St. Petersburg Paradox
Version 1.0.0 · Updated 2026-07-30
CORE DEFINITION
A coin-flipping gamble with infinite expected payoff, yet rational individuals are only willing to pay a small amount (e.g., 20 yuan) to play. It demonstrates that "expected value" cannot be the sole basis for decision-making. For an individual with only one life, a huge potential gain (infinite) accompanied by a high risk of total loss is meaningless. We pursue "utility" rather than "monetary amount."
SCAFFOLDING EFFECT
Reduce cognitive load
Diminishing marginal utility. It proves that "expected value" cannot be the sole basis for decision-making. For an individual with only one life, a huge potential gain (infinite) accompanied by a high risk of total loss is meaningless. We pursue "utility" rather than "monetary amount."
Anchor fast decisions
This paradox was proposed by Daniel Bernoulli in 1738: the game involves flipping a coin repeatedly until the first head appears, and if the first head appears on the nth toss, the payoff is 2^n yuan. The mathematical expectation is Σ(1/2ⁿ·2ⁿ)=∞, but people are only willing to pay a very small entry fee. The root cause lies in diminishing marginal utility—the satisfaction brought by each unit of wealth decreases as wealth increases. A rational person should decide based on "expected utility" rather than "expected monetary amount," which compresses the infinite expectation into a finite value through logarithmic utility.
MINIMUM ACTION
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/St._Petersburg_paradoxverified
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