What question about your game and learning math/probability are you trying to answer?

Mostly 1) do the players actually learn anything that would transfer outside the immediate game 2) how much (if at all) things like their enjoyment affect whether they learn

If you want "an effect" you want a comparison of two arms. But you can only have one arm have an intervention, and the other just be the baseline arm with no treatment at all (or just the 'background treatment' of being a college undergraduate). For example, you can take a set of undergrads, and advertise that you are testing probability aptitude or something, and then the control arm just gets the test, while the test arm gets your game and the test afterwards.

Thanks! Isn't "undergrads with only the test vs. undergrads with the game and then the test" kinda the same as "undergrads with only test vs. undergrads after the pretest and the game", though?

I always found it slightly puzzling that LW folks who get into practical data analysis start with F methods, and not B. Isn't B kind of a LW "thing?"

F is what we've been taught, and what most of our supervisors understand. I'm not really familiar with B stats.