Better than 50/50
You're walking in the forest and come upon a bridge. A mysteriously cloaked figure jumps out holding two envelopes. "Each of these envelopes contains a different number. You may pick either envelope. I will only let you cross if you can tell me whether the number in the envelope you pick is larger or smaller than mine" Despite being put off by the disruption, you take an envelope and ask: "Can I look inside my envelope before making my guess?" The cloaked figure is surprised because, until now, everyone has ignored him and his envelopes. After some consideration, he says: "Sure." You open the envelope, thinking: "I don't even know how large a range he's picking from. This is a total 50/50..." OR. IS. IT?? What I love most about the solution is it doesn't come from gimmicks, hacks, or any external information. It is, in its purest form, a strategic decision framework. You magically improve your odds with something equally random....