Quote:
Originally Posted by Mr Spyutastic
It's kind of like if I made a bet with you saying I could guess the color(black or red) of every card in a well shuffled 52 card deck that was face down.
And then I go ahead and do it without getting a single one wrong, and you accuse me of cheating. Then I come back and I simply say, "Where's the proof? Stop jumping to conclusions."
Which is true you have no hard proof, but it's also obvious I cheated.
Good post. And even your scenario has a few key facts which – put together – constitute proof.
Fact #1: in a 52-card deck, there are 26 red cards and 26 black cards.
Fact #2A: the deck was correctly shuffled such that the distribution of red and black are essentially random. (e.g. we know an automatic shuffler was used)
or...
Fact #2B: the deck was riffle shuffled seven times before the game began, and mathematician Persi Diaconis once proved that seven riffle shuffles will completely randomize the deck.
Fact #3: the chances of correctly guessing the color of any one card is 1 in 2.
Fact #4: the chances of correctly guessing the color of any one card 52 straight times would be 1 in 2^51, or one in 2,251,799,813,685,248. (I say 5 because you could then use the process of elimination to know that 52nd card.)
Of course, those facts prove one of the following:
#1: you hit that 2.25 quadrillionth shot (again, which is theoretically possible).
#2: you had additional information that enabled you to more guess more accurately than the normal 50 percent, which in turn increased the likelihood of being correct 51 straight times.
#3: you had rock-solid information that enabled you to make a correct guess on each card.
If it's #2 or #3, you cheated. The method of your cheating remains unknown by the information above. If someone is trying to prove how you cheated, they still have a lot of work to do. If someone is simply trying to prove that you cheated, their work is pretty much done.