Babbage&Lovelace) or even be programmable!