[Editor’s Note: This answer is penned by Dan Lubin, author of The Essentials of Casino Game Design, one of the world’s top experts in the field of casino table games.]
Three Card Poker and Let It Ride are two of the oldest proprietary table games, meaning that they were among the earliest of the new inventor- and company-designed games supplied to the casinos starting in the late 1980s. Prior to that, casinos and card rooms offered only the traditional public-domain games of blackjack, craps, baccarat, and roulette.
The patents for both Three Card Poker and Let it Ride have now expired, so they too are in the public domain. Thus, there’s less incentive for game distributors to support the originals, as competitors and casino operators can run them for less cost after re-trademarking them; Platinum Poker is DEQ’s version of Three Card Poker and Take it or Leave it is Galaxy Gaming’s version of Let it Ride, both of which have found little demand in comparison to newer and hotter games.
That said, Three Card Poker is still easy to find, considered a mainstay table game to offer, while Let it Ride is less popular and fading considerably. Let it Ride is a paytable game (you play against a paytable and not the dealer with your final hand), so it’s more volatile and lacks the potential for a showdown win if the dealer has a weak hand.
Unfortunately, there’s no easy resource where you can locate specific games at specific casinos. You can call local casinos and inquire, as well as show your support for certain games by playing them, although casinos look closely at how many patrons are playing at which tables in their pits. Casinos have many ways of counting "butts on seats," a critical indicator of a game's popularity, and if you frequently find yourself playing alone at a table, that game’s days might be numbered.
As far as Three Card Poker and Let It Ride tables being crowded, I assume that’s because casinos reduce the number of tables if the game has a reduced amount of patronage. Obviously, two half-full Crazy-4-Poker tables become one full table after one is removed, which halves the operating costs. In this case, some players are always at that table, which is often the case for Three Card Poker. For games that go through more droughts than activity, they get uninstalled, which is the case for many instances of Let It Ride.