Quote:AxiomOfChoiceThat is not quite the same thing. I think you want the birthday problem.

Estimating the number of shuffle-ups is interesting. Now I am sure that there are more than a billion a day, but of course there were a lot less in earlier days.

i don't think there are a billion single-deck shuffles on earth in one day. There are only 86,400 seconds in a day. Even if there were 10,000 shuffles every second, that's not a billion. I don't think there are anywhere near 10,000 shuffles a second... I am talking about real, physical cards, not inside computers.

Quote:MathExtremistThat assumes you're shuffling randomly. Humans don't do that...

What are non-magician humans doing then that allegedly causes the order of cards in a deck to be repeated?

Quote:geoffIt's similar to the birthday problem, but it's actually different. The birthday problem is for when any pair matching amongst the group works. Here it one specific person matched with one amongst the rest.

I don't think so. I think we are asking what the probability that two decks of shuffled cards have ever been the same.

Quote:sodawateri don't think there are a billion single-deck shuffles on earth in one day. There are only 86,400 seconds in a day. Even if there were 10,000 shuffles every second, that's not a billion. I don't think there are anywhere near 10,000 shuffles a second... I am talking about real, physical cards, not inside computers.

I think that if we include shuffling machines we get to a billion a day. It's one deck per 7 or 8 people on earth.

Quote:AxiomOfChoiceI think that if we include shuffling machines we get to a billion a day. It's one deck per 7 or 8 people on earth.

why would, on average, every 7 or 8 people on earth need to have a deck shuffled once per day? not that many people are playing cards each day on earth. It's a tiny, tiny minority.

Quote:sodawaterwhy would, on average, every 7 or 8 people on earth need to have a deck shuffled once per day? not that many people are playing cards each day on earth. It's a tiny, tiny minority.

Well, it's an average. It gets skewed by extreme cases. The guy sitting alone at the 3CP table getting 40 hands per hour really brings that average up.

How many casinos are there in the world? How many magicians practicing? How many bridge clubs? How many backroom cards games? How many automatic shuffling machines being tested? How many groups of guys playing a hundred hands of poker over some beers on a thursday night?

Quote:AxiomOfChoice

How many casinos are there in the world? How many magicians practicing? How many bridge clubs? How many backroom cards games? How many automatic shuffling machines being tested? How many groups of guys playing a hundred hands of poker over some beers on a thursday night?

fewer than a billion per day, that's for sure. haha.

Quote:paisielloWhat are non-magician humans doing then that allegedly causes the order of cards in a deck to be repeated?

Let's say you have 52 cards (one deck). The top ten cards are labeled A, B, C...J, where A is on top and J is the tenth card down. Cut the deck in half so you have 2 piles. One pile has A-J cards and the other has none of those ten. Shuffle the two piles perfectly. The order of the cards, starting from the top, is now: AxBxCxDx...xJ where the x cards are the cards that were shuffled between the A-J cards. If you deal those cards, one to me, one to you, one to me, one to you....one of us will get all A-J cards and the other will get all the "x" cards.

I'm not saying that's what happened in that scenario, but you get the point -- shufles aren't random. An AP playing blackjack can track slugs of cards through the shuffle (ie: everyone gets a ten or A one round. Well just like the A-J example above, they're gonna be clumped together for the next shoe.). Or they can sequence the cards (ie: the C card is an ace, so if the AP sees the AxBx combo come out of the shoe, they could expect to see the Ace (C card) come out next). Of course, that requires a weak shuffle AND a dealer who can riffle the cards almost perfectly.

Quote:RSShuffle the two piles perfectly.

And how does a non-magician human do that?