We've got two impossibilities that rely on people's inherent misunderstanding of probability.
First up: 5-card mind control: In front of your friend lay down (in this order) the King of Hearts, the Seven of Clubs, the Ace of Diamonds, the Four of Hearts, and the Nine of Diamonds. Ask him to mentally choose any card. 80% of the time, they will choose the Four of Hearts. Try it!
The key to this one is dropping just a hint that you might try to influence their decision. Once you intimate that, they'll eliminate the ace of diamonds as too obvious. They'll eliminate the seven of clubs since it's the only black card. They'll eliminate the King of Hearts as the only face card, and (for some reason), nobody seems to like the nine of diamonds.
Next, a twist of probability that blew my mind when I first experienced it: grab a deck of cards (shuffled), and think of any two random card values (from ace through king). What would you guess the odds are that two cards of exactly those values are right next to each other in your deck? 20%? 10%? 1%?
Amazingly (and to just about everyone's disbelief), it seems that about 70% of the time, any two named values will just happen to be side by side in a shuffled deck of cards!
(by the way, math wizards: if you can figure out a way to calculate the exact odds on this, I'm all ears. After hours of playing with the numbers, I finally gave up and just did a brute force calculation: after 50 trials, I ended up averaging about a 70% success rate)
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