Dollars to donuts
This is, of course, an American phrase and hence I have listed it here using its US spelling, despite the fact that here in the UK a donut is most definitely a doughnut.
'Dollars to donuts' is a pseudo betting term, pseudo in that it didn't originate with actual betting involving donuts, but just as a pleasant-sounding alliterative phrase which indicated short odds - dollars are valuable but donuts aren't. The phrase parallels the earlier English betting expression 'a pound to a penny'.
Even in the USA, the original spelling was 'doughnut' - the 'donut' spelling came in well after this phrase.
The phrase appears to have originated in mid 19th century USA. The earliest citation I can find for it is in the newspaper The Daily Nevada State Journal, February 1876, which despite being a conspicuously American publication, preferred the 'dollars to doughnuts' spelling (the 'donut' spelling was a mid 20th century adaptation):
Whenever you hear any resident of a community attempting to decry the local paper... it's dollars to doughnuts that such a person is either mad at the editor or is owing the office for subscription or advertising.
It doesn't crop up in print until some years later, apart from a similar citation in a March edition of the Nevada State Journal, which suggests that the (unnamed) author of those pieces either coined the term himself or appropriated some street slang that he had heard.
The phrase didn't settle down to its current 'donut' version for some time. In 1884, there's a reference in G. W. Peck's Boss Book to 'dollars to buttons' and in August 1904, The Boston Herald referred to 'dollars to cobwebs'. Buttons and cobwebs were presumably chosen for their obvious lack of value but failed to catch on as they lacked the perky alliteration with dollars.