An elegant little prop and piece of set dressing on the original show, Tri-D Chess serves a dual purpose: to allow Kirk to show that sometimes instinct was more effective than logic, and to display that holy cow this is science fictiony! Although some fans have filled in the blanks on the regulations, there's no canonical rules to the thing, which explains why James T. was able to hornswoggle our pointy-eared friend more often than not. It can't be a hard game to play, though...how difficult can it be when every space-high-school Herbert was in the Tri-D Chess Club instead of duking it out on the intermural Kobayashi Maru team?
Still, as Spock (and Reed Richards) have both been heard to observe, things change. Imagine a reality where the adventures of James T. Kirk have been...bear with me on this one, unlikely as it is...have been rebooted, so they no longer need necessarily follow the entire history of before. Think of it as an Elseworlds, a What If, a chance to kill off a klepto ex-teen actress. All sorts of unlikely and impossible things could be changed in the timeline: exploding planets, inter-crew romances, the popularity of the Beastie Boys.
But imagine one more dramatic change in this new timeline where black is white, redshirt is blueshirt and Biff Tannen has totally taken over control of the gambling racket in Hill Valley, California...imagine what if Tri-Dimensional Chess was supplanted by an entirely new game all together?!?
Replace Star Trek's most famous science-fictiony game with Charles Darrow's easy-to-learn, difficult-to-master classic board game of Depression-era economics and slumlordery, and it puts a whole 'nother spin on the Trek universe. For one thing, the Ferengi would win the Galactic Monopoly Championship every single year. Klingon versions would feature head-ridges on Rich Uncle Pennybags (or, in the original Klingonese, je'tennuS lo'laHghach) and a "Just Visiting Rura Pente" space. The Romulan version would shimmer and disappear every few seconds for an hour or so, and the Tribble version would quickly fill and overflow a room with small plastic houses and silver dog tokens.
But how, oh how would this change affect our favorite old crew of the United Starship Enterprise? (No bloody A, B, C, or D.) Do you wonder? Huh? Huh? Huh? Do you? Huh? Huh? Don't you wonder about that? Huh? Huh?
Well, if you do...I think it would go...something like this: