Since I had never heard of this "bad luck" thing I had to look it up. From what I've read, it didn't imply bad luck at the horse track. It was that the $2 bet was common at horse tracks, gambling was evil, so if you had $2 bills in your wallet, you were perceived as a gambler. $2 also paid for a prostitute, so having $2 notes caused people to think you frequented brothels. Nothing to do with bad luck. Apparently it was also the going rate to pay someone to vote for a particular candidate, so you were branded as someone who sold their vote. Once again, nothing to do with bad luck. The other one was that "deuce" was also a nickname for the devil. To negate that curse, you tore off a corner of the bill. That's the only one where "bad luck" makes sense. It's so weird how these superstitions get morphed and perpetuated.
The "bad luck" $2 bill myth goes back quite a ways, and is a pretty well-established "myth." Does anyone really know the exact reason why they're considered "bad luck?" Of course not, and it depends on who you ask, but that's how these things spread in popular culture. This is superstition, not science. The accumulation and aggregation of the various reasons adds up to "bad luck" as a mass phenomenon for most people. Here's what the CNB Bank of St. Louis says on their website on the $2 bill: "The $2 bill was often thought to be bad luck, as “deuce” was a name for the devil. Recipients would tear off one corner, believing it would negate the bad luck of the bill. This caused many of the bills to be taken out of circulation as mutilated currency." This article also mentions the history of the $2 bill being "bad luck" REWIND: Bad luck bill? The strange history of the $2 bill A 1948 article/book review from the New York Times (might be behind a paywall) called "Why Two-Dollar Bills Are Unlucky; A TREASURY OF AMERICAN SUPERSTITIONS" suggests that this "myth" goes back quite a ways. I couldn't read the full article, but the title is probably enough for this thread's purposes. "The Two Dollar Bill Documentary" from 2015 apparently discusses the bad and good luck aspects of the $2 bill. I haven't seen it, but I would like to. The IMDB blurb says: "Everyone has had a two dollar bill before, right? Most people believe they're out of print, good or bad luck, or a rare commodity. But in this comprehensive documentary, all aspects of the "deuce" are explored - from its history to the superstitions surrounding it; from its use by special interest groups to the way it's perceived by consumers and vendors. The film even looks at the bill's popularity at adult establishments and the subculture of users that cherish the bill."