I've heard this riddle a while ago and it is quite interesting.
Say I've got two sons and one million dollars to spare. Each boy gets one dollar as a start and from there I give them dollar by dollar with a chance of:
First son: $\frac{A}{A+B}$.
Second son: $\frac{B}{A+B}$.
Where A represents that amount of dollars the first son has at the current stage, and B represents the amount of dollars the second son has at the current stage.
At the first stage since they both have $1$ dollar it mean that the next dollar has $\frac{1}{2}$ chance to go each of the sons. Say it goes to the first son then at the next stage the first son has $\frac{2}{3}$ of getting the next dollar while his brother has only $\frac{1}{3}$ of getting the dollar.
What is the expected value of the losing son?