The way of looking at the balance of luck and skill is over a given number of hands. Although tenbob over-egged it a big, in one hand, it's mostly luck. Over 10 hands, it's still significantly more luck than skill. Depending on the game, skill may be starting to show after around 100 hands, but luck is still probably a bigger factor, as you can easily have a session of over 100 hands where you miss most of your hands, or get lucky just a couple of times, to have the effects of luck swamping the trend created by skill. Over 1000 hands, you'll generally see skill coming into prominence, with luck starting to balance out, but again a serious up or down swing can bias that. Only after more like 10,000 hands will you have a large enough sample to expect the main factor to be luck.
If you translate that into sessions, you can get lucky once or twice against an opponent and take them to the cleaners, whether they're a pro or not. Over a 2-3 hour session online, the pro's skill would be starting to tell, although in a day's play, even pro's have losing days. Over a month of regular play (averaging 2+ hours a day) you'd expect skill to be raising its head, and starting to show whether you're profitable on average, although a seriously good or bad streak would still off-set that. Only over the period of a month or so full-time, or several months frequent part-time play can you expect skill to be the dominant factor, so never rush into judgement (positive or negative) about your own ability after just a few hours or even a few days of play.