You're about to flip a quarter while your friend guesses which side will come up. You agree to switch turns after one incorrect guess each. He gets 2 in a row right before guessing wrong, and now it's your turn. You incorrectly guess the outcome of the first flip he does, and now it's his turn again. He guesses 250 flips correctly before you give up (132 heads, 118 tails). You're absolutely dumbfounded and check the coin again just to reassure everything is right. What do you conclude has happened (What's the most likely explanation)? How many correct guesses would your friend have to make in a row in order for you to stop believing it was chance based? The chance of correctly guessing 250 coin flips in a row on one try is 2^250 or 1 in 1.8*10^75 Assumptions: You start triple checking everything and flipping at different speeds past flip 15 to ensure 'randomness' and minimal human error. Your friend is not manipulating the coin in any predictable way below a success ratio of 1:1.85.