MENTAL MODEL · M0394

Two Envelopes Problem

DecideHigh supportDecision Science

Included

Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

You are given two envelopes, one containing twice as much money as the other. You pick one, and someone asks if you want to switch. Your reasoning: if you switch, there is a 50% chance of doubling your money and a 50% chance of halving it, so the expected value is 1.25 times the current amount, so you should switch. But if you had initially picked the other envelope, the logic would be the same. The result is that you would keep switching envelopes forever.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

A greedy logical loop. When you always think "the grass is greener on the other side" or "the next job will be better," you might be falling into the two-envelopes paradox. This abstract calculation based on expected value often ignores sunk costs and switching costs, leading you into an endless "job-hopping loop."

anchor

Anchor fast decisions

Two envelopes contain amounts a and 2a respectively. After randomly selecting one, you face the decision of whether to switch. The naive expected-value argument suggests "always switch," which contradicts the symmetry intuition, revealing that the expected-value calculation depends on the prior distribution.

MINIMUM ACTION

In progress 0/4

Practice this model in one real situation:

Write down the expected value expressions before and after switching
point out that the implicit uniform prior is invalid
set a reasonable prior and recalculate
understand that the conclusion depends on the distribution assumption.

Check to track your progress (stored locally)

Learning progress0%

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Source support: Explicit

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en.wikipedia.orghttps://en.wikipedia.org/wiki/Two_envelopes_problemZH · Explicit
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