Came to the comment(s) looking for this game. I've played this! Fun!
It's interesting to explore the spectrum of what people find fun. In large groups, it seems like games that tilt heavily towards luck can be a great deal of fun for everyone, while "board gamers" (like me) enjoy games where you can learn and leverage strategies to gain advantage, and the role of luck is diminished (to varying degrees).
As a board game host, you have to get that spectrum, gauge group size and preference, and pick a game that will work for them. Strategic games, in particular, take learning the rules, learning the strategies, practicing them, learning your opponents... it can take a dozen games before you're competitive. And for a lot of people, almost none of those games will be any fun.
A few games kind of nail this with an unexpectedly even playing field, where strategy helps, but luck offsets it. If luck really offsets it, very strategic players will also find that it's no fun.
Some luck-based games I really like include Lords of Vegas (not to mention... just Vegas), Bunny Kingdom, and Flip 7.
A lot of card-based strategy games like Terraforming Mars and Wingspan certainly have some amount of luck in them, but it can be dwarfed by good synergy / strategy.
I think for big groups it’s not so much luck/randomness that is the key but complexity. Low complexity games are going to play better. They can be pure skill games. Many drinking games are (beer pong etc).
Luck/randomness is directly against determinism. A way of making feel less mechanical and opening up the combinatorial state space? Essentially increasing the fun/interest without introducing high complexity necessarily? As well as narrow the skill range as you say, but not necessarily over longer time horizons.
Like you can do a 2d matrix of luck and complexity.
Tic tac toe - low randomness, low complexity
Chess - low randomness, high complexity
Poker - med randomness, high complexity
Roulette - high randomness, low complexity