Why Bankers Went Bust

Why we're in a recession!: I'm reading slate. There's some cool mind-math puzzles that Larry Summers had to answer to get a job. I'm reading. I'm thinking. And I'm getting the answers wayyyyyy wrong. Wrong, as in, not the same as what they say is the right answer. But then, I think some more, and realize WAIT... WTF.... Their answer is TOTALLY not right!!! I'm hesitant (though, still enthusiastic) about my protest because I had the same emotional objection to the Monty Hall problem, and eventually came to realize the right answer WAS right. But in this case, the problem seems practical and tangbile enough to where I think their answer is what f'ed up America's banking system.

Here's the question, answer, and their solution (from slate):

There's a dollar on the table. I'm going to flip a coin. If it comes up heads, I'll double the money. If it comes up heads again, I'll double it again. Whenever it comes up tails, we stop.

But there's a catch: You have to pay a fee to play. How much are you willing to pay?

The answer: infinity. You should theoretically be willing to pay any amount, since the probability on any given flip is that you win 50 cents. (On the first flip, $1 x 1/2 = $0.50. On the second flip, $2 x 1/4* = $0.50. On the third, $4 x 1/8 = $0.50. And so on.) So the potential winnings extend infinitely.

Of course, you can't offer the guy infinity dollars. So the interviewee is forced to either settle on a real world number—as much as the player can afford—or delve into marginal utility theory. Either way, the interviewer gets a sense of how the person's mind works. (This answer is understandably baffling to most people. See philosopher Ian Hacking wrestle with it here.)

They're so freaking wrong!!! Infinity isn't right. Because 99.99999...% of the time you'd GO BANKRUPT. And only once in a bazillion (haven't worked out the exact math, might be more like a gazillion) you'd become rich. Except we only live once. So you can't go risking inifinite money for a tiny chance of bigger inifinite money. You have to play the game as if you had your kid's college fund on the line, not some theoretical iterative game.

My real answer: I'd pay $1.50 It's even chance from the first flip whether I lose 50 cents or make 50+ cents. And that 50+ cents could get huge, so it makes putting my 50 cents on the line worth the risk to play.

I think--- what would you pay? What do you think about the inifinity answer?

EDIT: okay, I wouldn't gamble with my kid's college fund. I'd pay $1.50 to play if I had 50 cents to lose!

Edit2: okay okay the author Chris Beam does get to the same moral that I went to. Obviously I should have finished the article before ranting. "Theoretically, [the game] is worth an infinite amount of money. But in the real world, it's not worth infinity." Agreed.