Riley Lark just posted the first “Flunecy” episode; the last paragraph reminds me of game rules. He asks:
how do you decide where to draw the line? When do you say “this is fundamental and we need to understand it before we move on,” and when do you say, “you can sort of see how this works from this picture; now let’s move on?”
I wonder how parallel this is to learning to play a board game or a card game?
Usually somebody is there who knows the rules, and you hear the basic idea and a few tips, and everybody agrees that we’ll all start playing and learn as we go. When is that sufficient, and when do you actually have to read the rules?
I think that reading and internalizing rules is an interesting skill. Does that skill help with mathematics—or is it just something (like number theory, Riley might agree) that gives you formal underpinnings but is not really essential to becoming mathematically powerful? Don’t know.
I made some curriculum having to do with this. Like many math teachers, I like NIM games, but I’ve gotten tired of explaining the rules. So I made NIM problems where groups also have to learn the rules without prior explanation.
This is one of those cooperative-learning deals where each group gets 4–6 cards that they deal out; each member can look only at their own cards; they can share the information; the group has a problem to solve. You’re probably familiar with the format.
In this case, the problem is to learn to play the game and figure out how to win. The image at right links to a pdf. Print it out, cut it up, and pass out the cards. Seems to work pretty well.
This is from United We Solve; I learned this NIM variant in Winning Ways.
A Best-Case Scenario 
I so much enjoy figuring out rules that it’s hard for me to separate that skill from the skill (and joy) of learning mathematics. I’m glad you wrote about this – I have a lot of theories about how to teach board and card games quickly, and have never really connected those with my classroom for some reason. Thanks!