Any math wizards out there?

[Erreek]

I was playing with a few friends for low stakes in a home game when a hand was delt that caused some confusion. What happend was the whole cards were delt from one deck, and the flop was delt from another. Now, it was pretty much a family pot to the flop were Player One bet out and got one caller, Player Two. The turn and river went bet and a smooth call. The board was 5d 8d 2d 2s Jd. Player One had Ad 4c for the nut flush. Player Two had Kd Kh for the 2nd nut flush. After the hand, Player Two noticed the flop was delt from the other deck and demanded his money back.

Did dealing from the other deck, although no cards were duplicated, change the odds in any way?

[ncray]

Of course it changed the odds. The most noticeable differences would be that it's much more likely to get a set of kings and possible to get even 5 or 6 of a kind with kings. Since there are now 13/52 diamonds in the new deck vs 11/48 from the old deck, it is more likely to make a diamond flush from the new deck.

[Erreek]

Forgive me if i'm wrong, but I think you looked at my question too simple mindedly.

Yes there were 13/52 physical diamonds to cards in the deck but only 9/48 that would make the hand still valid. If the four cards weren't in play, how does it change the odds of the hand happening the way it did? A good analogy is if someone forgets to take a joker out of the deck and the cards are delt. If it was delt, it would be mucked and the next card after would be delt. There still would be 52 cards even though there is 53 physical cards. It wouldn't change the odds. The part where I get lost is what happens when one of the four cards from the actual example gets played.

then again, i could be way off.. hence the reason why i posted

[qpw]

It would potentially change the odds because there are no cards lost to the hole cards of the folded players.

Whatever cards are significant, there is a probability they were dealt to folded players from the first deck whereas the second deck will contain all cards pre-flop.

[Erreek]

It could potentially change the odds? You would think it either would or wouldn't lol

anyways, I think what you're saying is that if someone mucked a diamond preflop it would change the odds of the flop being three diamonds. While I will agree with that, I think any one unseen card in the muck is equal to any one unseen card in the deck. That being the case, if the hands are mucked blind preflop they are basically being put back in the deck.

Yes, there might have been a diamond mucked preflop but there also might have not been one. I'm asking if it changes the odds, not the outcome.

and on that note I apologize if I sound cocky... especially if I am wrong. A friend of mine and I have had this debate a few times and we can't seem to settle it, so i thought i'd post it here for some help.

[qpw]

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It could potentially change the odds? You would think it either would or wouldn't lol

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I was just being pedantic. It is possible that the particular arrangement of dealt cards is such that the odds don't change.

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anyways, I think what you're saying is that if someone mucked a diamond preflop it would change the odds of the flop being three diamonds. While I will agree with that, I think any one unseen card in the muck is equal to any one unseen card in the deck. That being the case, if the hands are mucked blind preflop they are basically being put back in the deck.

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No. Suppose you were playing with ten dealt in. It's quite possible that all the remaining diamonds are dealt out. Clearly there is now, using the same pack, a zero probability of another diamond appearing. With the new pack, even if you ignore the visible diamonds, there is similarly clearly a non-zero probability of a diamond appearing. Two different probabilities therefore two differnt odds.

Thus the gameplay has changed and the game should be considered void.


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Yes, there might have been a diamond mucked preflop but there also might have not been one. I'm asking if it changes the odds, not the outcome.

and on that note I apologize if I sound cocky... especially if I am wrong. A friend of mine and I have had this debate a few times and we can't seem to settle it, so i thought i'd post it here for some help.

[/ QUOTE ]
Hope to have been of some help.

[Erreek]

Okay there's something i'm missing. Analogy..

Two packs of playing cards. I take 13 cards from one deck and throw them out the window. Aren't the odds of getting delt a diamond the same for each deck?

You seem like youre saying that the 13 cards thrown out the window could've been 13 diamonds so that deck has less(or none) of a chance to deal you a diamond.

Yea, ten handed, all diamonds could've been delt and mucked but couldn't they also still be in the deck?

I don't see how it changes the odds.

[qpw]

I see what you are getting at, but I don't really think that's the point. You have changed the odds in the specific game.

True player 2 could not know in what way the odds have been changed, but he's quite entitled to demand the game be voided since, for example, if he loses he might, mindful of the fact that he could have won if the cards had been dealt from the correct deck, tilt.

[Erreek]

well put

thanks for the insight

[pzhon]

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Did dealing from the other deck, although no cards were duplicated, change the odds in any way?

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Under the condition that no cards were duplicated, the conditional probabilities are the same as the normal probabilities. However, the hand should still be voided.

[img]/images/graemlins/diamond.gif[/img] The rules say the hand is void.

[img]/images/graemlins/diamond.gif[/img] It's hard to tell whether a card was duplicated.

[img]/images/graemlins/diamond.gif[/img] A player who knows that the hand might be called a misdeal when the river is dealt has an advantage. Let's suppose a flop bluff push is marginally unprofitable. If there is a significant chance that hand will be voided when the turn and river are dealt, this changes the risk-reward ratio of bluffing and might make the play very profitable. This is because you get paid 100% of the time if everyone folds, even if the turn or river would have invalidated the hand. If you get called, you might only have to pay out 80% of the time. That's huge.

Similarly, suppose you have put $10 into the $20 pot, and are considering calling a pot-sized push with a 30% chance to win if the hand is not voided (say with a flopped OESD), and a 20% chance the deal will be voided. Ordinarily, calling invests $20 to get back $18, which is not good enough. Here, if you call, 20% of the time you get back $30, and 24% of the time you get back $60, a total of $20.40, so you should call. You have extra outs to tie.


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