Scientists Prove Fair Draft Picks Are Harder Than They Look

Round-robin is the world's most common way to divide things fairly: one person picks, then the next, then the next, and back around again. It runs fantasy football drafts, schoolyard team picking, office Secret Santa swaps, and even how some companies hand out bonus pools or shift schedules. It feels obviously fair, because everyone gets the same number of turns. Three researchers at Oxford and the University of Edinburgh decided to test that assumption with math instead of vibes.

Their first finding is about strategy. When pickers aren't just honest but scheming — thinking several moves ahead about what everyone else will grab — figuring out the best plan turns out to be brutally hard. The researchers proved it's PSPACE-hard, which is computer-science speak for "as hard as the toughest games ever studied, like playing perfect chess." Even in simplified cases with just two or three pickers, the problem stays hard. There is no clever shortcut app that can solve your draft for you.

The second finding is about fairness. With only three people who value items independently, the researchers found scenarios where every possible stable outcome leaves someone envious of another person's haul by more than one item. That's a real crack in the system. The good news is cheerier: when people value items simply and predictably, every outcome is close to proportional, and with just two people it's genuinely envy-free.

So what should you do with this? Don't agonize over draft order or spend hours gaming your office gift exchange — the perfect strategy is likely out of reach anyway. And if you've ever suspected that a rotation or picking order quietly favored someone, this paper says that hunch isn't paranoia. Simple turn-taking is a good rule of thumb, not a guarantee.