# A lesson in card statistics

## Also, cat’s ‘gifts’ allowed man to survive in prison

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Question: If you place two shuffled decks side by side and turn through all 52 cards of each deck one at a time, top to bottom, how many matched pairs can you expect — 0 to 52?

Answer: Most people say four or five, reports John Haigh in "Taking Chances." But consider the experiment a pair of cards at a time. Whatever the top card is on the left, there is a 1/52 chance of matching the top card on the right. The same holds for the second card, third card, etc.

If each turned pair has 1/52 chance of matching, and you turn through 52 pairs, the AVERAGE number of matches will be ONE (52 x 1/52). People tend to guess higher because they think early matches/mismatches change the chances of matches below. They do, but that is a red herring. Before the cards start turning, you can view all cards top to bottom as being independent, on average.

Actually, 74 percent of the time there will be only one match or none (2 matches —18 percent, 3 —6 percent, 4 —1.5 percent, 5 or more — 0.4 percent). This is the same problem as 52 hedonistic couples randomly re-pairing partners in the dark. "On average, just one original couple are together at the end of the stay."

Question: How did the gross habits of a jailhouse cat save an otherwise doomed gentleman?

Answer: Cat owners are exasperated at times over the not-quite-dead "gifts" lovingly laid at their feet by their pets, says Ruth Brown in Exploring magazine of the Exploratorium Museum in San Francisco. But when Sir Henry Wyat, circa 1480, found himself on the outs with King Richard III and thrown into a dungeon to starve, a friendly cat brought him an assortment of mangled birds, rats and snakes, and a kindly jailer agreed to cook them up.

Wyat "lived in relative comfort in this manner until the death of the king, after which he was ultimately released."

Question: You just bought a state lottery jackpot ticket at odds of 50 million to 1. So, which is more likely, your hitting it big and getting rich, or the world being hit by a doomsday asteroid before the drawing next week?

Answer: Space scientists put the risk of a dino-demiselike 1-2-km comet or asteroid hitting Earth out of the cosmic shooting gallery at about 1 in 10,000 per century, or 1 in 1,000,000 per year, 1 in 50,000,000 for the next week. So it's a wash — about the same odds of you winning and the world getting creamed — for the ticket you currently hold.

Send STRANGE questions to brothers Bill and Rich at strangetrue@compuserve.com.