Quote:
Originally Posted by The Big K
The exposed card should be shuffled into the deck and the flop dealt without a burn. If you aren't give the card a chance to come out again, then there is no reason an exposed turn or river to be shuffled in. The question in my mind is when to shuffle it. Do you deal the rest of the flop and then shuffle before the third card, or should it be shuffle in first and then deal the flop? I'd lean towards the former.
This is a fair point, but there are some complexities to this:
* Shuffling an exposed card back into the stub makes the card more likely to appear than any other unknown card (because you know it's in the stub, and not possibly in one of your opponent's hands). Not shuffling it back in obviously makes it less likely (as in, 0% likely).
* Setting an early turn aside and shuffling it in before the river balances these two forces nicely, as gives it the closest chance to appear as any other unknown card. This mitigates the changes in EV you'd see for drawing hands as fairly as possible.
* I haven't run the numbers, but shuffling a card in before the flop (making it more likely to be in the stub, and giving it 5 chances to appear rather than 1) seems like it would dramatically increase the chance of seeing the card. I don't like this. It obviously also changes the other cards which would have been on the board, which doesn't bother me as much, but is a key thing we try to maintain if possible.
* Shuffling the card in before the turn or river might make the numbers more even, but add additional delay which just doesn't feel right. Also they give the potential for additional error as you have another card you have to keep track of and make sure not to accidentally muck.
* Not shuffling it in might be less fair, but if you tell the players that it will happen before you re-do the flop, then anyone who is drawing for that card to appear (read: set mining) can just fold and get out for a small amount, so the damage is somewhat self-limiting. In the normal early turn or river procedures, the player will have already invested more to get to that point, so the unfairness is also magnified.
Overall, I think I still prefer my solution, but I'm less sure about it now. Shuffling it in might well be slightly better, but figuring out where to do so best would require some math which I definitely couldn't do tableside in the heat of the moment. I would probably choose to do it before the river just to make the procedure as familiar as possible to all involved.
Finally, to respond to one other point raised, I agree you usually want to keep your burn cards to protect the integrity of the deck, but we also balance this against a desire to keep the order of the cards if possible in some situations where the burn serves no contextually legitimate purpose. In this case it's so farfetched to think that this situation is the result of planned collusion that it doesn't bother me not to have one in this edge case. Having said that, if the card were somehow marked, this would expose the turn card while flop betting was going forward, so I guess I wouldn't be too upset to see the top card burned here either, it's just not my gut instinct.
Last edited by dinesh; 12-06-2018 at 11:27 AM.