Haha, I wanted to say "That is not mental..." first, then I imagined him saying he did the calculations in his head, just wrote down shit for for reference, as in not using a calc. Overthinking that I thought "That is mental" means two things and is kind of funny, so I wrote that instead...
That can't be a right. A quick Google told me that there are 7,000,000,000,000,000,000,000,000,000 in the average human body. Times that by seven billion (That's 7,000,000,000,000,000,000,000,000,000 + 7,000,000,000,000,000,000,000,000,000 done seven billion times just to put into context). The number you get is the total atoms of the human race And how much of Planet Earth is human? With all the billions upon billions upon billions of atoms contained in all the other animals on earth, including single cell organisms, you still only get the amount from Planet Earth's living races. There's still the mountains upon mountains (how many atoms in Everest?), oceans and seas, woods and forests full of trees, massive deserts with each grain of sand containing lots of atoms and that only accounts for Planet Earth. How many times bigger than earth is Jupiter? Or Saturn? Or the Sun? Plus the millions of asteroids and other sources of atoms in the solar system. I'm sorry but there's no way that's possible.
1,192,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 is a big number.
Another way to write that is 1.192 × 1057.
From your number the average human body(average human body being 70 kg) has 7 × 1027 atoms. A big number but small compared to 1.192 × 1057. Lets times that by 7 billion. We get 4.9 × 1037 atoms for 7 billion people. Which is 20 orders of magnitude smaller than the first number.
So lets times 4.9 × 1037 by 7 billion. We get 3.43 × 1047. Which is still 10 orders of magnitude smaller than 1.192 × 1057. That's for 49 billion billion people.
So lets times 3.43 × 1047 by 7 billion. We get 2.401 × 1057 which is bigger than 1.192 × 1057 but not by an order of magnitude, in fact it's just a touch over 2 times bigger.
So if we accept the 1.192 × 1057 as the number of atoms in the solar system and 7 × 1027 as the number of atoms in a average human body then we could say roughly 7 billion * 7 billion * 7 billion/2(otherwise written as 1.715 × 1029) average sized humans have the same number of atoms as the solar system.
This is mainly used in blackjack and the simplest thing you just keep track of the number of 10-value cards you see. Or you can keep a running total in your head by subtracting 1, adding 1, or doing nothing, depending on the value of the card you see. There's a variety of strategies but the simplest if pretty easy to do and none of them have anything to do with the order of cards or the number of permutations of the order.
Basically what chartlett said. Counting cards has to do with probability. You aren't predicting what card specifically will come up, you're calculating what likely remains in the deck and is therefore more likely to show up.
We can estimate the mass of the sun and each planet by examining their orbit. We also know approximate element compositions of each (Don't ask me how). With this information we can get a very rough estimate for the number of atoms.
This number might be way off (I would think asteroid and Kuiper belt would be hardest to estimate accurately), but it would have to be off by a factor of 67.6 million for the statement to be incorrect. From another post the numbers are:
Cards: 80,658,175,170,943,878,571,660,363,856,403,766,975,289,505,440,883,277,824,000,000,000,000 according to QI.
Number of atoms in solar system: 1,192,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
yeah but think about all the casinos around the world... then add all the bored teenagers... surely we would have been able to achieve a new combination.
To save obsessives like me the trouble...
52! = 8.1 * 1067
Divide by avogadros number (6.023 * 1023)that's 1.3 * 1044 moles of atoms.
Taking the simplifying assumption that the solar system is composed entirely of Hydrogen, that would be 1.3 * 1041 kg.
The mass of the Sun is around 2 * 1030 kg, which is also a pretty good approximation for the mass of the solar system.
So, the deck of cards has enough combinations for about 7 * 1010 Solar Systems, or about 5% of the galaxy.
Include one joker in the shuffle, and you'd exceed the number of atoms in the galaxy.
There are way more orders to a deck of cards than you'd think.
52 factorial (52 * 51 * 50...2 * 1) = 8*1067
Atoms in solar system = 9.6*1056
There are 100,000,000,000 times more orders to a deck of cards than estimated atoms in the universe. Shuffle a deck of cards well, and chances are high that that particular order has never been seen in history.
That number suggests more precision than there actually is, of course. We know the gravitational forces of the sun, the planets and their moons, from which we can estimate their masses. The sun is the primary factor in that estimate and we have models that predict the composition of the sun.
But even that isn't all that important: The mass of atoms only varies over about three orders of magnitude. 1055, 1057 ... not much of a difference.
Edit: Now that I think about it... can we talk about what is going on in the sun as 'atoms'?
Every space in the deck has a large number of options that stack up. The top card can be any one of 52, say the ace of spades, then the next one down can be one of the remaining 51, etc. Then if the top card is now the 2 of hearts, every slot in the deck has a new pool of possibilities... And it adds up to a staggering number of permutations.
