The TDA forum doesn't accept new registration, so I can't get their opinion about this.

The current rule for a premature turn card is to use the river card as the turn card, then shuffle the prematurely dealt turn card together with the deck to deal a new river card. The problem with this rule is that:
- The procedure is very complex.
- It's counter intuitive. I think 99% TD (or home game organizer) who doesn't know this rule will rule differently. If a rule is so counter intuitive, something must be wrong.
- More importantly, it CHANGES THE MATHS. The odds of the prematurely dealt card appearing will be reduced. To understand this, just think of a case where the deck only has 3 cards A, K, Q. Normally the chance of an A appearing on the turn or the river will be 66.7%. By using TDA's procedure, it will be reduced to 50%.

The only good thing about this rule is that it "retains the original board as much as possible", which is completely and utterly irrelevant, except to a few superstitious players. And I don't think we should create a rule just to please this kind of players.

I have a suggestion for a new rule: we will simply shuffle the prematurely dealt card with the deck (without the burn card), then deal a new turn card normally. I think this is much simpler, easier to understand to everyone, intuitive, and most importantly, it doesn't affect the maths in the slightest, so no players will be punished or can profit from a dealer's mistake.

What're your opinions?

I don't see how using TDA's procedure reduces the chance to 50%. I'm not getting the math.

I've never run across a floor who didn't know the procedure, it happens with enough regularity they've all done it before. If they don't know this one there are likely many more gaps in knowledge.

I think you're missing a key piece in the math. Let's take a common extreme of 8 handed Big O. Under normal circumstances one specific card is 1 in 44 to come out on the turn because you have only eliminated 8 cards. If you now know it's in the stub it becomes 1 in 8. On the river 1 in 7. I'd call that a pretty significant impact on the math and your suggestion would increase the already elevated chances of one specific card coming out.

My preference would be to simply discard it and do a new burn/turn but there are a few games you can't spare 2 cards and you'd need a different set of rules for those. It's probably not worth it.

Using the TDA's procedure, the A card (which was prematurely dealt) is set aside. The dealer then deal the turn using either K or Q (say it's K). Then the dealer shuffles A together with the Q and deal the river. The odds of A gets dealt on the river is 50%.

I didn't say the TD does not know this. I say that anyone who doesn't know this rule will never rule as suggested by the TDA, because it's counter intuitive.


What is 8 handed Big O? In Hold'em I don't think it changes anything.

We can't discard the card, because it would affect the odds. E.g. someone drawing to a flush will only have 8 outs now.

In Big O each player gets 5 cards. You used a 3 card stub in your example, I used a more common short stub.

In the other extreme of let's say 8 players dealt in holdem, the odds on the turn change from 1 in 47 to 1 in 31. It's still significant.

The odds change either way, I'm saying they change less if you discard it than it does if you know one card that is still in the stub. The current rule might be partially a way to even out the odds - 0% on the turn but higher than normal % on the river.

It has an exactly analagous effect in hold 'em. After the flop, you know your 2 hole cards, plus 3 board cards, leaving 47 cards. If you have an early B&T and see the As, you now know the As is in the stub. If you were playing 9 handed, this means the As is now one of 31 cards in the stub.

If you shuffle it in immediately, the As now has a 1/31 chance of appearing as the turn, and a 1/30 chance of appearing as the river, or a 6.45% chance of appearing by the end of the hand. Every other card has a 1/47 and 1/46 chance, or a 4.26% chance of appearing by the end of the hand. The As has a 51% higher chance of appearing compared to any other card.

If you follow the normal procedure, the As has a 0 chance on the turn, and a 1/30 chance on the river, or a 3.33% chance of appearing by the end of the hand. This is a 28% lower chance than any other card.

As Reducto said, this effect is significantly more powerful in games where even fewer cards are left in the stub, such as a full table of Big O.

This is the reason we use the procedure we use. You are going to change the math either way once the card gets exposed, so we use the process that minimizes its effect.

