The crux of the matter to me is that poker is a game of imperfect information, and the plays we make are based on probabilities. A player can know these probabilities precisely, but a player should never (ethically) have prior knowledge of the specific card to come (or not come). Back to my example, on the flop, Player A knows the has a 46 to 1 chance of hitting
on the turn and 45 to 1 chance on the river, a 39 to 8 chance of hitting a any other spade on the turn and 38 to 8 on the river, and a 44 to 3 chance of hitting any other 10 on the turn and 43 to 3 on the river.
When the
is exposed, if we preserve the Order of the Cards(lets say by setting aside the river burn and river card and reshuffling the stub for the turn), not only does this change the odds for the remainder of the hand (46 to 1 and 46 to 0 for
, 39 to 8 and 39 to 7 for any flush), most damningly to me, it gives players specific, unwarranted, pre-existing knowledge of the arrangement of the deck. Specifally, players know exactly a card that WILL NOT come on the river.
Before the
is exposed, players also know that, say, the odds of the
appearing on the board are 46 to 1 and 45 to 1. These probabilities are the only information they know, and the premise under which the game is played. Let's say after the
is exposed, the procedure is to immediately reshuffle the deck and deal a new turn. But, before doing so, the dealer peeks at what "should have" been the river, and it is indeed the
. After the entire stub is reshuffled, the odds of the
coming and 46 to 1 and 45 to 1, exactly the information that was available to them before the accidental exposure of the card. Basically, it is a factory reset to the conditions that existed before a card was exposed.
The integrity of the game is FAR better protected by preserving the knowledge with which players are operating (specifically, having no prior knowledge as to which cards will or will not come) than by preserving the original order of the cards (which none of us should know, as we shouldn't be "peeking" at the stub.)