It's impossible produce a result incompatible with classical mechanics in a single constant-sized observation, because the classical players can get any result by just playing randomly.
The advantage that GHZ has, similar to the Mermin-Peres magic square game, is that the quantum players should win 100% of the time while classical players win less than 90% of the time. This gives much faster Bayesian updates away from classical mechanics towards quantum mechanics as you collect samples (compared to CHSH). But you do still need multiple samples.
On the other hand, seeing the GHZ game fail would be instant total loss for quantum mechanics. If the win rate is supposed to be 100%, and you see a loss (that you can't attribute to noise or something), then in that case a single test would have caused you to totally discount quantum mechanics.
The advantage that GHZ has, similar to the Mermin-Peres magic square game, is that the quantum players should win 100% of the time while classical players win less than 90% of the time. This gives much faster Bayesian updates away from classical mechanics towards quantum mechanics as you collect samples (compared to CHSH). But you do still need multiple samples.
On the other hand, seeing the GHZ game fail would be instant total loss for quantum mechanics. If the win rate is supposed to be 100%, and you see a loss (that you can't attribute to noise or something), then in that case a single test would have caused you to totally discount quantum mechanics.