Random Number Generation

So for say 52 cards being randomly shuffled, I have X amount of permutations....

I have a shuffler which does this.

This shuffler is in a casino.

It is required by law to be randomly shuffled when in play.

But some permutations are not all random? Is this statement correct?

So if I am shuffling, I wont actually go through all X permutations if not all permutations are considered random?

In reality I have alot less than X permutations?

If all of these statements are true, how many permutations out of X are considered random?

I don't consider it truly "random" unless each of the 52! permutations is equally possible. This depends on any number of things, including the method in which the cards are shuffled. However, even if you could do one trillion shuffles in one one-trillionth of a second, you aren't going to get anywhere near that many before the expected collapse of the sun.

Did you know that, if you divide a 52-card deck into two 26-card piles, do a "riffle shuffle" (alternating cards from each pile) such that the top and bottom cards are the same as before, and repeat this seven times, the deck is back in its original position?

Its theoretically impossible to prove randomness

https://www.random.org/analysis/

Quote: ThatDonGuy

I don't consider it truly "random" unless each of the 52! permutations is equally possible. This depends on any number of things, including the method in which the cards are shuffled. However, even if you could do one trillion shuffles in one one-trillionth of a second, you aren't going to get anywhere near that many before the expected collapse of the sun.

Did you know that, if you divide a 52-card deck into two 26-card piles, do a "riffle shuffle" (alternating cards from each pile) such that the top and bottom cards are the same as before, and repeat this seven times, the deck is back in its original position?

Oh yes I do, but I have this feeling that casinos - at least mine - have grossly and purposely misinterpret the 7 riffle shuffle. I only say this because at my casino they take 7 decks and riffle each one, 1 time each and its done although they must check with the pit in order to proceed, it seems wrong for some reason. I take it as 7 riffles per 1 deck, although that would take forever with 8 decks now that im thinking about it.

Quote: heatmap

So for say 52 cards being randomly shuffled, I have X amount of permutations....

Not arguing with that.

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I have a shuffler which does this.

This shuffler is in a casino.

It is required by law to be randomly shuffled when in play.

So far, so good. Except to say that only a thorough shuffle would achieve random. E.g. if the shuffler just cut the deck ten times and rearranged the order, then obviously that's not anything like random. If it generated 52 non-equal numbers based on the decay of some cesium atoms, that would probably be deemed acceptable. Surely the nature of the shuffle has to be deemed acceptibly thorough and not determinable between shuffle and game.

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But some permutations are not all random? Is this statement correct?

If I knew what it meant, I'd be inclined to say it's not correct.
It's outcomes that are random. If one outcome is Ace through king exactluy like unshuffled decks, then it would be suspicious, but no less one of the x permutations and no less random. Remember X is very big. In the lifetime of the casino, you would probably not encounter the same permutation twice, or indeed see every permutation once.

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So if I am shuffling, I wont actually go through all X permutations if not all permutations are considered random?

You won't actually see all perutations over a hundred lifetimes, but the second part of your sentence is meaningless. Who says not all permutations are considered random?

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In reality I have alot less than X permutations?

No. X is fixed unless someone such as the pit inspects each shuffled deck and says 'That's not random enough for my liking'

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If all of these statements are true, how many permutations out of X are considered random?

I consider all permutations that come out of a good shuffler to be random. YMMV.

Quote: ThatDonGuy

Did you know that, if you divide a 52-card deck into two 26-card piles, do a "riffle shuffle" (alternating cards from each pile) such that the top and bottom cards are the same as before, and repeat this seven times, the deck is back in its original position?

Persi Diaconis can do that.

At 6:00 he begins discussing Casino Shufflers, RNG's and Slot Machines: