I understand the purpose of burning the cards - so that one cannot possibly use any marks to see the next card in deck. But in home games, sometimes the dealer will forget to burn a card on the flop, turn or river and everyone will shout at them. Sometimes the shouting is timely and the to-be-burnt card is not shown, but sometimes it's too late and the to-be-burnt card is shown to everybody. Should we discard the card and use the next one or once it's shown we should stick with it and potentially fine the dealer? Are there any established rules/customs on this?
If the card is known, you fix it if no action has taken place. If action has taken place, you continue the round using the card.
You might also consider just letting it lay and play always, because you can never be quite sure the dealer actually did not burn. Unless someone happened to see them not burn it is never really clear.
Note if you're on the flop or turn, you still fix the deck by burning so that the sequence remains as shuffled.
This is the way it is going to be ruled in most casinos by experienced floor people.
You continue action if there has been any action, any action including just the first player checking, because any action has given players in later position information that may give them an unfair advantage because of the mistake of the dealer. So you play it out as though the card seen is the correct card. This is OK because even though the card is not the correct card it is still a random unknown card, meaning it does not affect any players statistically.
Another answer said you shuffle the deck, that is wrong, you do not shuffle the deck.
I dont think there are any hard and fast rules to be honest.
I have seen some places where they burn 3 cards pre flop and then 1 on the turn and river.
If you notice in time then i believe the etiquette is to swap the card for the next one in the deck. If its not spotted in time I believe the hand is played out as it is (but this may vary from casino to casino)
If no actions have taken place on the hand, the correct way to handle this is to place the card back into the deck, shuffle the deck, and correctly burn and turn the next card.
I agree with Gaz Winter, I don't think any rules are official here.
When I play homegame with friends, if this kind of mistake happen, then the card that should have been burnt is pulled out (I prefer let the card visible I don't put it back in the deck, like that all players can see it) and you place on the table a 4th card, the one that should be on the flop (if it happen on flop stage ofc).
It sounds like you should just stop burning cards in home games since they cause grief without meaningfully affecting the game otherwise.
The considerations are these:
(1) Everyone must have equal information. The fairness of the game is paramount. (2) Once betting action has taken place, cards stand as dealt. (3) If at all possible, the cards dealt should be the same ones initially destined from the shuffle.
Standard casino procedure is this: if the burn card is shown, and this is discovered before any betting action, then the dealer announces it, shows the card to everyone, burns it, puts up the proper card, and moves on. If there is betting action on the improper card, it stands, and the dealer will burn an extra so that the next round's card will be the same as destined.
If the 3-card flop contains the first burn, and the dealer is not 100% sure which it was, the flop stands, and the next card is burned, leaving on top of the deck the proper next burn. If the dealer can reconstruct the proper flop, he must, and the extra exposed card is shown around and burned. Again, if the is betting action on the improper flop, it stands, and an extra card is burned to make the turn and river cards as destined.
The bad case is when betting action on the flop is not complete before the dealer reveals the proper turn card. In that case, the exposed card is set aside, betting action is completed. The dealer burns again, and places for the turn card what would have been the river card. The exposed card is then added to the stub (no burn cards), which is re-shuffled, so that the river card will be new (but possibly could be card shown early). An early-exposed river card is treated similarly.