There's something so wrong with that logic. Imagine it as: Mark: "I've thought of a number between one and a billion and written it down. The number I wrote do

There's something so wrong with that logic. Imagine it as: Mark: "I've thought of a number between one and a billion and written it down. The number I wrote down was 6,822,172" Recursing (you): "ok" Mark: "ohh you believe me? Then let's take a bet, if I did write down 6,822,172 then you win. If I wrote down any other number between one and a billion then I win". Would you take that bet? I think you'd be suspicious. Mark: "I predict that Recursing would take that bet, happily, because why wouldn't they believe me? Therefore them taking the bet is very strong evidence that I actually did write down 6,822,172". You can't use your prediction about someone else's behaviour as evidence!