Sunday, July 15, 2012

Clearly I've discovered the point where I need to stop reading wikipedia

Dollars to donuts

"Betting dollars to donuts may not be such a good bet today." What?

I understand the writer of the article has tried to take some inflation-based view that the relative prices of dollars and doughnuts has changed such that...

I don't know. I miss something here.  Let's break it down into the cases:

  1. You lose, and lose some quantity of dollars.  Let's say these are old dollars, so you lose $1 ~ 12 doughnuts.
  2. You win, and win some quantity of doughnuts.  Again, olde-timey case here, so you gain 12 doughnuts ~ $1.
  3. Losing again, but with magic future dollars, such that $1 ~ 1 doughnut.
  4. Winning, magic future, blah blah, 1 doughnut ~ $1.
So, in half of these cases, you lose "something like a dollar" and gain "a quantity of doughnuts."  I fail to see any point where this is a bad bet.  You get doughnuts out of it 50% of the time (assuming a constant prior, although the article claims "the person is confident in the outcome of an event" without really specifying whom.  If both are "confident," then the constant prior is probably accurate enough).

Sure, a dozen doughnuts is better than one doughnut, but you're still left with N(doughnuts) > 0.

And if you lose, you pay the jerk a dollar and go buy your own doughnuts.  

Buy me some too, because now I really want some doughnuts.


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