Science Puzzle
The Doubloon Ratio
You are watching someone flip a fair gold coin. It has come up heads ten times in a row. Every flip has been fair; there is no trick.
What is the probability that the eleventh flip will come up tails?
The Answer
Exactly 50%. The coin has no memory of what came before. Each flip is a completely independent event, and a fair coin always has an equal chance of heads or tails regardless of its history.
The feeling that tails is "due" is called the gambler's fallacy. It arises because we correctly know that in a long series of flips, heads and tails will roughly balance out, and we incorrectly apply that long-run fact to the very next individual flip.
The long-run balance happens because of the enormous number of future flips, not because any single upcoming flip is tilted. The eleventh flip does not know about the first ten. It is always 50/50.
The principle: Independent probability. Each event in a fair random sequence is independent of all prior events. The gambler's fallacy mistakes a long-run average for a prediction about the next outcome.