TITLE: Is it possible to obtain a non-skewed coin from a skewed coin?
QUESTION [12 upvotes]: I was thinking about a puzzle, unfortunately I do not remember where I saw it, which asked about

Given a skewed coin where the $p_H \neq p_T$ where $p_H$ and $p_T$
  are probability of observing head in one coin flip and probability of
  observing tail in a single coin flip, respectively. Is it possible to
  obtain a non-skewed coin by flipping the given skewed coin?

Even keywords for more search are greatly welcomed.

REPLY [24 votes]: Yes, this is a very famous trick by von Neumann:
Say player I wins if in two consecutive coin tosses we get heads followed by tails. Player II wins if in two consecutive coin tosses we get tails followed by heads.
Toss the coin until one of the players wins - rejecting both tosses every time neither player wins. You can calculate that each player now has a 50% chance of success. However, if the coin is heavily skewed, you may have a very high average waiting time (infinite for a one sided coin) for one player to win.