"Poker is a game of chance"

[Zele]

You can kind of quantify it by looking at your "Sharpe Ratio", which is your WR/SD. Obviously this quantity depends on the time frame you're looking at. Let's say at LHE my WR = 1.5 bb/100 and sd = 17 bb/100, then my SR is 0.09, and over 100 hands LHE is 8% skill and 92% luck (for me). Of course this depends on a particular definition of luck.

Over 10,000 hands, my WR and SD are 150 and 170 bb/10,000, respectively, so we could say over this period poker is 47% skill and 53% luck.