Tag: random numbers

Guest Post: Random Number Prediction–A Class Exercise

Prof. Andrew Stapleton at the U. of Wisconsin-Lacrosse shares a teaching tip when discussing random numbers.

Predict a “random number” by alternating four-digit contributions. Start by determining a 5- digit number and writing it down in dark ink on a large piece of paper and sticking it in your briefcase. I act like I am picking random numbers, but I know exactly how to get to the number I have pre-determined.

Here is an example: I tell my class, “Let’s pick some numbers, I’ll start”: 4729 Mine I already know that the final number – the one written on the large piece of paper in my briefcase is 24727.

I then ask for two students to give me each a two-digit random number. The greater the number of participants the greater the impact. Student one chooses “58” and Student 2 chooses “32.” So 5832 yours

4167 Mine I act like I am thinking about another random four-digit number, but what I am doing is making their digits and mine add to 9999. (i.e., 5832 + 4167 = 9999)

I again ask two different students to each give me a two-digit random number. One gives me “69” and the other “02”. So 6902 yours

3097 Mine Again I make theirs and mine add to 9999, but I don’t do it right away. In fact, I act like I am really just pulling my digits out of thin air.

Sum = 24727. I then add all of these together. I tell them I had a dream about what number we would collectively come to in this exercise and wrote it down on a piece of paper and I get it out and unfold it. Once they see it matches, they are baffled and are eager to learn how I did it.

Solution: I simply take my original 5-digit number and subtract 2 from the last digit and put it in front of the first. This is because whatever you choose – I will choose digits that add to 9. So, the second set adds to 9999 and the third set adds to 9999 – just shy of 20000, in fact 19998. So, I subtract those two from the end and stick the “2” in the front.

OM in the News: How the Famous Book, “A Million Random Digits,” Wasn’t So Random

“A Million Random Digits” was the largest table of random digits ever published

For 65 years, Rand Corp.’s reference book “A Million Random Digits with 100,000 Normal Deviates” has enjoyed a reputation as the go-to source for random numbers. Simulation and sampling problems are facilitated by these random numbers, as are many problems in our text. (See Table F.4 on page 799 of Module F, Simulation, for a small excerpt).  As Gary Briggs of Rand Corp. noted in The Wall Street Journal (Sept. 25, 2020) “it was really hard to get really high-quality random numbers.”

Well, after all of these years and worldwide usage, Briggs found some errors. While many of us would consider the errors minor, he found them “soul crushing,” adding, “the idea that I’m finding errors that we’ve ignored for 65 years is upsetting.” Before modern computers, he says, “it was really hard to get high-quality random numbers.” The book changed that for a generation of pollsters, lottery administrators, market analysts and others who needed means of drawing random samples.

Here is a bit of history: Rand collected a million digits using Douglas Aircraft Co.’s machine that registered random fluctuations in voltage and converted them into strings of 1s and 0s. A circuit board converted sets of 1s and 0s into digits 0 to 9, which a third machine translated into holes punched into 20,000 computer cards. Technicians fed the cards into an IBM data-processing machine, which generated a million-digit number filling 400 pages of tables.

How did the digits lose their “randomness?” Briggs thinks a technician dropped cards and put them back in the wrong order!

“A Million Random Digits,” by the way, became less relevant as powerful computers generated instant randomness.

Classroom discussion questions:

  1. How much difference would such errors in the Rand book make in your problems in Module F?
  2. Why are random numbers an important tool?

Good OM Reading: A Million Random Digits With 100,000 Normal Deviates

million random digitsJay just called from the snowy Denver POMS meeting, asking me to review the new edition of this classic book that we reference in Module F, Simulation. The book is Rand Corp.’s 600-page paperback, “A Million Random Digits With 100,000 Normal Deviates” (which delivers exactly what it promises), selling for $64.60 on Amazon.com. Exhibiting the great sense of humor that OM profs have, 400 people have submitted online Amazon reviews, writes The Wall Street Journal (May 1, 2013). Most of them mocked the 60-year-old reference book for OM professors, pollsters and lottery administrators.

“Almost perfect,” said one reviewer. “But with so many terrific random digits, it’s a shame they didn’t sort them, to make it easier to find the one you’re looking for.” Five stars from this commenter: “The first thing I thought to myself after reading chapter one was, ‘Look out, Harry Potter!’ ”

Several reviewers complained that while most of the numbers in the book appeared satisfactorily random, the pages themselves were in numerical order. Rand said its long list of random numbers, first published in 1955, is one of its all-time best sellers. “It’s a tool of some sort, but it’s beyond my clear understanding,” a Rand spokesman admitted.

One Amazon reviewer panned a real-life copycat publication called “A Million Random Digits THE SEQUEL: with Perfectly Uniform Distribution.” “Let’s be honest, 4735942 is just a rehashed version of 64004382, and 32563233 is really nothing more than 97132654 with an accent.”

“We are always amazed by the creativity of our customers,” said an Amazon spokeswoman.