I subscribed to the Internet Archive's RSS feed for noir films. This movie, called Two Dollar Bettor, looks good!
Bank controller John Hewitt is a much-respected member of the community. One afternoon he is persuaded to make a small two-dollar bet at the racetrack and collects a couple of hundred dollars when his horse wins. Such a return-on-investment intrigues him and he begins to frequent the track and making larger bets. After a short period of winning, he hits a losing streak and his savings are soon wiped out. He then starts to take money from the bank and is soon thousands of stolen-dollars behind. Mary Slate, secretary of his bookmaker, advises him that the bookmaker has a sure thing, and if he will liberate $20,000 or so from the bank, he can get in on it and solve all his problems.
If you've seen and would like to review it in the comments, please do! Two Dollar Bettor (1951)