A Coin tossing strategy for a High-Low guessing game

Abstract

Consider the following guessing game: Lucy thinks of a number that is in between 0 and 100 and James tries to guess it as fast as possible. Lucy says ’Higher’ when the guess is too low and she says ’Lower’ when the guess is too high. A good strategy for James is tossing 100 fair coins where the first guess is equal to the number of coins that show heads. If this guess is too low he retosses all the tail coins and if the guess is too high he retosses all the head coins. What is the expected number of tosses in this strategy? This leads to all kinds of coin tossing problems. Most notably a problem by Råde. I discuss this problem and I consider how James may improve his strategy by adapting the coins. This leads to recursive problems.MathematicsElectrical Engineering, Mathematics and Computer Scienc