What if I told you to choose a card at random? Simply choose one from a standard deck of 52 cards, think of a card, do not draw one from a real deck... Make sure you have one in mind before you read on.

The illusion

Assuming that you have a card in mind, I bet you chose the Ace of Spades. Of course, I don't know the card you were thinking of, but that is the one I bet on. Every textbook on probability says that I have a 1/52 chance of having guessed right. Actually, that is not quite true... About one out of 4 readers will choose the Ace of Spades, and one out of seven will choose the Queen of Hearts, as shown by a study of the researcher in psychology of magic Jay Olson and his collaborators.

In this experiment, is the choice of a card purely random? And what does random mean anyway? Even if purely random is not properly defined, most would agree that it means no information at all, or...