[GMan42]

Another wrinkle in this whole thing (I love useless theoretical discussions like this) is that the rankings' relative scarcity change a lot based on how many cards are dealt. In a 7-card game like 7CS or Hold'em, straights and flushes move much closer together in frequency compared to a 5-card game, and if I'm not mistaken, one pair hands are actually more common than high-card hands (although changing hand rankings to reflect this would be silly). If you dealt a game where each player had 10 cards, it would be extremely difficult not to make a straight or a flush, and high-card hands become even rarer than 4 of a kind.