When I am not traveling, I usually bathe our kids. We have to decide who "goes" first, i.e., gets the first bath. For some reason, it is more desirable to be the second one to be bathed. Not sure why, but I suspect that it has to do with the incorrect perception that bathing second gives you more "play time". I think I would rather bathe in the clean water and thus go first, but I am not a three or five year old.
To decide who goes first, I play "ga-ee, ba-ee, bo", or rock-paper-scissors with my five year old. Actually, we play a modified version with rock-paper-pencil... I think I offered "pencil" instead of "bazooka" or whatever ordnance he originally threw in as a mod.
He asks me "what's your strategy?", to which I respond, "what's YOUR strategy?". He answers back with a smile, "my strategy is for YOU to tell me YOUR strategy". It makes me smile each time. He's so open that he actually tells me exactly what he wants. Then I go with one of two scripts:
Me: "My strategy is to tell you a strategy, then forget that strategy."
Me: "My strategy is to do paper, but if you know that I'm doing paper, you'll do pencil. Then I should do rock, but if I do rock, you'll do paper...", etc. I do this until we both get lost.