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