This talk was inspired by a problem on the $1989$ Putnam Mathematical Competition: If p is an irrational number such that $0 < p < 1$, is there a finite game with an honest coin such that the probability of one player winning the game is p ? We consider several solutions of this problem. An extension of the problem leads naturally to an example of a continuous strictly increasing function with derivative equal to zero almost everywhere. Refreshments will be served.