Compare unopened-envelope expectations and observed-amount updates under an explicit finite prior for the smaller amount.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
For a smaller amount X, both unopened envelopes have expectation 1.5E[X]. After observing y, prior mass at X=y and X=y/2 determines the two possible counterpart amounts.
Assumptions and limits
One envelope contains X, the other 2X, and the chosen envelope is selected uniformly. A finite positive prior is supplied explicitly. No universal 50:50 posterior after an observed amount is assumed.
Worked example
With equally weighted smaller amounts 10 and 20, both unopened envelopes have mean 22.5. Observing 20 gives an expected counterpart of 25; observing 40 gives a counterpart of 20.
Worked reading and practical questions
- Two Envelopes Before and After Seeing an Amount
- Finite Priors Explain Boundary Effects in the Two-Envelope Puzzle
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Frequently asked questions
What does this calculator assume?
One envelope contains X, the other 2X, and the chosen envelope is selected uniformly. A finite positive prior is supplied explicitly. No universal 50:50 posterior after an observed amount is assumed.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.