Problem of the Week 1082
A Fair Game with an Unfair Coin
What value of p makes the game fair to each player?
Source: Problem posed by Stephen Herschkorn in Math Magazine (June 2007, #1746) for the two cases 1 HEAD wins and 2 HEADS win, with Bob getting an extra toss only if he throws TAILS on his first throw. There are algebraic answers in the published cases and one wonders whether there are algebraic answers in many of the other cases.
© Copyright 2007 Stan Wagon. Reproduced with permission.