1
general::
Also, put one's money on. Bet on; also, consider likely or nearly certain, expect. For example, Jean put her money on Contender but the horse came in last, or I'm sure the President will speak to the crowd; I'd put money on it. This idiom was first recorded in 1931.
American Heritage Idioms
2
general::
Phrase(s): put one’s money on someone or something (to do something)
1. Fig. to bet money that someone or something will accomplish something. • I put my money on the favorite to win the race. • Donna put her money on the winning horse. 2. Fig. to predict the outcome of an event involving someone or something. (This is not a wager.) • I put my money on Bob to get elected this time. • Alice put her money on the most popular candidate.
McGrawhill's American Idioms And Phrasal Verbs