Nim: the game of, three piles of stones two players take
it in turn to remove some stones from any pile. They can
take any number from 1 to the total in the pile
of thier choice. The winner is the one to take the last
stone. In this version it’s the operator versus the
computer, with the operator having the first choice.
The computer always wins.

It could easily be adapted for the user to decide who
has first choice. The students who lose each time,
when starting first, will be convinced that is the reason.          
It’s more than likely they will still loose.