Most non-luck-free games use either open-ended randomizers (like dice, or spinners) or closed-ended randomizers (cards, chit pulls, etc).
But there is an alternative, which is simultaneous revelation of chosen selections (rock-paper-scissors). One example of games that use this type of randomizer are games with written orders, like Diplomacy - which is so completely driven by the diplomatic factor that most people regard it as being luck-free.
Are there any games that use rock-paper-scissors type mechanics as an explicit randomizer?