Wiktionary
vb. (context idiomatic English) To suggest that something is very likely to be true or that one has a strong hunch about something. Related to the earlier 'bet dollars-to-buttons' and 'bet dollars-to-dumplings' that appeared in the 1880s, meaning 'almost certain' because the dollars are bet against something near worthless, and perhaps zero shaped.
Usage examples of "bet dollars to donuts".
And I'll bet dollars to donuts that Dee manages to get Alex to take her out to dinner tonight.
Even if no one was willing to take Galactic credits for room and board, Mike was willing to bet dollars to donuts a case of six gross Number Two hooks would open doors.
They were Homicide, they were bent, and he'd bet dollars to donuts they weren't even investigating the case.
They were Homicide, they were bent, and he’d bet dollars to donuts they weren’t even investigating the case.