Dollars to doughnuts (in this case, slang for "zero", presumably since both have the same shape) means that you are so confident that you are right that you will bet money against nothing in return. It's the same sentiment as "dollars to dimes", taken one step further, and randomly obfuscated. Though it does help you to sound like either a '40s noir private eye or a good ole boy, depending on context.
. Furthermore, the 'doughnuts' saying's days are becoming numbered simply due to inflation, IMHO, as the time rapidly approaches that someone betting with doughnuts would actually be paying more for their wager than the allegedly confident party who is betting dollars ...

