Stumped on a puzzle

[The Dude]

[Stratego]

Here's another puzzle.
Let's say I have a magic bag that generates white queens and black queens. There is currently one white queen and one black queen in the bag. You'd reach into the bag and pull out one of the pieces. If you pulled out a white queen the bag regenerates another white queen, if you pull out a black queen the bag regenerates another black queen.

What's also interesting is that the bag is tied to bank account. The first time you pull out a white queen you get $2 in that bank account. If you continue to pull out white queens the bank account will double each time there's a white queen. But if you pull a black queen the bank account stops growing, but you immediately get all the money from that bank account.

So (assuming money is a good thing for you) you'd want to pull white queens until you reach a satisfactory level of money then pull the black queen to get the money. Theoretically there is infinite amount of money you can earn from this game. However, you're unable to look into the bag or manipulate it in any way so that your'e sure to get a certain color. It's a 50/50 chance.

How much would you pay to play this game/have this bag?

[Showboat]

Theoretically you should be willing to pay an infinite amount of money..... I think

[OGPhilly]

[OGPhilly]

Your scenario is racist btw Stratego.

[Showboat]

I heard a similar puzzle on a BBC podcast and if I remember rightly the mathematician on there said you should spend any amount.... something to do with the madness of infinities or something. That's way I said an infinite amount... not my working out lol.

[Showboat]

This is my favorite chess puzzle. Composed by a 10 year old Paul Morphy (the most bad ass chess player ever imo). Don't google it cause it's quite cute and feels nice when you get it.

Edit: Woops! forgot to say white to move and mate in 2.

[OGPhilly]

[Stratego]

[Stratego]