[PairTheBoard]

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There are people who are genuinely confused about whether or not to switch envelopes, who might think the two bets above are the same. But it takes only logic, not probability theory, to see that the bet in (2) can be converted to an obviously poor bet of winning half the total amounts in the two envelopes if you have the smaller amount and paying two thirds of the total amount if you have the larger amount. That's not a mystery to me or anyone who thinks through it clearly

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So there's no mystery with the proposition bet? It doesn't produce a true paradox with equally strong arguments on both sides for why it might be a good bet? All it takes is simple logic to see why it's not a good bet? Yet the Envelope Paradox is essentially the same situation. Only in the Envelope "Paradox" the Proposition asks if you want to bet half the amount in your envelope giving you 2-1 odds.


PairTheBoard