Shuffling Cards

 Some time ago when doing simulation projects, we discovered some problems in code based random numbers.    We even tested them vs some physical machines.  To feed analytical simulation ofprocess.  Humans are well known to be terrible generators of randomness.  The article below points out that the problem is yet to be completely solved. 

On the Randomness of Automatic Card Shufflers   by Bruce Schneier

Many years ago, Matt Blaze and I talked about getting our hands on a casino-grade automatic shuffler and looking for vulnerabilities. We never did it—I remember that we didn’t even try very hard—but this article  shows that we probably would have found non-random properties:

…the executives had recently discovered that one of their machines had been hacked by a gang of hustlers. The gang used a hidden video camera to record the workings of the card shuffler through a glass window. The images, transmitted to an accomplice outside in the casino parking lot, were played back in slow motion to figure out the sequence of cards in the deck, which was then communicated back to the gamblers inside. The casino lost millions of dollars before the gang were finally caught. ... ' 

Its interesting that the comments point to further experience and research, including using a magician to detect regularity in in choice!

Fast Random Number Generation with Lasers

Fast Random Number Generation with Lasers

Pointer to this in Schneier:       In school one of my particular areas of interest was random number use and leverage.   We detected the fact that a number of available sources of such numbers did a poor job of generating them.   Fast was not as big an idea then as quality back then.    Why? , what are they used for now?   "  Random numbers are widely used for information security, cryptography, stochastic modeling, and quantum simulations.  "   ...  

The Need for Loaded Dice

I remember having to explain to managers why dice had to be 'loaded' in some of the simulations we built.  Isn't that biased?  Yes, but being loaded is required in accurate models.   The article in Quanta Magazine shows why.  See also the link to the MIT work, which further explains the why.

How and Why Computers Roll Loaded Dice
Stephen Ornes, Contributing Writer   in QuantaMagazine

Researchers are one step closer to injecting probability into deterministic machines.
Here’s a deceptively simple exercise: Come up with a random phone number. Seven digits in a sequence, chosen so that every digit is equally likely, and so that your choice of one digit doesn’t affect the next. Odds are, you can’t. (But don’t take my word for it: Studies dating back to the 1950s reveal how mathematically nonrandom we are, even if we don’t recognize it.)

Don’t take it to heart. Computers don’t generate randomness well, either. They’re not supposed to: Computer software and hardware run on Boolean logic, not probability. “The culture of computing is centered on determinism,” said Vikash Mansinghka, who runs the Probabilistic Computing Project at the Massachusetts Institute of Technology, “and that shows up at pretty much every level.”

But computer scientists want programs that can handle randomness because sometimes that’s what a problem requires. Over the years, some have developed sleek new algorithms that, while they don’t themselves generate random numbers, offer clever and efficient ways to use and manipulate randomness. One of the most recent efforts comes from Mansinghka’s group at MIT, which will present an algorithm called Fast Loaded Dice Roller, or FLDR, at the online International Conference on Artificial Intelligence and Statistics this August. ... " 

Simulating Loaded Dice

Intriguing.  We spent lots of time updating ow we generated random numbers,  sometimes laboriously checking internal random number generators.    I can think of ways this could be used to generate numbers more clearly understandable to decision makers.    Since many real systems use numbers that are 'loaded' by context.

 Algorithm quickly simulates a roll of loaded dice    by Steve Nadis, Massachusetts Institute of Technology in TechExplore

A new algorithm, called the Fast Loaded Dice Roller (FLDR), simulates the roll of dice to produce random integers. The dice, in this case, could have any number of sides, and they are “loaded,” or weighted, to make some sides more likely to come up than others. Credit: Jose-Luis Olivares, MIT

The fast and efficient generation of random numbers has long been an important challenge. For centuries, games of chance have relied on the roll of a die, the flip of a coin, or the shuffling of cards to bring some randomness into the proceedings. In the second half of the 20th century, computers started taking over that role, for applications in cryptography, statistics, and artificial intelligence, as well as for various simulations—climatic, epidemiological, financial, and so forth.

MIT researchers have now developed a computer algorithm that might, at least for some tasks, churn out random numbers with the best combination of speed, accuracy, and low memory requirements available today. The algorithm, called the Fast Loaded Dice Roller (FLDR), was created by MIT graduate student Feras Saad, Research Scientist Cameron Freer, Professor Martin Rinard, and Principal Research Scientist Vikash Mansinghka, and it will be presented next week at the 23rd International Conference on Artificial Intelligence and Statistics.

