Maybe you could just mention this briefly, as a sidenote, without theory. Something like: "Note that if we'd replace the numbers 1, 2, 3 with 1001, 1002, 1003, or 1000, 2000, 3000, nothing changes. (Show three versions of the same simple decision tree.)"
I made a series of game theory videos that carefully go through the mechanics of solving many different types of games. I optimized the videos for my future Smith College game theory students who will either miss a class, or get lost in class and want more examples. I emphasize clarity over excitement. I would be grateful for any feedback.