3 ms·
At least for me, the comparison to the expected payouts of the "finite versions" completely resolves the paradox. People aren't used to reasoning about infinit
by mgraczyk 11y ago
At least for me, the comparison to the expected payouts of the "finite versions" completely resolves the paradox. People aren't used to reasoning about infinities, especially when dealing with such tangible quantities as money. Very large and very small numbers confuse us. It's no wonder that when faced with astronomically large payouts at infinitesimal probabilies, our intuition disagrees with "the math". We think about money intuitively in terms of scales that are meaningful in the real world. We can't imagine playing against a casino with $10^100, so we would not be willing to pay $330 to play, which would be the expected payoff for such a casino.
On a related note, we don't have a way of measuring the value of money beyond quantities we subconsciously label " all the money". Is it better to have $10^90 or $10^100? In the computation of the expectation, the difference is crucial. To a human player, there is no distinction.
- a3voices 11y ago$10^90 and $10^100 are identical since both would represent 99.9999...% of all dollars. Spending just a small fraction would flood the market and decrease the value of USD. Consequently, unless you have a large military at your disposal, the U.S. government will come after you regardless of the money's legality since you represent a threat to the monetary system.
- cheepin 11y agoPresumably, with that amount of cash you could buy enough political power that the US military would be on your team