This question has a caveat that the game is played with the community cards dealt prior to the start of the hand, which isn’t standard poker play. The community cards are dealt: burn 1 card, 3 cards facedown (flop), burn 1 card, 1 card facedown (turn), burn 1 card, 1 card facedown (river). Then pre-flop betting starts. Also, all cards are standard, pristine, unmarked cards.
Let’s say hypothetically everyone finished betting after the flop, if the dealer flips the river card instead the turn card, does it materially affect the players? So basically the dealer turned the river card into the turn card and the turn card into the river card.
On the one hand, the cards were dealt in a specific order, so by revealing the river card instead of the turn card, the dealer is changing how people will bet; in other words, the dealer changed what suit / number shows up on the turn because they physically changed which card shows up first. On the other hand, before the card is flipped, no player has any information regarding what either card is. Before either card is flipped, to any player the cards could be anything except what is in their hand and what community cards have already been revealed. So from an information perspective, it should not affect any player.
Sorry if this post is written in a convoluted way. I am just not sure how to best capture the question. I am of the opinion that physically, the game is changed, but it does not affect the players’ play; players do not “change” how they bet just because the cards are out of order, they change how they bet based on what a card reveals. Because they know nothing about the turn or river cards before they are revealed, it does not matter the order in which they are revealed. However, I am not able to justify / disprove the other notion that it does change players play. The only thing I can think of is that prior to revealing, the probability of turn and river cards being any specific, unrevealed card is the same, and thus equivalently the same card.
If anybody could help me with rectifying this, that would be greatly appreciated. Thanks.