character creation – How can I limit (but not outright ban) exotic races?

Systems which offer a race/ancestry/lineage choice for character generation often feature both ordinary races (human, dwarf, elf, etc.) and exotic races (tiefling, shardmind, genasi, etc.). As should surprise nobody, players often gravitate to exotic races, leading to a group that can be described either as a statistical anomaly, if you feel charitable, or a bunch of circus freaks, if you don’t.

Now, arguably that’s not an issue. Adventurers are extraordinary and exotic. Normal statistics doesn’t apply to them. That’s a fine argument, except as a GM I just want to run a game that has a human instead of another tiefling. Please. Just this once.

I could ban exotic races, but I don’t want to be that draconian. I just want to reduce their frequency among player characters, let’s say no more than one exotic race in a group of four to give a concrete example. What’s a good method to enforce this? My criteria are:

  1. Should be efficient. For example, I could just randomly select a player and give them the right to use exotic races. But maybe that player just wanted to use an ordinary race anyway, so this is wasteful.

  2. Should be quick, that is, minimize the back and forth between players and GM.

Goal: Give me a method for session zero (or pre-session zero) that guarantees (or at least, pushes towards) a party of four with one or zero exotic races, optimizing for the criteria I outlined above.

Parameters: The method can involve changing the setting and lore, an algorithm I run with or without player input, or even mechanical changes to the game system. It should avoid cosmetic changes to the races, though (e.g., the mechanics of a tiefling, but looks like a dwarf). Keep in mind, though, that the less drastic and the more general your answer is, the better.

Why? Does it matter? It’s a well-posed question that accepts a procedure as an objective answer.

No, really, why? Because as a GM, all games I’ve ran in the past year have had an exuberance of exotic races and I want to change things up for variety’s sake. Otherwise I won’t have fun running the game. The GM is a player too; their fun and preferences matter as well.

Well, you should accept the way your players chose to have fun. This is answer is non-actionable (how do I even rewire my brain to change that?) and dubiously asymmetrical (why aren’t the players required to accept the way the GM chose to have fun?). Regardless, this is off-topic. Solving the Goal is required for this game to even exist. If solving the Goal then causes my players to not want to play then I will either not run the game or find other players.

Just ban all exotic races or play on a setting without exotic races. Technically this satisfies the Goal (because then each party is guaranteed to have zero or one exotic races, in the formal definition of “or”). But obviously it goes against the spirit of the question and this isn’t math.stackexchange, so I’m not going to reword it to be super ultra formally precise. Basically, the method should possibly allow for a party with one exotic race.