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## Heads I Win, Tails You Lose!

Past columns in MathNEXUS have discussed the coin-tossing efforts of mathematician Persi Diaconis.

Now consider some research results from the University of British Columbia, where they "proved" one does not want to make a fair choice by flipping a coin randomly!

The research is traced back to an argument: How to divide patients randomly into groups for a clinical trial. Some of the researchers wanted to use a coin toss, while others felt that the coin toss method was not entirely random.

So, they did some research to resolve their argument. A group of medical residents were give some basic pointers on the "science" of controlled coin-flipping and only five minutes of practice. The experimental result: the subjects could produce a "Heads" 68% of the time!

What was behind their "learned" techniques?

• You do the flipping, starting by knowing which side of the coin starts faceup...plus you will be trying to control the number of flips (or rotations) of the coin.
• Practice flipping the coin the same way every time and with the same starting faceup. Plus, use the same force everytime....three or four flips (or rotations) is the ideal.
• If you are not the person flipping the coin, always choose the side of the coin that is faceup. Scientists (such as Persi Diaconis) supposedly have shown that the probability of the original faceup side landing to show that same side is 51% (based on an argument that the coin spends more time showing that side "up").
It is up to you whether or not you believe all of this. But, remember that the person flipping the coin might believe it...or use it.

And, if you have some spare time, give the suggested experimental approach a try.

Source: Wired, November 2010.