Numinations — May, 1998

How the Card Trick Works

© 1998, by Gary D. Campbell

If you followed the directions, and actually performed the “April Card Trick” here is what you should have observed. Each of two (or more) people would have likely picked different starting numbers and followed a different initial count as successive cards were turned over. Each would then receive a new count at random. Their new counts would average a bit over five with a tendency to actually be five, since all face cards are counted as fives. This means that, with 52 cards, there would be about ten counting cycles to get through the deck. If, at any point, your new count and another person’s new count happens to land you on the same card at the end of your counts, both of your counts are thereafter locked together for the duration. If this happens, both of you will encounter the same “final count.” Therefore, you will both hold up the same number of fingers when the last card is turned over. Hopefully, this was a surprise and a source of amusement or puzzlement.

The trick doesn’t produce this result every time. You can set up a sequence of cards where two selected initial numbers will produce different final numbers. The fact that probability is involved makes the trick more difficult for most people to figure out. With an average count of five, and ten counts to get through the deck (close, but not perfectly accurate assumptions), there are ten opportunities, each with one chance in five (on average), to “lock onto” the other person’s counting sequence. This means that a failure to lock by the final count has an average value of 4/5 to the tenth power. This means the trick works “correctly” about 9 times out of 10. If someone assumes that the trick must work every time, they might assume that one failure out of ten is due to a counting mistake on their part. All of this makes the trick suitable grist for an April Fool’s joke. Hope you enjoyed it!

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