Look no further than RDR for most'a that. Though I don't think anyone would be lookin' for arm wrestlin' gambling in the first place lol.
On the topic of billiards 'n other similar cuesport incarnations, Google claims ya wouldn't find much of it in America 'til the 19th century. It probably would've taken off sooner via French influence durin' Colonial times if the table 'n tools needed for cuesports wasn't so expensive from the sheer amount'a stuff needed. I reckon you could buy five boards 'n pieces for other games at the cost of a table, balls 'n cues. Maybe a fancy French tavern or two had a billiards table back in Colonial times, but probably not more than that.
And on that note, I was a tad sad that there wasn't at least one pool table in Blackwater. Pool's definitely one'a my favorite forms of board/table games (not that I bet when playin' with my bros, I ain't consistent enough t' walk away with winnings... consistently).