Simply put, FLDR is a computer program that simulates the roll of dice to produce random integers. The dice can have any number of sides, and they are "loaded," or weighted, to make some sides more likely to come up than others. A loaded die can still yield random numbers—as one cannot predict in advance which side will turn up—but the randomness is constrained to meet a preset probability distribution. One might, for instance, use loaded dice to simulate the outcome of a baseball game; while the superior team is more likely to win, on a given day either team could end up on top.... "

Generating Random Numbers

A new means I had not head of, how random, repeatable is the result?

Scientists Use Crystals to Generate Random Numbers
Popular Mechanics
Courtney Linder
February 19, 2020

Computer scientists at the University of Glasgow in the U.K. have generated random numbers through an automated system that completes inorganic chemical reactions and grows crystals within a computer numerical control machine. The researchers outfitted a camera to the device to record images of the solidifying crystals, then used image-segmentation algorithms to examine the pixels corresponding to the crystals; a binarization algorithm converted the data into a series of 0s and 1s based on the crystalline geometry, repeating the process until the desired binary-code length for encryption was realized. Comparing this random-number generator with the Mersenne Twister pseudorandom number generator, the researchers found the new system decrypted messages faster. ... " 

Creating Randomness

We may intuitively think that order is good and disorder is bad, but randomness is useful, for example in preparing samples of data to train learning system.    This mathematical article touches on the issue

Mathematicians Calculate How Randomness Creeps In by Marcus Woo in Quanta Mag
The goal of a 15 puzzle is to put numbered tiles in order. Now mathematicians have solved the opposite problem — how to scramble one.

You’ve probably played a 15 puzzle. It’s that frustrating yet addictive game with 15 tiles and a single empty space in a 4-by-4 grid. The goal is to slide the tiles around and put them in numerical order or, in some versions, arrange them to form an image.

The game has become a staple of party-favor bags since it was introduced in the 1870s. It has also caught the attention of mathematicians, who’ve spent more than a century studying solutions to puzzles of different sizes and startling configurations.

Now, a new proof solves the 15 puzzle, but in reverse. The mathematicians Yang Chu and Robert Hough of Stony Brook University have identified the number of moves required to turn an ordered board into a random one.  ... "

Simulating Quantum Computing

The ability to simulate quantum physics in a useful way is interesting here. 

AI can simulate quantum systems without massive computing power
It could help with both physics and quantum computers.
By Jon Fingas, @jonfingas in Engadget

It's difficult to simulate quantum physics, as the computing demand grows exponentially the more complex the quantum system gets -- even a supercomputer might not be enough. AI might come to the rescue, though. Researchers have developed a computational method that uses neural networks to simulate quantum systems of "considerable" size, no matter what the geometry. To put it relatively simply, the team combines familiar methods of studying quantum systems (such as Monte Carlo random sampling) with a neural network that can simultaneously represent many quantum states. ..... " 

Iota and Alpha

Been following the Iota Blockchain, especially as it relates to implementation of smart contracts.   Here a new post.  I note that the post below is quite technical. I mention it here for followers in this space.  For starters on this see my previous post and the Iota.org for more background.  Note also that if randomness is important, and here it is essential, the use of an excellent method of random number generation is necessary.

Alpha: playing with randomness
 By Alon Ga         IOTA    Official IOTA Foundation blog 

If you have been following the Illustrated Introduction to the Tangle series, you might remember a mysterious parameter called α, which affects the level of randomness in the random walk. In this article we will go into the specific way in which α affects tip selection, and mention some issues to consider when writing a software implementation.

Note that this article assumes a basic understanding of how the Tangle is built, and in particular what approvers and cumulative weights are. You should also be comfortable with the exponential function, and have some understanding of probability theory.  ... " 

Quantum Random Numbers

A long time interest of mine, especially as it relates to creating realistic process simulations.  But now important to do well in many areas.   A mostly non technical article:

How to Turn a Quantum Computer Into the Ultimate Randomness Generator in Quanta Mag  By Anil Ananthaswamy

Pure, verifiable randomness is hard to come by. Two proposals show how to make quantum computers into randomness factories. .... " 

Detecting Randomness of Numbers

Early projects had us looking to determine if numbers were random or not.    Signal vs noise detection.   Can be very important for scrubbing data before use.   Here an example of a means of detecting non-randomness.   In DSC. 

Random Numbers

A long time technical interest.  Used many random number generators, and in some cases tested them to determine their limitations.  Here a brief history.

Genes, Games, Randomness and the Power of Algorithms

In the CACM:  Sex as an algorithm.   Fascinating piece.  Not really technical, but a conceptually dense description.  Reminds me of some of our own experiments with genetic algorithms to solve complex corporate problems.  More in the tag below.  These were not really successful,  but why?

