Say, I have a coin and the up-face is two times heavy than the down-face. If I flip the coin as usual, the probability of face-down is two times of that of face-up. Now, if I make the following agreement: only if two successive face-down occurs, I output "face-down"; otherwise, I always output "face-up". By doing so, is the output sequence balanced?
More in general, say I have a sampling algorithm that output i from the space S with probaibility p(i). Now, if I want a new sampling algorithm that sample i from S in a random and uniform manner, i.e., selecting i from S with exact probability 1/|S|, how can I do?