Let me tell you about a particular supertask that I like quite a lot. It's called the deal with the devil. Okay, suppose you've made some really good investments, shrewd investment, and you have infinitely many dollar bills. You're carrying them with you. And let's say the serial numbers are one, three, five, and so on, all the odd numbers.
So you have all the odd-numbered dollar bills with you. And you enter this underground bar, and there's the devil sitting there at a table piled high with money. He has all the other bills, the even-numbered bills, zero, two, four, and so on. And the devil sees you and realizes that he has a particular attachment to your dollar bills, and that he will pay a premium to get your dollar, to get your dollar bills. He's willing to pay you two dollars per dollar just to get your dollar bills, okay?
So he says, "Yeah, I'll give you two dollar bills for each one of your dollar bills." And that sounds like, well, maybe it wouldn't matter, because if you have two for one, then it seems like, okay, you still have infinitely much money, and maybe you're, you're no better off, but it doesn't seem like you would be any worse off, and so what would be the harm in doing this? So the, so the devil, you know, you say, "What the heck? Let's do it. It doesn't, doesn't seem like it could harm me." So the devil makes a contract, and you sign it, and in the contract it, it specifies the details of how this exchange is gonna be carried out. And of course, it's gonna be carried out in this supertask manner.
So in the first half an hour, you're gonna make one trade. He's gonna give you two dollars, and he's gonna take one dollar bill from you. And then in the next, uh, in, did I say half hour? In the first half hour. In the next quarter hour, he's going to give you two more dollar bills and take one dollar bill from you.
And then in the next eighth, and so on, he's gonna give you two dollar bills and take one dollar bill from you, and so on, in the geometric series. And so therefore, after one hour, the whole exchange with all infinitely many trades will be completed. Okay. Except actually, he's very fussy about the order in which the bills are going to be exchanged. In the contract, you see now that you're actually undertaking this, uh, he always buys from you your currently lowest numbered bill, and he always pays you with higher numbered bills.
Okay. So you start the exchange, you know. Uh, on the first, you, you had bills, uh, uh, one, three, five, and so on, all the odd-numbered bills. So on the first half hour, he gives you bills, say, two and four, and he takes bill number one from you. Yeah.
Well, it's two for one. And the next round, he gives you, uh, six and eight, which are the next two even numbers that he has, and he takes from you bill number two, which he just paid to you. You know. It's your currently lowest numbered bill, yeah? So let's make a little graph and see what happens with this.
Yeah. Okay, so here's your bills, and here's the devil. So you have one, three, five, seven, nine, and so on, yeah? And the devil had, I think we said, well, let's just start with two. It's maybe, okay, two, four, six, eight.
Okay. So on the first round, he gives you two and four and takes from you bill one. Yeah. And then in the next quarter hour, he gives you six and eight and takes from you bill two. And on the next round, okay, he had 10 and 12, so he gives you 10 and 12 and takes from you bill three.
And on the next round, can you see what's happening? 14, 16. He gives you 14 and 16 and takes from you bill number four. Okay. And so we can see that if this process continues, if he always buys from you your currently lowest bill, then as the process continues, your currently lowest bill is gonna just be getting bigger and bigger. He's always paying you with higher numbered bills.
And so you can see eventually that every single bill is going to end up in the possession of the devil, and at the very end, after you've done all the trading, you don't have any money at all. Every single bill was bought by the devil from you at some stage. And so after all the trades are complete, the devil has all the money, and you have no money at all. Okay, so this is-- I like this example because it shows you how an ordinary way of thinking about supertask transactions don't always behave in the same way as finite transactions. And we have to pay attention to the details of how the process is unfolding in this infinitary manner, because the result is sometimes surprising.