  The Tower of Hanoi game is a classical puzzle in recreational mathematics
(Lucas 1883) which also has a strong record in pure mathematics. In a
borderland between these two areas we find the characterization of the minimal
number of moves, which is $2^n-1$, to transfer a tower of $n$ disks. But there
are also other variations to the game, involving for example real number
weights on the moves of the disks. This gives rise to a similar type of
problem, but where the final score seeks to be optimized. We study extensions
of the one-player setting to two players, invoking classical winning conditions
in combinatorial game theory such as the player who moves last wins, or the
highest score wins. Here we solve both these winning conditions on three heaps.
