The Missing Element in the "Doubling Every Day" Story

You've probably heard the old legend about the invention of chess: A king was so impressed with it that he offered its inventor anything he wanted, and the inventor said he wanted a grain of wheat on one square of the board, doubled on the second square, and doubled each square until all 64 squares were filled.

In some versions of the story, the king does the math, tells the inventor he can't do that but makes him a trusted advisor, etc. In other versions, the king starts having the request fulfilled and, when he realizes where it's heading (all the grain in the kingdom belonging to the inventor), he has the inventor beheaded instead.

The modern marketing version of that, emphasizing the power of "compounding" or whatever, is something like:

"Would you rather have a million dollars, or a penny doubled each day for a month?"

The "right" answer in the marketing scheme is the penny doubled each day for a month, which would come to more than $5 million.

But that scheme leaves one thing out: Risk that the scheme is a con or that it will fail.

If you hand me a million dollars, I have a million dollars.

If you give me a penny doubled every day for a month, I have $5 million.

But suppose that whatever your scheme is, it falls apart or turns out to have been a con after 15 days and I stop getting paid. My take that day is $163.84, and my total take is about twice that. In fact, it wouldn't be until day 27 of the scheme that my total take would come to more than a million bucks.

So unless I am very confident that your proposition will hold up for 30 days, I'm better off just taking the million bucks.