What does the phrase "dollars to donuts" mean?

The almost forgotten terms 'dollars-to-buttons' and 'dollars-to-dumplings' appeared in the 1880s, meaning 'almost certain' and usually used in 'I'll bet you dollars-to-buttons/dumplings.'

They were replaced by 1890 with the more popular 'dollars-to-doughnuts' (a 1904 variation, 'dollars-to-cobwebs,' never became very common, perhaps because it didn't alliterate)."

[From "Listening to America" by Stuart Berg Flexner (Simon and Schuster, New York, 1982).]

On the origin:

As to why “dollars to doughnuts,” beyond the alliterative qualities, it was essentially just a way to say you’d bet dollars to something mostly worthless, relative to the dollars, emphasizing how sure you are that you’re correct.

Going back to the 1840s, there was a very similar expression with the same basic meaning “dollars to dimes.” Two other similar expressions also existed in the 1880s “dollars to dumplings” and “dollars to buttons.” A couple decades later, “dollars to cobwebs” also popped up, but none of these had the staying power as “dollars to doughnuts.” In all cases, the latter thing is the worthless item relative to the value of the dollars, but you’re so sure about what you’re saying, you’ll happily bet your dollars to someone else’s doughnuts over the matter.

http://www.todayifoundout.com/index.php/2015/06/origin-phrase-dollars-donuts/

If you say that something will happen, dollars to donuts, you mean you are sure it will happen. Dollars to donuts the company is going to fold. I'll bet you dollars to doughnuts she won't come to the party.

Hope you are satisfied with the answer.

One is wagering something of great value against something of relatively no value as an assertion of assuredness concerning their point of belief.