Comments on: Shuffling a pile of papers

Question: Shuffling a pile of papers

Wolfdog — Wed, 16 Jan 2008 06:54:06 -0800

I have a moderately-sized pile of papers (say, several dozen) in front of me. What's a quick way of getting them thoroughly shuffled by hand? I am familiar with lots of shuffling algorithms, but they don't work well by hand, and techniques like riffle shuffle that work well with small, stiff cards don't work well with standard sheets of paper.

By: edd

edd — Wed, 16 Jan 2008 07:20:33 -0800

I'd deal or separate into six piles and restack based on the roll of a die. Rinse and repeat until you're satisfied they're shuffled to your satisfaction.

A proper shuffle algorithm results in an unbiased reordering. Many shuffles (like riffle) don't. There's got to be some balance struck between bias and practicality and without knowing why you're shuffling it's hard to say what the best way would be.

By: b1tr0t

b1tr0t — Wed, 16 Jan 2008 07:22:19 -0800

Do the papers have unique identifiers on them?

If so, shuffle the IDs using playing cards, a perl script, or whatever else you'd otherwise shuffle with. Once done, order the papers according to the randomized list.

By: Wolfdog

Wolfdog — Wed, 16 Jan 2008 07:32:50 -0800

...shuffle the IDs using playing cards, a perl script, or whatever else you'd otherwise shuffle with. Once done, order the papers according to the randomized list.
I'd like to do better than that, because putting the papers in order according to the computer-shuffled list is really quite slow. (Imagine taking a deck of cards and putting it in order according to a prescribed list!)

To address edd - riffling isn't perfect, but it you can do it seven times in as many seconds (or fewer) and end up with what I'd call an acceptably randomized deck. It avoids depending on an external random number generator, too, which is what I'd like, ideally. (Actually rolling a die is out of the question - slow! - and I want to don't have to depend on a computer being available.)

By: edd

edd — Wed, 16 Jan 2008 08:00:05 -0800

Don't worry about the die then. Just do it a few more times to compensate for any non-randomness in any choice you make. The pile shuffle is still probably most convenient for large flimsy sheets, otherwise just smear the sheets out over a large table and recollect them.

By: dsword

dsword — Wed, 16 Jan 2008 08:03:46 -0800

Each of the following should take under 5 minutes for a few dozen papers, I think.

-Throw them up in the air and then pick them up. Repeat as many times as you like. (Or smear them across a table as edd suggests).

-Alphabetize them according to the second letter of the first word appearing on the last line of each page, or some other arbitrary choice.

-Write numbers from 1 to 200 on slips of paper, one for each page to be shuffled. Don't worry about what they are, just make sure that all numbers are at least 2 apart. Put them in a hat and grab your favorite book with more than 200 pages. Pull a number from the hat and bookmark the corresponding page of the book with the first paper in the stack. Repeat until the numbers are gone and the papers are all in the book. Pull them out of the book in a stack.

By: fearfulsymmetry

fearfulsymmetry — Wed, 16 Jan 2008 08:05:32 -0800

Throw them all up into the air then pick them up again.

Spread they out on the floor and stir them around with your hands a few time

Pass them from one hand to the other add a few on the top then few on the bottom, repeat a few times.

By: dsword

dsword — Wed, 16 Jan 2008 08:07:10 -0800

Note: for the alphabetizing method, you might get several stacks with more than one paper. Re-alphabetize those stacks according to some other arbitrarily chosen letter.

By: Skorgu

Skorgu — Wed, 16 Jan 2008 08:21:03 -0800

I'm failing absolutely at finding a cite for it, but repeating a biased shuffle will not compensate for the bias, it will likely increase it. If you're going for random-ish this isn't a problem but if there are real-world consequences for predictability it's something to keep in mind.

By: Wolfdog

Wolfdog — Wed, 16 Jan 2008 09:12:21 -0800

I'm failing absolutely at finding a cite for it...
See here and here - repeated riffling actually is good.

By: Skorgu

Skorgu — Wed, 16 Jan 2008 09:51:50 -0800

Thanks Wolfdog, that wikipedia article section about Poorly Implemented Knuth Shuffles is what I was going for. Riffle is unbiased but with limited randomness so repeating it is good, but if your algorithm is poorly done and introduces bias repeating it won't help.

There was a great, illustrated blog post on just this issue but I can't find it now. Oh well. Randomization is subtle and easy to get wrong.

By: edd

edd — Wed, 16 Jan 2008 09:57:31 -0800

Skorgu: It might depend on the exact nature of the bias, but in testing the bad shuffle here repeated shuffles look dramatically less biased, based on the value ending up in the first element of the array. I imagine that if the shuffle was biased based on the actual value rather than the previous position you may well end up more biased with repeated shuffles. In Wolfdog's case I'd imagine this isn't an issue.

By: mu~ha~ha~ha~har

mu~ha~ha~ha~har — Wed, 16 Jan 2008 13:31:38 -0800

Ohh. Good question. Throwing them definitely! Which is always fun. But you might look crazy and your papers might get lost or crinkled... make that will - if you do it right.

Hmm fan them out into a spiral (as in a circle that spirals vertically)
*Maybe alternate a chunk of them facing up then a chunk down and so on as you go?* Then divide the circle into whatever fraction you see fit. Stack, then spiral and divide again.
*Sift through each section quickly to glean a rough idea many 'up' pages match and then adjust the placings of your next spiral accordingly, all right way up this time.*

That's just my speculations though. I think the size of your spiral, which fraction you went with and how many pages you actually had perhaps would matter. Admittedly I haven't had breakfast yet (or possibly even read the post properly?) but I think that would work?