Popehat has quit twitter.

You can find him on Mastodon now.

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Can ChatGPT be modded up Insightful here?

re: sorted deck

I said that to make it easier for the reader to verify that there is indeed hidden order in 7 perfect shuffles. If you want to go thru the hassle, start with a what you believe is a random deck, and write down on paper each card in order, and then do the perfect shuffle as described above 7 times, and then compare the order to what you wrote down on paper.

As to a card shuffling machine, I would make it do my description of perfect shuffle, but do random cuts. Applies to a human shuffler too.

As in, pull a random sized chunk of cards from the near middle of the deck (say 11 to 29 cards - near quarter to near half of deck), at a random offset from the top, and then randomly place that chunk on either the bottom of the deck or on the top of the deck. Then shuffle. Rinse and repeat at least 4 times and make sure that the cuts go to both top and bottom.

You may have noticed that in my 7 perfect shuffle described above, neither the top card or the bottom card ever change. This is why there must be random cuts from middle placed on top of deck and bottom of deck. To get those cards to move in the stack. If you do not do cuts from the middle, cards near the bottom will tend to stay there, and cards near the top will tend to stay there. You have to do a random cut before each shuffle, whether the shuffle is perfect or not.

And you have made my point.

Your definition of perfect is not what I was describing.

The article also explains why seven shuffles "is just as close to random as can be" -- rendering further shuffling largely ineffective.

Is not accurate.

I was just noting that there is hidden order. Note that I never mentioned cutting the deck.

With a 52 card deck, 7 perfect shuffles returns you to your starting point. It is not random. Try it. You need to be consistent. Start with your deck stacked by suit and order so you can verify easily after the process. You need to split the deck into two stacks of 26 the same way every time. Say top 26 to right hand pile, and the bottom 26 to left hand pile. The easiest way is to count off the top 26 into a new pile, flipping them one at a time. And then turn that pile over. You need to decide which pile will contribute the bottom card, and stick to that choice. Let's say left is first bottom card. Then, to do the shuffle, turn both piles over. Being able to view the value of the card has no bearing on this. Pick from the left (turn the card over) and start the new deck. Then the right (turn the card over), alternating left and right piles. Repeat 6 more times, following the exact same procedure each time. Check the deck, it should match what you started with.

It may all depend upon the observation of what is being viewed.

You may want to research that.

November 15, 2020 Adrian McMenamin
Updating the five minute and the five byte rules

(As been pointed out I misread the original paper – it was $20,000 for a 540MB disk or about 3 cents per KB – quite a major error of scale. I also realised I wasn’t using the same comparison points as the original paper – so I’ve updated that too – the break even point is now 5 seconds on cache-ing and not 1/10th of a second. Obviously that’s a big difference, but the same general points apply. Sorry for my errors here.)

Q.E.D.

Why not split the difference and spring forward one half hour and then stop changing clocks. It's not like it has to be a whole hour offset from Zulu time.

Alas, all of my old posts have been disappeared.

You can not trust what you observe due to gravitational lensing.

Maybe this was why Twitter was hacked.

Need some Lithium? https://www.nasa.gov/feature/l...

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