Probably because we were not successful in creating the right representation of the problem to work with.  Never obvious.    Even less so for this kind of solution method.   Also such genetically found algorithms are by their nature 'black boxes' whose operation cannot be directly explained.    Worth the scan or read for broad insight into the idea of genetically finding useful solutions.

Random but with Geometric Order

A mathematical, but but not very technical article, but the implications are not easily thought about. The non-order called randomness has a remarkable number of practical applications.  Such as crytology, for example or creating 'natural'  imagery. It turns out that if you build geometric structures based on randomness, they turn out to exist in classes.  Is that itself a kind of order?  Visually striking example images.

In Wired:   Mathematics are building new models of geometric randomness. by Kevin Hartnett

" ... these random shapes can be categorized into various classes, that these classes have distinct properties of their own, and that some kinds of random objects have surprisingly clear connections with other kinds of random objects. Their work forms the beginning of a unified theory of geometric randomness.

“You take the most natural objects—trees, paths, surfaces—and you show they’re all related to each other,” Sheffield said. “And once you have these relationships, you can prove all sorts of new theorems you couldn’t prove before.” ... " 

Caution with False Patterns

A favorite topic of mine, and a nice piece on caution about finding patterns in data.  Our brains are wired to find patterns, for survival and efficiency.  Worth repeating ...

The inherent clumpiness of randomness
Finding patterns isn't really a question about random processes; it's a question about the human brain. By Mike Loukides  

I've always been interested in random processes. I steered away from writing a Math Honors essay in High School about randomness: that route certainly lead to madness. But the fascination with randomness has persisted, and particularly with what I call the "inherent clumpiness of randomness."  ... "

Signals and Noise in Observation

On signals and noise and observation, in Nicholas Carr's blog Roughtype:

" ... From Nassim Nicholas Taleb’s  ... book Antifragile: Things that Gain from Disorder, but I found this bit to be intriguing:

The more frequently you look at data, the more noise you are disproportionally likely to get (rather than the valuable part called the signal); hence the higher the noise to signal ratio. And there is a confusion, that is not psychological at all, but inherent in the data itself. Say you look at information on a yearly basis, for stock prices or the fertilizer sales of your father-in-law’s factory, or inflation numbers in Vladivostock. Assume further that for what you are observing, at the yearly frequency the ratio of signal to noise is about one to one (say half noise, half signal) —it means that about half of changes are real improvements or degradations, the other half comes from randomness.  ... "

Random Freebies Creating Loyalty

In Retailwire: This is a classic psych finding, that random rewards can produce a kind of loyalty. Though mostly found in experiments with pigeons.  This was an experiment that was proposed in one of our grand experiments, but ultimately not implemented.  How well does it work with loyalty programs?   Still interested in a well constructed experiment.

Exploiting the non Randomness of People

Fascinating piece in the Wolfram blog on methods to exploit the inability of people to create random patterns, using the example of the 'Where's Waldo' search game. Nicely done analysis using Wolfram analytical software.  Applications for the real world?   I recall examples we worked on to find 'hidden' items in a space.  To what degree does this work best when the human is trying harder to be random?  They mention another example of building a system to win the rock-paper-scissors game against humans.

Role of Intuition in Analytics: Abductive Reasoning

Intuition, creativity, even directed randomness are parts of analytics.  And thus also part of what we are now calling 'Big Data'.   Now how we do implement the use of intuition?  By setting up easily used sand boxes that allow us to test alternative solutions easily.  In the design world this is called 'abductive reasoning'.  It uses simulation methods to perform testing.  Worth examining. On this topic Tom Davenport writes in   The HBR and discusses further.

   " ... Many people have asked me over the years about whether intuition has a role in the analytics and data-driven organization. I have always reassured them that there are plenty of places where intuition is still relevant. For example, a hypothesis is an intuition about what’s going on in the data you have about the world. The difference with analytics, of course, is that you don’t stop with the intuition — you test the hypothesis to learn whether your intuition is correct. ... " 

  Well said.  We have been doing it for years.  Consider also adding a gamifying process to both evaluate the results and varying their application.

Randomness Ruling Our Lives

Late to it, but completing: The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow.  Always looking for books that do a good job of providing explanations of arcane subjects like probability and statistics. This book does that.  I particularly liked the sections on Bayes Theorem, Pascal's Triangle and the underlying meaning of randomness.  The author tells a good story with real world examples.  He also frequently covers the history of each topic in some depth, which may or may not be to the taste of some.  I enjoyed it all, well done.   The Amazon description writes:

  " ... With the born storyteller's command of narrative and imaginative approach, Leonard Mlodinow vividly demonstrates how our lives are profoundly informed by chance and randomness and how everything from wine ratings and corporate success to school grades and political polls are less reliable than we believe.... "