In September I published a puzzle called Losers and Winners. At least five people solved the puzzle (unlike my first puzzle, which no one solved without hints). Here are a few hints, in white text, meant to be read in order.
Suppose I give you a bag of marbles and tell you that all the marbles are either green or black. You repeatedly reach in, pick out a random marble, and then put it back. You find that out of 100 draws, 70 of the marbles you took out of the bag were green. What's the probability that the next marble you'll draw will be green? Or, to put it another way, what's your best guess (expected value) of the fraction of marbles in the bag that are green?