Here’s the puzzle/problem:
Let’s presume we are best friends. I own the house next to you. I make a gaming proposition along the following lines: You throw a coin over and over again. So long as it comes up heads, you keep throwing. When it comes up tails you stop and I pay you $$$ — depending on how many heads you threw.
If you threw a tails to start, you get $0.
If you threw a heads then a tails, you get $1.
If you threw 2 heads then a tails, you get $2.
If you threw 3 heads, you get $4.
If you threw 4 heads, you get $8.
If you threw 5 heads, you get $16.
And on and on. The payoff doubles everytime you add an extra heads.
Since this game consists entirely of me giving you money (from 0 dollars to ?? dollars) — you will have to buy an “entry” —
How much will you pay me to play this game (once)?
Note: This is not a loophole question, you will know when you have the right answer.