A small amount of basic theory (which areas to target and which to avoid, how to keep your numbers low in the early game, etc) is enough to look like a master among casual players; but the advanced game can be fiendishly hard.

> did find a way to win consistently...

Against who? You were playing against beginners?

And if you played against yourself, did you still win?

Plot twist: GP is the author of the paper, and your question is how they demonstrated that "both players playing perfectly leads to a draw".