Are Two Heads Better Than One? · eieio.games

A probability puzzle explores whether adding a second unreliable witness (who lies 20% of the time) improves your ability to guess a coin flip. Surprisingly, it doesn't — going from one to two friends keeps accuracy at exactly 80%. The reason: when the two friends disagree (32% of the time), you gain zero information, perfectly offsetting the benefit of when they agree. Adding a third friend (odd number) does improve accuracy to 90%, but a fourth friend again adds nothing due to possible 2-2 ties. This pattern mirrors Condorcet's jury theorem, which explicitly sidesteps even-voter cases for the same reason. The insight is illustrated with Python simulation code and step-by-step probability math.