The reason Rock Paper Scissors works as a conflict resolution tool is not that it's fair in the statistical sense — coin flips are equally fair — but that it requires both parties to actively participate in the outcome. When you throw, you made a choice. When you lose, you lost to someone who also made a choice. That distinction matters psychologically in a way that passively receiving an arbitrary result doesn't.
The game has been used for this purpose long before anyone thought to study why it works. In schools, teachers use it to resolve "he went first last time" disputes without adjudication. In workplaces, coworkers use it to decide who makes the coffee or takes the meeting nobody wants. In legal settings, a federal judge famously ordered two sets of attorneys to use it to decide a deposition location after they'd been unable to agree through formal procedure. It settled in seconds what filings had failed to settle over weeks.
The applications scale because the game's structure doesn't change with context. Two people want the same thing, neither has an obvious stronger claim, and negotiation has stalled. RPS resolves this faster and with less residual resentment than most alternatives. Both parties had equal probability of winning, both actively chose, and now there's an answer. The key that most people miss is that it needs to be established as the agreed mechanism before the result is known — you can't propose RPS after you've already seen your opponent's throw, and you can't propose it in a situation where the other person feels coerced into agreeing.
There's a reason the game has persisted across two thousand years and every culture that encounters it. Conflict requires resolution. Fast, equitable, unargue-able resolution is hard to design. Rock Paper Scissors solves that design problem with three gestures and ten seconds. The simplicity is not a limitation. It's the entire point.