Jimulacrum
Full House
Approach #1 (top screenshot) of preserving the "natural" remaining burns and board cards and then re-rolling the errant cards used to be the standard. Now, approach #2 (bottom screenshot) is the standard. Approach #2 is the better choice by far.
The obvious weakness in approach #1 is that you have to do all this pre-dealing that not only exposes the backs of upcoming cards, but also sets you up to sometimes have players muck their hands into the pre-dealt board, which is even more of a disaster than the original error.*
However, my main problem with the "preserve the original cards" approach is that it lends credence to the Sacred Order of the Cards mentality. It creates the impression that observing the preordained order is still important—so important that we're going to override the usual rules of dealing procedure and deal board cards face-down in advance just to accommodate it.
The best approach is "random is random." This is the nature of the game being played, after all. If something irregular happens, re-roll. It's a simple solution, it's easy to employ consistently, and it protects the game from a range of shenanigans.
At this point, the Sacred Order of the Cards types are sure to be losing their minds and declaring this must be a misdeal, we have to just split the pot or return all bets, or whatever solution they can hack together in the moment. This goes to a key gripe I have with this school of thought, which is that it grants the dealer (and sometimes other players) unusual power to create improper advantage through procedural errors. For example, if all board cards must stand as preordained, a dealer can prematurely deal the turn while there's a $100 bet pending to see if his flush will come in, and then say "Oh, whatever, I'll just fold" if he whiffs—or insist he was going to call if it does come in. If cards being pitched into a pre-dealt board necessitate a misdeal (actually a foul), then someone who realized his hand is no good can get a refund by fouling the board. Sacred Order people insist that preserving the original order—which they don't actually know, of course—is paramount, above all other considerations, even fairness of the game.
This is the same kind of mentality you see in Blackjack sometimes, where one player will get angry with a second player and blame him for "taking away" a card that would have busted the dealer, in the process of the second player simply playing as he sees fit. The first player, of course, will never admit that the cards were only in that order by chance, and the second player could have been setting up the dealer to bust instead. First player is just mad because he lost, and he doesn't understand probability well enough to see why his argument is bogus.
This is the same kind of mentality you see in Blackjack sometimes, where one player will get angry with a second player and blame him for "taking away" a card that would have busted the dealer, in the process of the second player simply playing as he sees fit. The first player, of course, will never admit that the cards were only in that order by chance, and the second player could have been setting up the dealer to bust instead. First player is just mad because he lost, and he doesn't understand probability well enough to see why his argument is bogus.
