[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...