That knowledge - based on seeing 10 in my envelope - allows me to rule out every other event (an event being a particular sum being in the other envelope) except for 5 and 20. So that's my sample space - just two events. — andrewk
I have no idea what a Frequentist would do. — andrewk
Based on your knowledge you know that the sample space has to follow the algebraic form of [X,2X],and you know by the definition of a sample space, that your sample space can only contain possible outcomes (or at least I hope you do).
Therefore your sample space could never be [5,20], as it does not follow the form of [X, 2X]. Your sample space could be [5,10] or [10,20] but there is no way you can mathematically justify a sample space of [5,20] as it is not consistent with [X,2X]. — Jeremiah
What if there are two people and each time both are randomly given an envelope. Is it then beneficial for both to switch the envelopes? — BlueBanana
I have flipped a coin and know the result. I will let you bet on it with a 2:1 payout if you win. However, I decide how much you have to bet, and only after you tell me your guess.
Should you bet? — Michael
I don't understand how this is supposed to be comparable or relevant to the envelope paradox. — BlueBanana
As you've stated it, it's not an advantageous bet if you have to bet twice as much when you lose. — BlueBanana
It's just that if you pick the loser then I will offer someone else who picks the winner a £10 bet. — Michael
For the participants it’s still just a 50% chance with a 2:1 payout. — Michael
True, but notice that you can't make profit out of betting in this system. Taking part in it still isn't profitable. — BlueBanana
There's a 50% chance of winning and the payout is 2:1. — Michael
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