Arithmetic Expected Value
Updated 2026-08-11
INTRODUCTION
English translation pending.
CORE DEFINITION
The oldest tool of probability theory, developed from the problem of dividing stakes in an unfinished game, which Blaise Pascal and Pierre de Fermat worked out in their 1654 correspondence. The core claim is that multiplying each outcome by its probability and summing the products gives a single figure that predicts the average result of repeating the decision many times. The key qualification is that the figure is only meaningful for decisions that can actually be repeated, and that it depends entirely on the quality of the probability inputs.
SCAFFOLDING EFFECT
Reduce cognitive load
- Outcome listing: write every possible result with its payoff and its probability before comparing options - Product and sum: multiply each payoff by its probability, then add the products into one comparable number - Input audit: mark which probabilities come from data and which are only impressions
Anchor fast decisions
Expected value converts vague possibility into one comparable number by weighting each outcome by its probability. Its force comes from the law of large numbers: when the same kind of decision is repeated many times, the realised average converges on the expected figure. For repeatable small decisions the expectation therefore governs the long-run direction of accumulation, while for a one-off decision it is only a reference point, since a positive expectation does nothing to lower the chance of a single failure.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- mungermodels.comhttps://mungermodels.com/models/arithmetic-expected-valueverified
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