The expected value is infinite, but how much would you pay?
Game rules: Keep flipping a coin until tails appears. The game ends when tails first appears; if there are n heads before tails, the payout is 2ⁿ KRW. What would be a "fair" price to pay to enter? Play the game and see how it feels.
Expected value: The probability of receiving a payout of 2ⁿ KRW is (1/2)ⁿ⁺¹. Expected value = Σ 2ⁿ × (1/2)ⁿ⁺¹ = 1/2 + 1/2 + 1/2 +... Each term adds another 1/2, and because this continues forever, the expected value is infinite! Yet when people are asked, most are unwilling to pay more than a few thousand won.
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How much would you pay for this game?
💡 It is called a "paradox" because there is a huge gap between the mathematical expected value (infinity) and people's actual behavior (their willingness to pay only a small amount). Economists explain this with the idea that "the value of money diminishes as wealth increases" (utility theory) — gaining the first 10,000 KRW has a greater proportional increase in utility than gaining 1,000,000 KRW.