The term “Dollars to Doughnuts” alludes to odds in a bet. Dollars versus doughnuts that are worth far less than a dollar. The phrase first appeared in print in the Daily Nevada State Journal in 1876:

Several Benoites took a vantage of the half fare tickets offered to those who were to attend the ball given by the railroad boys at Carson last night, and attended it. It’s dollars to doughnuts all enjoyed themselves.

Also used is the term “Dollars to Buttons” since buttons were worth far less than a dollar.