>>17374356It's random, and it wouldn't make a difference in prize, either. Someone on Reddit confirmed it, and I confirmed their finding.
When you hit Play to subtract your 100 PokeMiles, it'll randomly generate your reward right then and there. You can open up your rewards list in another tab and confirm this for yourself, if you'd like. So in actual fact, you never have to play the game. You can just hit "Play", then refresh.