|
United States24745 Posts
On August 19 2011 14:22 cz wrote:Show nested quote +On August 19 2011 14:20 micronesia wrote:On August 19 2011 14:16 cz wrote:On August 19 2011 14:10 micronesia wrote:
This isn't surprising to me, although another aspect of this to consider is that decks are often re-organized... so the first shuffle or two after that is much more likely to be similar to another shuffle. If you shuffled a deck of cards rather randomly for four hours then sure... you aren't getting another shuffle like that in the foreseeable future. True. Someone on reddit said it was calculated that it took 9 or so shuffles to be pretty much certain that a brand new deck was random/never before seen. I don't know how he defined "shuffle" or "pretty much certain" though. Depending on how you shuffle the deck you might not be randomizing it much at all. If you just weave the two decks together one card at a time then you get a fully predictable pattern :p BTW the number of shuffle to create a random situation is pretty much arbitrary just like saying the number of times you need to flip a coin to be pretty much sure that you'll see tails at least once. Right, but if you define "shuffle" and the number of shuffles you can have a confidence interval for how likely this is to be a unique deck order. Same thing with the coinflip: you create a confidence interval which is mathematically correct given the premises (50/50 chance of head or tails). That doesn't tell you how it will end, but give a big enough sample and it is true. For a deck of cards though, even a crappy shuffle is going to rapidly reach a 99.9999999999999% confidence interval for a new order, just because you have 52 cards instead of a 50/50 coinflip.
Yes, but how you decide when it is random 'enough' to be 'random' is still completely arbitrary.
|
The calculations are confusing me, but is it actually accurate, I mean isnt' there something liek hwo if you have 40 people in a room, you're more likely that there are two people who share the same brithday in that room than not, even though there are 366 days.
In that same sense, even tho there are X amount of possible combinations, it doesn't take 0.5X in order for the possibiilyt of that series to have existed before.
|
On August 19 2011 14:24 micronesia wrote:Show nested quote +On August 19 2011 14:22 cz wrote:On August 19 2011 14:20 micronesia wrote:On August 19 2011 14:16 cz wrote:On August 19 2011 14:10 micronesia wrote:
This isn't surprising to me, although another aspect of this to consider is that decks are often re-organized... so the first shuffle or two after that is much more likely to be similar to another shuffle. If you shuffled a deck of cards rather randomly for four hours then sure... you aren't getting another shuffle like that in the foreseeable future. True. Someone on reddit said it was calculated that it took 9 or so shuffles to be pretty much certain that a brand new deck was random/never before seen. I don't know how he defined "shuffle" or "pretty much certain" though. Depending on how you shuffle the deck you might not be randomizing it much at all. If you just weave the two decks together one card at a time then you get a fully predictable pattern :p BTW the number of shuffle to create a random situation is pretty much arbitrary just like saying the number of times you need to flip a coin to be pretty much sure that you'll see tails at least once. Right, but if you define "shuffle" and the number of shuffles you can have a confidence interval for how likely this is to be a unique deck order. Same thing with the coinflip: you create a confidence interval which is mathematically correct given the premises (50/50 chance of head or tails). That doesn't tell you how it will end, but give a big enough sample and it is true. For a deck of cards though, even a crappy shuffle is going to rapidly reach a 99.9999999999999% confidence interval for a new order, just because you have 52 cards instead of a 50/50 coinflip. Yes, but how you decide when it is random 'enough' to be 'random' is still completely arbitrary.
Yeah, you have a probability. Same thing as in the OP, with the 2.5 x 10^54:1 odds of shuffling a new deck order. At some point you do decide that the number sufficiently approaches infinity that you call that point "random." If you are saying 70% chance or so, then it's awkward, but when you are quickly into the 10^40 or range it's pretty much random.
|
On August 19 2011 14:26 Zlasher wrote:
The calculations are confusing me, but is it actually accurate, I mean isnt' there something liek hwo if you have 40 people in a room, you're more likely that there are two people who share the same brithday in that room than not, even though there are 366 days.
In that same sense, even tho there are X amount of possible combinations, it doesn't take 0.5X in order for the possibiilyt of that series to have existed before.
That's talking about the odds that there has ever been a duplicate deck order. I'm talking about a specific case, where you shuffle a deck and get a specific order, and saying that that is essentially unique in history.
For it to be the same as your analogy, instead of walking in and saying there is a >50% chance that in a group of 40 people two of them share a birthday, the analogy would be you or someone else in particular that you choose beforehand (and know their birthday) walking into a room and having someone have the same birthday as them. That is significantly less likely than the first analogy, because you are not talking about "any duplicate" but "a duplicate that is the same as this specific example"
The math I did was this: take the number of unique orders created so far (I gave that to be 10^13 or something, using some very generous circumstances), then have that be divided by the total number of possible combinations. So say there are 1000 possible deck orders, and 10 have been done before. That means there is a 100:1 ratio in terms of deck-orders-done-before:deck-orders-not-done, which means a random shuffle would have a 100:1 ratio of falling within the "never-before-seen" category.
When you divide exponents you just subtract, so 10^67 / 10^13 came out to something around 10^54, which is the ratio between seen-before:not-seen-before deck orders. That means you have a 1 in 10^54 chance of shuffling a before-deck-order, which is essentially zero.
|
I remember one time when we were about to play and my cousin asked me what the next cards were going to be. I got 3 first right and even for that it is a miniscule probability.
132600
Big numbers are scary big, but we are in the lower end of numbers aswell as size so it's all to scale IMO.
|
What is also funny about cards...when we were bored as high schoolers, we started playing this game where one person would take a deck of cards and pull the top card. The other person would have to guess the value of that card. If they got the value, then try to guess the suit. If they got it right, cool, if they got it wrong, you did not tell them the card you just reshuffled it and pulled the top card.
It was dumb and boring, but could amuse us for awhile. Also, it was almost astounding how often you could get it right if you tried.
|
On August 19 2011 13:43 cz wrote:
Actually, a more interesting question is how many cards you have to look through before you are 99% certain that this order has never occurred before. I'd guess it's within the first 5-10 cards.
9, 52!/43! is ~1.33e15 is like 3%. Factorials always grow faster than I think
|
Thats pretty cool, although I think your 1000 shuffles a second is kinda light. Theres like 8 billion people in the world and why would 2000~ peope be playing cards at any given time. I think it'd be higher.
|
On August 19 2011 16:01 GrapeD wrote:
Thats pretty cool, although I think your 1000 shuffles a second is kinda light. Theres like 8 billion people in the world and why would 2000~ peope be playing cards at any given time. I think it'd be higher.
Doesn't really change anything. Instead of it being 10^54 or whatever, if it's a billion shuffles per second for the past 1000 years the odds just go down by 10^6, to 10^48. Still 1:10^48 odds of a repeated deck order. Even at at trillion shuffles per second for the past 1000 years we are still at 1:10^45 odds.
|
That's pretty amazing read, as a math nerd, I'm surprised I never quite realized this and how epic 52 factorial is.
But also, wtf no bridge across the amazon 0_0 That's nuts, there is like zero interaction across it or something?
|
On August 19 2011 17:25 Pufftrees wrote:
That's pretty amazing read, as a math nerd, I'm surprised I never quite realized this and how epic 52 factorial is.
But also, wtf no bridge across the amazon 0_0 That's nuts, there is like zero interaction across it or something?
Apparently there weren't any cities on either side, so people just used boats / ferries.
|
|
|
|
|
|
EPT