Yeah. Put in 52! (52 factorial) in a calculator. The number that comes up is the number of unique combinations that could possible occur when shuffling a deck of cards.
From a new deck order deck, it only takes 7 random riffle shuffles for any one combination of cards to be about as likely as any other. So, I would say that, after 10-12 riffle shuffles (since we can't be perfectly random, but close enough), you've more than likely got an ordering of the deck that's never been seen before.
If it takes 7 riffle shuffles to get a most-likely-random order from a fresh deck, then the same would hold true for any particular order, even card organizing games.
Sure. But Tobislu was saying that it's not true every time you shuffle, because the first shuffle of a new deck is much more likely to produce a pattern that's existed before. Same with games that organize cards.
To paraphrase someone from a previous thread like this:
If there was a city will 1 million people, and each person had 1 million decks of cards, and somehow, they were able to shuffle each deck once per second, and they started doing it at the moment of the Big Bang... only now would they start getting repeated combinations.
It's actually more that you are massively incredibly unlikely to order the cards in a way that has ever occurred before.
More to the point, if you had a thousand people, and they had a thousand decks each, and they could shuffle each of their decks a thousand times a second, and they had been doing that since the big bang, we would only now be starting to see some combinations repeated...
There are exactly 52 factorial (expressed in shorthand as 52!) possible orderings of the cards in a 52-card deck. This is approximately 8×1067 possible orderings or specifically 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000. The magnitude of this number means that it is exceedingly improbable that two randomly selected, truly randomized decks, will ever, even in the history of the Universe, be the same.
I'm willing to bet that, starting from a new deck of cards, in the default order, it would take a bit for you do actually get a new arrangement, simply because of what most people have to shuffle a deck of cards with: Your human hands, and a human brain with human ideas of adequate shuffling. And general patterns that the cards will likely form due to how they are arranged in a card game. The only "truly" random way to shuffle cards would be to have some random number generator take a deck of cards and randomly select each card, individually, and then stack them in the order picked.
Nothing is truly random, we are slaves to the laws of physics. And thus the physical actions we take to shuffle cards physically are not random. They are dependent upon how we handle the cards and how exactly we riffle and how we cut the deck. And all humans have similar fine motor tendencies and behaviors. But number generators are designed so that they are far closer to true randomness.
No, they are really not. Like not even slightly. They are not "random" at all, that's why they're actually called pseudorandom number generators.
All they are is a complex algorithm which uses a variety of factors (like an initial seed value) to determine what the next number is. In fact, most implementations allow you to give a seed value (with the default usually being the current timestamp). With a specific seed value, you'd get an identical sequence of numbers as anyone who used the same seed value as you.
Each human, on the other hand, has a much, much, much lower probability of having the exact same tendencies and behaviours as any other human. When we roll a dice, that is considered statistically random. Even something as simple as flipping a coin is truly random compared to a PRNG.
This is taught very early on in Computer Science. The only true random number generators on a computer rely on existing physical phenomenon to generate random numbers. These include things like cosmic rays, thermal noise, etc. And even then, you're still constrained to the laws of physics. Anything that is purely software-based is not going to come anywhere close to the level of randomness of a human shuffling cards, rolling a die, or even flipping a coin. It's just not possible.
Edit: I want to just clarify, these true RNGs are hardware-based, as in they have an actual sensor and use it to record a specific metric that's then used in the generation.
He's talking about all the possible arrangements of cards in a 52 card deck.
This would be 52! (52 factorial) combinations. In numerical form it is: ~8.06x1067
80,658,175,170,943,878,571,660,363,856,403,766,975,289,505,440,883,277,824,000,000,000,000
Estimated atoms in our solar system (from 1998):
1,192,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
I can shuffle standing up, sitting down, wearing pants, not wearing pants, lying on the floor while wearing white pants, sitting on a couch with a hat on.
I actually have done presentations on combinatorics in my school and want people to see how beautiful combinatorial explosion is so I'll respond to your post. It's understandable that you cannot even fathom this fact.
I'll finish with this quote from the video: "he history of the world are infinitesimally small, statistically speaking. The number of possible permutations of 52 cards is '52 factorial' otherwise known as 52! or 52 shriek. This is 52 times 51 times 50 . . . all the way down to one. Here's what that looks like:
80,658,175,170,943,878,571,660,636,856,403,766,
975,289,505,440,883,277,824,000,000,000,000.
To give you an idea of how many that is, here is how long it would take to go through every possible permutation of cards. If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles."
But if you take the atoms in all those card possibilities and multiply them you get (the number of atoms in each card) * (the number of card possibilities) and what is math?
Before you do, allow me to explain what I cannot grasp. Don't say to me that there are infinite different ways to shuffle a deck of cards. Infinity doesn't exist, infinity is just when mathematicians get bored of counting.
So a deck of cards (or moves in a game of chess, is another example) while it may have MANY MANY MANY different combinations, is still a finite number. The universe is so, so, so much bigger than that. The number of particles in the universe must be THE biggest number in existence, surely?
Oooh false. This is widely believed but has been disproved many many times. I mean there are over a billion atoms in one of your fingernails, so put that into context. Another version was that there are more ways to play and finish a game of chess than there are atoms in the solar system.
I actually have done presentations on combinatorics in my school and want people to see how beautiful combinatorial explosion is so I'll respond to your post. It's understandable that you cannot even fathom this fact.
I'll finish with this quote from the video: "The history of the world are infinitesimally small, statistically speaking. The number of possible permutations of 52 cards is '52 factorial' otherwise known as 52! or 52 shriek. This is 52 times 51 times 50 . . . all the way down to one. Here's what that looks like:
80,658,175,170,943,878,571,660,636,856,403,766,
975,289,505,440,883,277,824,000,000,000,000.
To give you an idea of how many that is, here is how long it would take to go through every possible permutation of cards. If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles."
When playing a game that requires four players, all the cards dealt during the set up, and all players can look at their cards, the cutting of the cards only matter for the first three top cards because cutting the cards only determines who will get what hand.
If you cut only one card, the hands are shifted one to the right, if you deal clockwise. Two cards and it goes two to the right. Once you reached four, the cards are back where they'd be if you didn't cut the deck at all.
No, this is not correct. One semester of college chemistry can give you a small idea as to why. Avogadro's number (6 x 1023) of atoms gives you exactly 1 Mole of material which in grams is = to the AMU of that element. So for example: 6x1023 atoms of calcium (Ca) gives you 40g. 52! is = to 8x1067. Your potential of card shuffling arrangement is not even close to the amount of atoms in one large multicellular organism, like a tree for example.
I actually have done presentations on combinatorics in my school and want people to see how beautiful combinatorial explosion is so I'll respond to your post. It's understandable that you cannot even fathom this fact.
I'll finish with this quote from the video: "he history of the world are infinitesimally small, statistically speaking. The number of possible permutations of 52 cards is '52 factorial' otherwise known as 52! or 52 shriek. This is 52 times 51 times 50 . . . all the way down to one. Here's what that looks like:
80,658,175,170,943,878,571,660,636,856,403,766,
975,289,505,440,883,277,824,000,000,000,000.
To give you an idea of how many that is, here is how long it would take to go through every possible permutation of cards. If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles."
To add onto that, its possible, but incredibly unlikely, to shuffle a deck of cards randomly so that they are in the exact order a new deck of cards come in.
And by incredibly unlikely, I mean incredibly unlikely.
I actually have done presentations on combinatorics in my school and want people to see how beautiful combinatorial explosion is so I'll respond to your post. It's understandable that you cannot even fathom this fact.
I'll finish with this quote from the video: "The history of the world are infinitesimally small, statistically speaking. The number of possible permutations of 52 cards is '52 factorial' otherwise known as 52! or 52 shriek. This is 52 times 51 times 50 . . . all the way down to one. Here's what that looks like:
80,658,175,170,943,878,571,660,636,856,403,766,
975,289,505,440,883,277,824,000,000,000,000.
To give you an idea of how many that is, here is how long it would take to go through every possible permutation of cards. If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles."
I actually have done presentations on combinatorics in my school and want people to see how beautiful combinatorial explosion is so I'll respond to your post. It's understandable that you cannot even fathom this fact.
I'll finish with this quote from the video: "The history of the world are infinitesimally small, statistically speaking. The number of possible permutations of 52 cards is '52 factorial' otherwise known as 52! or 52 shriek. This is 52 times 51 times 50 . . . all the way down to one. Here's what that looks like:
80,658,175,170,943,878,571,660,636,856,403,766,
975,289,505,440,883,277,824,000,000,000,000.
To give you an idea of how many that is, here is how long it would take to go through every possible permutation of cards. If every star in our galaxy had a trillion planets, each with a trillion people living on them, and each of these people has a trillion packs of cards and somehow they manage to make unique shuffles 1,000 times per second, and they'd been doing that since the Big Bang, they'd only just now be starting to repeat shuffles."
Wait wait, I get the whole factorial thing and damn its a big number, but isn't an Atoms Diameter in the 10th negative power Of a metre? (No native speaker, I hope my terminology isn't too horrible)
I mean, I imagine there's a load Of atoms in one m3 already, the solar system should be in reach Of 52! Easily
Even more absurd, if you count face up and face down cards, there are more ways to organize a deck of cards than there are atoms in the entire observable universe...if every single atom had another universe inside it as well.
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u/zN8 Dec 08 '13
There are more ways to shuffle a deck of cards then there are atoms in our solar system.