>> How much should you be willing to pay for each go?
>
> Infinite. Sum(n,0,inf)( (1/2)^n * 2^(n-1) ) = sum(n,0,inf)(1/2) = inf.
>
> Of course it only makes sense to play if both you and the casino have
> infinite time and infinite money.

What if you don't have infinite time?

>> Does it depend on how many goes you are going to have?
>
> No, each round of game is independent, is it not?

Yes, but somehow you have to calculate the "realistic" amount that you will 
win in finite time, so you can decide how much you are willing to pay for 
this game.

If I offered you a go for $2 would you take it? How about $5, $10, $100 ? 
There is a stark contrast to these values and the theoretical infinite 
average expected winnings.

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