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Best of Donald Catlin

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Tom and Ray's Proposition Bet

8 April 2012

If you are a regular reader of this column, you know that I occasionally discuss a particular proposition wager, sometimes called a sucker bet. One of the classics is discussed in the archived article called "An Earful of Cider"; you might check it out. The reason I occasionally discuss these wagers is not to teach you to fleece others but rather to illustrate that one must use care when analyzing wagers. Things are not always as they seem.

The proposition bet I am discussing here comes to us from Tom and Ray Magliozzi, otherwise known as Click and Clack, of the NPR radio show Car Talk. This was a recent puzzler on their program. Here it is.

Consider two players A and B. Player A has a bag that contains three cards. One card is red on both sides, one is green on both sides, and the third is red on one side and green on the other. A offers B the option of reaching into the bag and randomly choosing one of the cards in such a way that only one of the sides of the card is seen by both players. Suppose that the upside of the card is red. A then offers to guess the color of the downside of the card for even money. Should B accept this wager?

Obviously the card that is green on both sides was not chosen. So the only possibilities are that the card's down side is either red or green with a 50 -50 chance. So even money sounds like a fair bet. Or is it?

When B chose a card at random the chances were two out of three that he chose a card with the same color on either side. So if A adopts the strategy that he will choose the color of the bottom to be the same as the color of the top he will be right two out of three times on average. As long as A adopts such a strategy he has the advantage and this is certainly not a fair bet. Simple but deceptive. See you next month.


Don Catlin can be reached at 711cat@comcast.net

Donald Catlin

Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers
Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers