No two card shuffles will EVER be the same.

[HungLikeJesus]

Flint, I calculate that in 9x10^33 shuffles of the deck, the probably of two shuffles resulting in the exact same ordering is 50% (assuming complete randomness in all shuffles).

[Flint]

Originally Posted by smoothmoniker

You've assumed that shuffles produce random distributions.

No, I haven't actually:

Originally Posted by Flint

Of course, the part I didn't include is how these are not really random deck shuffles. Card are arranged in typical, repeating patterns, due to the fact that we are shuffling from a partially ordered state, based on the card combinations that happen during the course of card games.

Originally Posted by Flint

Well, in reality, one shuffle does affect the next one, because it isn't really starting from a random order. But I'm assuming the shuffles are random for the purposes of this discussion.

Okay I guess I did say that, but with a qualifier. And it's partially because I don't know how you could calculate in that variable, and, if it would even make a difference, considering that all 52 cards have to be in position; doesn't this quickly become just more random data?

Originally Posted by smoothmoniker

Picture a deck with the 7 of Spades as the top card. You split the deck in half, and shuffle the cards together.

There are not 52 possible locations for the 7S to appear, post shuffle. Given a standard shuffle (small groups of cards falling together at a time), the 7S will always appear in the top 5 or 10 cards. This last number is a conjecture, but it will certainly not appear much deeper than that, and will not appear in the bottom half of the deck at all, unless the shuffler simply "cuts" instead of shuffles.

So, you're cutting down the variables a bit for that one card, or for any cards that were used in the play of the last hand. I'll even further this to say that the same cards might appear in similar places if the same players were playing the same games, but... with the size of the numbers we're looking at here, I don't see these little possibilities having much impact. And, as always, it's all 52 cards in the exact same position we're talking about, not just a few cards, in a somewhat similar position.

Originally Posted by smoothmoniker

Assume that a large number of people regularly open brand new decks, which have the same starting order, and then give one shuffle. There is a much more limited (relatively) set of possible distributions for that first shuffle, that first permutation.

That's another good point. Of course, that deck is only new once. I would say that not enough new decks of cards have ever been produced to make much impact on the unimaginably huge number of permutations we're dealing with. Remember, I had every person on the Earth shuffling cards as a full time job, from now until an impossible number of years after our sun has burnt out and no trace remains that planet Earth ever existed. So, new decks of cards...I'm not so concerned with that.

Originally Posted by deadbeater

There, one could find certain duplicate hands, if dealt in a different order.

I'm talking about the whole deck, not just one hand. And order matters.

Originally Posted by lumberjim

flint's suppostitions are only accurate if the assumption is that you will experience all of the possible combinations before you get the same one twice.....which is quite ludicrous.

No, I just don't know how to calculate the probability that and I want somebody to do it for me. What I have shown, though is how the number of permutations is much larger than our brain can even comprehend.

Originally Posted by HungLikeJesus

Flint, I calculate that in 9x10^33 shuffles of the deck, the probably of two shuffles resulting in the exact same ordering is 50% (assuming complete randomness in all shuffles).

Now we're getting somewhere. Thanks, HLJ. I'll take you on your word (and these number are so big, I don't think it matters how far off we are from being exactly right).
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Now, to get through 9.e+33 permutations, everyone on the Earth (6,648,429,413 people) shuffling decks of cards as a full time job (one shuffle per 10 seconds, 8 hour days, five day weeks) it would take 257,553,876,374,935,601.83683591322334 years before you had a 50% chance of having the same shuffle come up. Hey, we’re finally out of exponential notation! Too bad, though, I don’t think human civilization has been, or will be, around for that long. Anyone have something concrete to bring this number down into the realm of might-ever-actually-happen?