Numinations — May, 1998
How the Card Trick Works
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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