If the first button he pushed is the one with twice the amount, then the other button would leave him with $500,000. However, if the first button he pushed is the one with the original amount, then the other button would give him $2 million. We don't know what the relative probability of each setup is though (as it may not be half)... so pressing the other button is not guaranteed to give a larger payout than keeping the $1m. I think it would be rational to keep his choice and go with the $1m.
If the first button he pushed is the one with twice the amount, then the other button would leave him with $500,000. However, if the first button he pushed is the one with the original amount, then the other button would give him $2 million. We don't know what the relative probability of each setup is though (as it may not be half)... so pressing the other button is not guaranteed to give a larger payout than keeping the $1m. I think it would be rational to keep his choice and go with the $1m.
Hi Umar,
It’s actually a paradox. I’ll post a discussion soon. Greg