I believe over multiple poker hands that advantage from luck would quickly diminish and then disappear. I would be very surprised if any normal chess player, a total novice at poker, would be able to beat the best poker player in the world if they sat down to play for a couple of hours straight.
Skill would win out, but "hours" is not even the right ballpark.
For comparison, 50K hands is a standard length for heads up matches between pros, with the understanding that even then the best player is not guaranteed to win. In live play, you'd be looking at 50-100 hands per hour.
It's true that with a greater skill gap you'd need less time, but you'd still be looking at thousands of hands if you wanted something like 95% confidence that the better player was up.
I think you're overstating the variance. If you watch high level poker play you will consistently see the same players at the final table of big tournaments. Sure, a few lucky random players will go pretty deep in the tournament, but they just don't do it nearly as frequently as the top few guys.
A competent but not great player has a chance of beating a pro in one session, but it's definitely pretty slim.
When poker players measure variance, it's $$$ over time. And while some pros are indeed good are surviving the bubble in fishy tournaments, none make a perfectly consistent income. Even amongst crushers, the variance can be massive.
For every tournament you make a big score, you crash out of 5 and get min payout on a few more.
Many of the biggest names in poker have been the biggest losers in a given calendar period. For example, Gus Hansen and Daniel Negreanu are two of the biggest winners of all time yet also have some of the biggest documented losses...