I can understand the reasoning of you and Reducto why you prefer the current system....

but there is NO WAY that is the REASON that system is used. The reason is that superstitious people want to keep the cards that come out as close as possible to how they would have been had no error been made.

It is the same reason that an exposed hole card is replaced with the original burn card; this actually is a terrible procedure because it allows the back of the top flop card to be seen, defeating the purpose of having a burn card to begin with!

That is a fair point, though I think it is the procedure I would use even if I specifically ignore the superstition element. (Seriously, what procedure would you suggest instead? As mentioned above, discarding the card altogether goes too far in the other direction, IMO.)

Perhaps it would be more fair to say: it's not like this is the first time someone has raised this suggestion. The reason neither TDA nor RRoP has implemented it is because it is considered less fair than the current procedure, and possibly also because it gives the sacred order of the cards people some succor.

I disagree, the current procedure changes the odds much more than the suggested change of rule.
Supposing we know everyone's hole cards, and even the burned card. The odd that the As will appear on the board is known, and will be the same if we follow my suggested rule. If we follow TDA's rule, the odds will be reduced.

So by using TDA's rule, we artificially change the odds, and will punish/benefit certain players. Using my suggested rule, nothing changes, no player is affected, except for the shared knowledge that the As is inside the stub.

What I mean is that, supposedly if the dealer hadn't made a mistake, then player A would have 4.3% (or whatever) chance of catching the As by the river and win. But the dealer did make a mistake. Using my suggested rule, player A still have 4.3% chance to win. But using TDA's rule, player A's chance will be reduced to something like 4.2% or whatever, and it's unfair.

But you don't know everyone's hole cards. Your math is all wrong as a result, as are your conclusions. This is very similar to how people fail to understand the Monty Hall problem and end up thinking that it's 50/50 whether they switch doors or not. In this case it's actually the opposite game form: you don't know what's behind door #3, so your odds are different than if Monty opens it up and shows you a goat (i.e. you know the other hole cards).

If you played a game where everyone's hole cards were face up, then sure. Then the 16 other hole cards would have 0% chance of being on the flop and turn, and the As will have the same probability of showing up as all the rest of the cards that you now know remain in the stub.

But they're not. You are mis-using (or rather, failing to use) conditional probability correctly. You know the As is in the stub, but you don't know the same about the rest of the unseen cards. This changes the probabilities of each card later appearing on the board, and makes it more likely that the As will appear on any given street than any other unseen card.

When you count your outs, do you assume you know all the outs that exist in other people's hole cards so you can discount them too when you run your odds calcs? No, because you don't know what cards are where, so to you they are all equally likely to come on the board or be in someone's hole cards. The same is true of all the other unseen cards here, but specifically not true of the exposed As, which changes the probabilities.

It looks like the math has been covered. I want to touch on a few more things:

You were able to describe the rule in a single, short, clear sentence.

Play in any home game and you will find multiple players who do not know the reasons behind multiple rules.

Intuitiveness is prioritized in elements of the experience that are designed to be or feel invisible to the user. The procedure behind premature turn should be the exact opposite of that, no matter which one you choose. Intuitiveness takes a back seat to the reasons behind it and an understanding of what is going on. That's why a floor is present every time.

I don't think superstition has anything to do with wanting to keep a card that would've been on the board .. on the board. That being the River that is now the Turn.

We've talked about what I'm about to state and the potential issues with it. But someone can run the math anyway for comparison.

So we know that the 'original' 3rd Burn and River were 'not' going to be the exposed card, so we keep them in the role they would've played in this hand. The exposed card wasn't going to show up on the River anyway, so why are we doing Turn/River math here? Not needed.

So you Burn and put out the River as the Turn. Now you put the exposed card back into the deck and shuffle. The odds of that card coming out on the River 'really' don't change at all from the odds that it was going to be the Turn in the first place (since the Burn and River card were already 'set') and if you want to do the math its exposed card/(stub-2) now as opposed to card/stub.

