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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.

Mauro ALLEGRANZA
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Confused
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  • It makes no difference whether the fourth card shown to the players was called the "river" or was called the "turn" or if it was called the "foobingbaz" or anything else. It makes no difference whether the fourth card shown to the players originated from the fourth position in the deck, or the fifth position of the deck, or the sixth, etc... The probabilities remain the same. Related: If you draw two cards, what is the probability the second card is a queen? – JMoravitz Dec 20 '21 at 17:58
  • That said, burning the cards is also pointless from a pure math perspective assuming fair shuffles and fair players. The only reason it is done is for historical reasons and as an attempt of an anti-cheating measure, trying to keep people from marking the backs of cards and knowing what the next card about to be flipped is ahead of time. – JMoravitz Dec 20 '21 at 18:00
  • So the other point brought up was that because the deck is fixed after shuffling, swapping the 4th and 5th card changes what the actual card is, hence the betting and pot size. Although the probability of the cards are the same, the reasoning is that because the cards already have a determined suit/value, by changing it, you are affecting how players will bet. And therefore, you should not be allowed to swap the order in which they will be revealed. – Confused Dec 20 '21 at 19:51
  • "swapping the 4th and 5th card changes what the actual card is" And... there are just as many times where the the 4th card was this and the fifth card is that as there are times where they were reversed. The amount of times players have one set of information is just as much as the other set of information. It balances itself out. – JMoravitz Dec 20 '21 at 20:52
  • Again, I encourage you to think about the much smaller more tangible question of asking what the probability the first card in a deck is a queen in the two scenarios: (1) Where we just draw the first card naturally VS (2) Where we swap the first and second card first without looking, and then compare that further to the question linked above of what the probability the second card is a queen. The point is that unknown information does not influence our opinions on probabilities. Yes, if we were to have first looked at the turn card before the river, it affects us, but not if we don't look. – JMoravitz Dec 20 '21 at 20:55
  • Your question is not fundamentally different than the linked question, it is just a larger scenario than just talking about two cards. This is like complaining that a fair well-shuffled deck with fair players must be dealt out one card to each player in sequence versus dealing two cards at a time to each player. In either scenario every player gets two random cards and which two cards those are happens to be a particular pair just as often in the one pattern of dealing as in the other with no bias. Again, the only valid complaint should be concerns about cheating if players are not fair. – JMoravitz Dec 20 '21 at 20:57

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