I've seen advice to hard-mulligan for Prince Keleseth. In other words, if you don't get Keleseth in your starting hand, the suggestion is to throw everything back. The rationale is that playing Prince Keleseth on curve makes such a large improvement to your win-rate that you should maximize your chances of drawing him (for instance, winrate if you get Prince Keleseth in your opening hand is about 73%; the next closest card is a 61% winrate if you get Corridor Creeper).
Is this strategy correct? Or are there circumstances where it makes more sense to avoid hard-mulliganing for Keleseth? Maybe there are matchups when you should also keep a good 1-drop (like Flame Imp or Kobold Librarian), if you have one, or maybe keep Corridor Creeper?
I do see from hsreplay.net that players do seem to be keeping certain cards (one-drops, Southsea Captain, Corridor Creeper) on the mulligan more than half of the time. This is more often than we'd see if players were hard-mulliganing for the Prince. In other words, the data suggests that a significant fraction of players must be following some other mulligan strategy. So which is the optimal strategy?