There was a short lived method where the Dealer would Burn and put the River out there, but face down in the River's spot on the board. Now put the exposed card back into the deck, shuffle and take the top card as the Turn. This is the same math as the current method but 'superstitiously' puts the River on the board where it would've been and keeps the math for the Turn card exactly what it would've been.

The Dealer made a mistake, now players 'know' that a card is in the stub and not in somebody's hand or mucked.

Just shuffling the whole deck does change the math. This card now has two chances to come back out whereas before it only had 1 chance and you've changed what would've been the 3rd Burn and River as well.

IMCO (crazy) the math for the exposed card doesn't change at all under the current method since the 3rd Burn and River were 'set' per the shuffle already. The math for the exposed card was already reduced by being exposed and I'm not really into increasing the chances of it coming out even more by giving it 2 chances to show up. GL

But this is wrong. If the dealer hadn't made the mistake Player A had a 100% chance of catching the card. But we can't replicate the 100% chance because that would give the player a huge advantage of getting to know the turn card before he acts on the flop.

So yes by definition the odds have changed.

So what we hope for is to make the impact on play as small as possible.

There are 2 problems with your method.

1 As noted by others the probabilities from a players perspective have changed. Before the turn was exposed a player would believe the chance of a A appearing on the turn or river (assuming it was not in his hand or on the board) would approximately 4.3%.

Once the A is exposed the players perspective of the odds shifts. Doing it your way the players are now acting with more information. If the game is 9 handed the players would now see the odds of the A coming on the turn or river as roughly 7%

but doing it the standard way the odds of it coming on the turn or river from the players perspective are now 3.7%

so whichhas less impact a shoft in the pl;ayers perspective of the odds from 4.3% to 7% or a change from 4.3% to 3.7%?

2) whatever card it was that would have been the river had a 100% actual chance of coming out if play went to the river. using your method that chance drops significantly chance drops significantly. Using the standard method it still has a 100% chance of appearing. This would seem to impact the game far less. (yes the fact that it is coming on the turn instead of the river can impact play)

You guys have presented some very fair points. I agree that from a player's perspective, using the TDA procedure will keep the odds closer to the original.

You are correct that if holding the mathematical probabilities constant was the primary goal, your method would be better. However, that really isn't the goal with a procedure like this. The goal is to continue the game with as little disruption as possible, fairly.

If a casino regularly reshuffled both the Turn and the River back into the deck before re-dealing the turn, the hue and cry that would arise from the less maths driven players would shut things down. (and that's the majority of players in case you weren't sure)

Regardless of whether anyone could prove it on any given hand, the eventual loser would scream and cry about how the dealer's mistake changed the entire outcome of the hand and caused them to lose.

Personally, I prefer dealing out the correct River face down, then shuffling the stub and the early turn card together to get a new Turn.

Wouldn't dealing the correct river face down invalidate the reason for having burn cards?

Man this pisses some people off bad. I tried to explain to a guy once and he refused to speak to me for 2 days. They just cant see it.


a. not at all

b. why is this irrelevant again?

oh boy dont get me started on this one, yes it does, amongst a myriad of other things

Sometimes you have to let one rule slip in order to correct something else. But that is why using the 'real' River as the Turn is a better option (from that angle) as you don't have a card sitting out there on the table 'for all to see'.

On a similar note, we don't burn the re-shuffled stub for the 'new' River ... so that impacts the reason for burn cards as well. Should we make sure that the dealer doesn't re-shuffle the deck until action is complete on the Turn so that a card being used on the board isn't on top? GL

Yes. The correct procedure is not to reshuffle until you need to. This also saves a step if the hand ends on the turn.

More importantly they should wait to reshuffle to reduce the possibility of exposing more cards with action yet to come.

For those people reading this thread that don't understand the Monty Hall problem, it was made much easier for me to understand when there is 100 doors. Your choice is 1 door (out of 100) or to switch to 99 doors (98 of which were opened).

Lits of maths going on in here. It's good.
But even if the rule was only created that way for the superstitious, isnt that good enough reason to keep it going? Arent those the player s you WANT in the game? The ones who dont know/understand/care about that.