[atrainpsu]

The stack sizes would be 500,000 big bets, which would likely take over a million hands, which is clearly the long run. Against a great limit holdem player (I'm not sure Ivey is a great one), I think our newbie would have maybe a .1% chance of winning.
There is no way, the number is exactly 0% because it is possible (although infinitely small) that our newbie has the best hand almost every hand.
Also after 50-100K hands, our newbie may have grasped enough of the game to be at the level of someone like ourselves and would therefore be less of a dog.

If this headsup match was played many times, and the top pro won over 99% of them, then you could prove to a mathematically educated person that this game is a skill game, however there would still be people that don't understand and just think the pro is really lucky.