Shades of Monty Hall
Should you switch?
A man walks into a casino and spots an interesting new game. He is presented with two buttons, either of which he can push. One of the buttons will win him a certain amount of money and the other will win him twice the amount, although he doesn’t know what the amount is. So he pushes one of the buttons at random and is surprised and very pleased to learn he just won $1 million. Suddenly, the machine presents him with two new buttons. He can push one to keep his original choice, keeping the $1 million. Or he can switch his choice to the button he didn’t push. What would you do and why?
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.