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Suppose someone offers you the chance to play the following game:
You are given an initial stake of $1. A fair coin is flipped. If the result is TAILS, you keep the current stake. If the result is HEADS, the stake doubles and the coin is flipped again, repeating the process.
How much money should you be willing to pay to play this game?
Outcomes:
The expected value doesn't converge but it grows extremely slowly, where almost all the benefit comes from an extremely tiny chance of extremely large gain. The obvious question is counterparty risk: how much do you trust the person offering the game to actually be able to follow through with what they offered?
If we think of this as a sum over coin flips, each flip you think is possible gives another $0.50 in expected... (read more)