A conundrum

Rambling on 96 months ago.

Two identical envelopes, one containing twice as much money as the other are shuffled. You may open one then decide which one to keep.

You open one, which contains $20.

You are offered the chance to take the other envelope instead.

Should you?

Common sense tells us that it doesn't matter, but consider this:

The other envelope contains either:

  • $10, in which case you lost $10, or
  • $40, in which case you gain $20.

Since there is an equal chance you will gain more than you could potentially lose, doesn't it make more sense to take the other envelope?

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Comments (3)

Nigel said: (95 months ago)

Take the other envelope.

:) Chris said: (95 months ago)

Sure - but the conundrum is, why does this defy common sense that it shouldn't matter?

huxley said: (94 months ago)

a lot depends on your personality type

One factor you don't mention is if you keep the first envelope you have a 100% chance of winning $20.

If you take the other envelope, you have a 50% of losing $10 and a 50% chance of gaining $20. You are trading off certainty for a potential gain (a gain which isn't enough to overcome most people's risk-aversion).

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