Opening 50 boxes at random gives you a 50% chance to hit the right box. But everybody else also has a 50% chance that’s independent from yours, so you just mult

Opening 50 boxes at random gives you a 50% chance to hit the right box. But everybody else also has a 50% chance that’s independent from yours, so you just multiply the probabilities together to figure out the overall probability. This makes it vanishingly unlikely to get it right with a lot of people. This strategy instead has you all collectively betting that the structure of the permutation is favourable, which doesn’t have that multiplicative problem.