Monty Hall-esque question

[mykey1961]

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If we played this game repeatedly and every time just ignored the envelope amount we would on average win $25 for every $50 bet.


[/ QUOTE ] This is both wrong, and a very bad example.

Do you mean we would on average win 1/2 the amount wagered? Or do you mean for just those times we bet exactly $50, we would average a $25 win.

Both are wrong.

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You took this quote out of context. In its original context it read,

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Prior to opening the envelope I think everyone here would say it's 50-50 that it's the smaller envelope. We'd all be willing to gamble on that given favorable odds. We'd certainly bet on it given 2-1 odds. After opening the envelope I doubt many here would want to call off the bet. As far as our bet goes, opening the envelope should not change the 50% chance that it's the smaller envelope. If we played this game repeatedly and every time just ignored the envelope amount we would on average win $25 for every $50 bet.


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Read in context it should be clear that the "bet" I'm talking about in what you quoted is the wager being discussed in that paragraph. The one that is made after the envelope is picked but before it is opened. The one that is not called off after the envelope is opened. It doesn't matter whether new envelope amounts are chosen each time, or the same ones are used each time, the statement remains true that for THIS wager, with the chance to call it off after seeing the envelope amount, If we played this game repeatedly and every time just ignored the envelope amount we would on average win $25 for every $50 bet.

For example, for THIS wager, if we decide to bet $1000 our EV will be:

(.5)2000 - (.5)1000 = 500

ie. +$25 for every $50 wagered.

Try reading my post again.

PairTheBoard

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How is getting 2:1 on half your envelope the best explanation?

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I think it's the insight that best satisfies this psychological condundrum.

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Ok for some reason THIS time you get to choose the amount you wager rather than having to wager 1/2 the amount in the envelope.