You could also do it without the actual programming if the overhead of writing things gets in the way (it would for most people).
If it is a simple enough game, people could design their algorithm and then step through it manually with each other. The difference between this and strategy-based board games would be sticking to an explicitly written down strategy.
Last night, here in Portland (OR), some friends and I got together to try to start Rationality Dojo. We talked about it for a while and came up with exactly 4 exercises that we could readily practice:
We also had a whole bunch of semi-formed ideas about selecting a target (happiness, health) and optimizing it a month at a time. Starting a dojo, in a time before organized martial arts, was surely incredibly difficult. I hope we can accrete exercises rather than require a single sensei to invent the majority of the discipline. So I've added a category to the wiki, and I'm asking here. Do you have ideas or refinements for exercises to fit within rationality dojo?