Short experiment with my brother today (sadly not requiring any invasive procedures):
17 coin tosses, correct predictions by brother before the coin landed: 9/17
17 coin tosses, correct predictions by brother after the coin landed; coin hidden to me: 9/17
17 coin tosses, correct predictions by brother after the coin landed; coin visible to me: 15/17
Chance of 15 or more correct guesses: 0.1%; *fanfare* telepathy exists![]()
All you'd have to do is guess right once and that'd be enough proof for some people.