The perfect play

> Disagree with your first point

You may, but it is possible for a much better player to lose (even in a "skill game") to a player with very little or no knowledge of the game. You may consider this "lucking out" but even the most skill-based games have an element of luck, and in edge cases new / worse players will beat better / experienced players - this is simply how these things work (and part of what we as humans generally find exciting about contests of skill).

This is why many competitive games limit the element of randomness among professionals by various means. In poker, all players have the opportunity to play very many hands - no single hand decides the outcome (unless they decide to go all-in, for example). Similarly, in 9-ball and tennis (among other sports), professionals at the highest levels play sets of games - because the outcome of a single game is not indicative of the involved players' respective skill levels. On any given day, given enough games, I would beat Jeannette Lee at a game of 9-ball, even though her skill at the game is leaps and bounds above mine. At no time (ever, haha) would I realistically be able to beat her in a best-of-nine game format. That is why she is world ranked and I am commenting on a website.

Saying that "only poker greats will play a perfect hand" is erroneous, many people play perfect hands. The difference is a professional will probably know (or suspect) that they are about to make the perfect play. They also will attempt to do so regularly, and know the difference between perfect, good, and bad plays, whereas bad/new players will not (or will much less frequently).