Any math wizards out there?

[Fonzy4]

Hmmm don't have to be a math wizard to answer, YES.

[Erreek]

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Hmmm don't have to be a math wizard to answer, YES.

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Under the condition that no cards were duplicated, the conditional probabilities are the same as the normal probabilities.

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so you just made yourself look smart

[elitegimp]

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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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I'm going to say "yes" here because

1) You wouldn't notice if a mucked card was duplicated, combined with

2) You are only concerned with the outcome of this particular hand.

Let's assume 6 handed, because you were playing with "a few friends." As others have mentioned, the composition of the deck you dealt from was 11/48 diamonds (22.9%). However, there were 4 mucked hands so in actuality the possible situations were

0 mucked diamonds: deck is 11/40 diamonds (27.5%)
1 mucked diamond: deck is 10/40 diamonds (25%)
2 mucked diamonds: deck is 9/40 diamonds (22.5%)
3 mucked diamonds: deck is 8/40 diamonds (20%)
...
8 mucked diamonds: deck is 3/40 diamonds (7.5%)

Now, if you were to repeat this infinitely many times, on average there would be 1.83 mucked diamonds per hand making the deck 9.17 / 40 (22.9%) and things would work out... but just because it's okay in the long run does not make it okay in on shorter scales. Even though 1.83 diamonds would be mucked on average, I can guarantee you that there were not exactly 1.83 diamonds in the muck this hand so the odds are different.

Note: I'm fairly confident that my numbers are right, but the whole point is that the expected number of diamonds in the muck is non-integer. Whether 1.83 is the correct number or not doesn't real matter...

[filsteal]

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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.


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pzhon,

I assume that by "no cards were duplicated," you're including ALL cards that were dealt, including those that were mucked, correct?

Because, in principle, mucked hands changed the distribution of the remaining deck. For example, if you're the BB, and you don't look at your cards, and it folds around to you, then you're slightly more likely than usual to have AA, because the mucked cards are slightly less likely to contain an A, because if they did then they would've been less likely to be mucked.

Similarly, in this hand, the number of mucked cards, as well as the situations and positions in which they were mucked, affects the conditional probabilities of certain flops in very tiny ways, even given the condition that no (non-mucked) cards are duplicated.

Granted, the effects almost certainly negligible, but still.


OP,

No, there aren't any smart people on this site.

[Bantam222]

The mucked cards don't change much...people like to argue that if everyone folds the odds of aces being delt are higher. This is very insignificant. Have you ever seen someone use this in a poker game? "hmm i have KK but an ace flopped. I fold because 7 other people folded preflop meaning they must not have had an ace so the odds are higher that villain has one." Also, this shouldn't even come into play if we are dealing with a flush becuase people won't change their preflop ranges based on if it is AKspades or AKhearts.

Having duplicate cards in the deck doesn't change the odds unless they are delt. If you took the deck before the flop is delt and stuck a bunch of new cards on the bottom--it wouldn't change the flop because they aren't going to be used. This same logic works if you shuffle a bunch of new cards into a deck. They don't change the odds unless they come into play.

Even though the odds aren't changed if you are playing in a casino i think they will still cancel the hand.

[DarkMagus]

I say that the odds would indeed be changed.

If no flush draw appears on the flop, then the hand is more likely to end on the flop, and less likely to result in a disqualification. This is because sometimes a duplicate card would have hit the turn or river, but actually ends up going undiscovered.

If the flush draw does appear, then it is more likely that the hand will be played to the river, giving more chances for the hand to be disqualified.

We aren't changing the number of flush hands that will count, but we are increasing the number of non-flush hands that count. So it seems to me that among hands that end up counting there should be a smaller probability of hitting a flush.