But that was one of the first rules that got tossed out the window. (No random elements was the hardest one to give up but the never-ending arguments that Qwirkle and Ingenious are abstracts wore me down)
Good old Blokus was a big factor in that decision. Definitely doesn’t have a theme, no hidden information, totally deterministic. And not only does it play up to four players, it plays best with four players.
And it’s not like it’s that new an idea. Chinese Checkers and it’s predecessor Halma date back to Victorian times and they play more than two players too. If you count Ludo/Parcheesi as abstracts (I mean, Backgammon is considered an abstract), we can talk about multi-player abstracts going back centuries.
Still, making a game for more than two players requires more decision space so everybody has a fair shake. It’s not a coincidence that the original Blokus has all four colors start in the corners where they develop some board space before meeting other colors while Blokus Duo has you in each other’s grill from the start.
Frankly, the more players you add to a game, the harder it can be to make sure everyone has an even playing field. And since abstracts tend to have simpler rule sets, that can make it more difficult. The random or hidden elements that can level the playing field aren’t there as much. It’s clearly not impossible but it makes it rarer.
Sometimes, the question isn’t if an abstract can be played with more than two. Without a special board, three-player Martian Chess is down right dreadful, for instance. So, it’s not enough that multi-player is possible. It also has to be good.
So, yes, multi-player abstracts are out there. And, like all things, not all of them are worth finding. But there are some good ones.