# Biased Coin

## An Advanced Mathematics Lesson Starter Of The Day

You’re playing football on a desert island and want to toss a coin to decide the advantage. Unfortunately, the only coin on the island is bent and is seriously biased. How can you use the biased coin to make a fair decision?

Reference: This question comes from the book “Are you smart enough to work at Google”.

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This question comes from the book “Are you smart enough to work at Google”. It’s an excellent read for anyone interested in logic puzzles and a diverse range of other topics which have been used as interview questions for prospective Google employees.

The answer to the puzzle as told by William Poundstone, the author of the book.

Firstly there is one method involving tossing the coin a large number of times to work out the value of the bias but the best answer comes from Google: “If you toss the coin twice. There are four possible outcomes: HH, HT, TH, and TT. Since the coin favours one side, the chance of HH will not equal the chance of TT. But HT and TH must be equally probable, no matter what the bias. So toss twice, after agreeing that HT means one team gets the advantage and TH means the other does. Should it come up HH or TT, ignore it and toss another two times. Repeat as necessary until you get HT or TH.”

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