Quote:
Originally Posted by bautzen
Thank you!
This is also the solution I got, and I was racking my brain where I got it wrong...
Nevertheless, quite counterintuitive, to pay an infinite large amount to win in the majority of times an actually quite small amount.
That is a good post. I was one of the randoms that snapped tweeted at TChan "How could it be less than a dollar?" before I even thought about it. Armed with the past and TChan's link: The "solution" is in the fact that if the game was actually being offered, there would be a finite amount of money that was available to win, whether it was capped by the booker or all of the money in the world. Since each flip has an expected value of $.50, the expected value of the game is the number of turns it takes to get to the max win x $.50.
So if there was a max win of $1,048,576.00, that's 21 heads in a row, with an expectation of $10.50, so you'd pay $10.49 to play. A max win of $536,870,912.00 is 30 flips in a row, so your EV in the game is $15.00.
Even if you were playing for every dollar that's ever been in existence, the game is worth like $30.00.
Cool discussion.