The Unbeatable Game: Dr. Nim
In the 1960s board game Dr. Nim, a pile of plastic can beat any human opponent. I, for one, welcome our 50-year-old plastic board game overlords.
Dr. Nim is less a board game than a simple computer; using mechanical controls called flip-flops, it implements the mathematical game of Nim. As mathematician/standup comedian Matt Parker shows in the video below, if you learn the simple rules of Nim (you don't need the board game to do it), you'll likely be able to bamboozle your friends, especially if they're tipsy—the game is inherently rigged in favor of the person setting the initial conditions of play (how many marbles there are and who goes first); beyond that you simply have to play a few rounds until your annoyed friends flip the table over and stomp off. While this game may not be "fun" in the traditional sense, it is certainly clever. Have a look:
For a bit more on the game itself and the math behind it, check the links in the video description. One of those links shows that the Computer History Museum has one of these board games in its collection; another points to the original instruction manual in PDF format (it's actually quite a read, going deep on binary arithmetic and boolean algebra as the thing wears on).