A 1 in a million chance of winning 1,000,005 gives an expectation of 1.000005, not 5.
You need to offer a prize of 5X to get an expectation of 5, and 6X to get a net gain of 5.
Using monetary prizes bigger than the value of all the wealth of the planet is the cause of the confusion. You cannot offer the bet because there just isn’t that much money in the world.
Using monetary prizes bigger than the value of all the wealth of the planet is the cause of the confusion.
I don’t think it is. The cause of the confusion is just that the sums are wrong (and the conclusion is wrong). Replace the opening statement with “I’m Bill Gates, I’m offering you a bet—the cost to take the bet is $1, the prize for winning is $58 billion. The odds of winning are 1 in 57.99999 billion”.
Now we’re no longer talking about unrealistic amounts of money, but it still isn’t good bet for Bill to offer, because it’s expected value is negative. You do need to invoke the fact that wealth is finite to explain why martingales) don’t work, but this “system” isn’t nearly as complicated as a martingale.
Well, technically you can offer a bet of a million billion zillion dollars, it’s just that anybody who calculates it’s expected utility as “chances of winning” x “one million billion zillion dollars” is a gullible fool.
If your premises go violate common sense, don’t be surprised if your conclusions violate common sense too.
Money is just a promise to deliver certain things that exist in the real world: things like goods and services.
The GDP of the USA is of the order of 10^12 dollars per year. Therefore the total wealth of the entire world today can’t be more than, say, 10^20 dollars.
10^100 dollars dwarfs this. What does this mean? It means that any dollar amount greater than 10^20 breaks our intuitive notions of what money is. 10^100 dollars is like a promise to make one plus one equal three.
“10^100 dollars is like a promise to make one plus one equal three.”
It’s more like a promise to dilute the value-to-money ratio by a factor of 10^80. Even if that much money could be printed, all that would be accomplished would be to put all the world’s wealth in one person’s hands and reduce everyone else to beggars.
The correct response to the question is, of course, to lynch the person threatening to print/mint that much excess money as a danger to the well-being of human civilization. Even if you aren’t a fan of human civilization, such a procedure is quite likely to damage everything else on the planet in the process of humanity’s destruction.
OK, so in the least convenient possible world, where Crono said 10^100, he meant 10^20. It seems to me the real issue here is that if you cannot (nearly) cover your end of the bet, negative utility is flat for very large negative dollar values, so you become risk-seeking.
The expected value calculation is wrong.
A 1 in a million chance of winning 1,000,005 gives an expectation of 1.000005, not 5.
You need to offer a prize of 5X to get an expectation of 5, and 6X to get a net gain of 5.
Using monetary prizes bigger than the value of all the wealth of the planet is the cause of the confusion. You cannot offer the bet because there just isn’t that much money in the world.
I don’t think it is. The cause of the confusion is just that the sums are wrong (and the conclusion is wrong). Replace the opening statement with “I’m Bill Gates, I’m offering you a bet—the cost to take the bet is $1, the prize for winning is $58 billion. The odds of winning are 1 in 57.99999 billion”.
Now we’re no longer talking about unrealistic amounts of money, but it still isn’t good bet for Bill to offer, because it’s expected value is negative. You do need to invoke the fact that wealth is finite to explain why martingales) don’t work, but this “system” isn’t nearly as complicated as a martingale.
Well, technically you can offer a bet of a million billion zillion dollars, it’s just that anybody who calculates it’s expected utility as “chances of winning” x “one million billion zillion dollars” is a gullible fool.
If your premises go violate common sense, don’t be surprised if your conclusions violate common sense too.
Money is just a promise to deliver certain things that exist in the real world: things like goods and services.
The GDP of the USA is of the order of 10^12 dollars per year. Therefore the total wealth of the entire world today can’t be more than, say, 10^20 dollars.
10^100 dollars dwarfs this. What does this mean? It means that any dollar amount greater than 10^20 breaks our intuitive notions of what money is. 10^100 dollars is like a promise to make one plus one equal three.
“10^100 dollars is like a promise to make one plus one equal three.”
It’s more like a promise to dilute the value-to-money ratio by a factor of 10^80. Even if that much money could be printed, all that would be accomplished would be to put all the world’s wealth in one person’s hands and reduce everyone else to beggars.
The correct response to the question is, of course, to lynch the person threatening to print/mint that much excess money as a danger to the well-being of human civilization. Even if you aren’t a fan of human civilization, such a procedure is quite likely to damage everything else on the planet in the process of humanity’s destruction.
OK, so in the least convenient possible world, where Crono said 10^100, he meant 10^20. It seems to me the real issue here is that if you cannot (nearly) cover your end of the bet, negative utility is flat for very large negative dollar values, so you become risk-seeking.