Chance News 48

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In other words, the population of a city is [according to Zipf's law], to a good approximation, inversely proportional to its rank [within its country]. Why this should be true, no one knows.

Steven Strogatz.
Guest Column
The New York Times
May 29 2009

Submitted by Paul Alper

Note: Strogatz is a good writer for the public and your students might enjoy reading this.

Laurie Snell


Winning system for dice game?

"Accused Cheater's Trial Includes Lesson In Craps"[1]
by Karen Florin, The Day (New London, CT), May 20, 2009

A Tennessee man has been charged with cheating at the craps table of the Foxwoods Casino in Ledyard, CT. During the trial he claimed that he was a "professional gambler who had a winning system that did not involve bribing dealers to pay him for late or illegal bets." (Closing arguments were scheduled for May 21, 2009.)

Jurors watched him provide an in-court demonstration of why his $3,000 or $5,000 bets are successful:

The makeshift craps table was “hot” for a while and [the defendant], who has spent the last eight months in prison, appeared happy to be reunited with the dice. He cradled them in his hand and shook them as [his] defense attorney ... walked him through an explanation of his strategy, which involves combinations of numbers that “go with” other numbers. If the shooter rolls a four, for example, [the defendant] recommends betting on 4, 6, 9, 10, 2, 3 or 11 to come up next.

The defendant described his success:

"The strategy works if you manage your money right and cash out when you're winning,” he said. He said his best run occurred in 2002, when he won $73,000 at Foxwoods. Other times, he won big and then lost big, he said.

A blogger commented [2]:

With 2 dice, odds of rolling 2 of a particular kind are 1 in 36, or 2.8%. Odds of rolling 2 of any kind are 1 in 6, or 16.7%. With 4 rolls, odds are 50-50. All rolls are independent, that is, for any particular roll, odds are 1 in 6.

Submitted by Margaret Cibes

Financial decision-making advice?

"Many Bought Shares High, Sold Low" [3]
by Mary Pilon, The Wall Street Journal, May 18, 2009

The article describes several people who took large losses by selling their stocks around the time of the "March 9 12-year low," and before the more recent 26% "rebound."

One financial advisor told an investor about his "two-Ambien" test for decision-making. (An Ambien is a sleeping pill.)

If two Ambien can allow you to sleep, ... then it still might make sense to stay invested.

Many advisors tell clients not to divest during "downturns," because "buying high and selling low is a formula for awful returns." One advisor says that:

They know that in hindsight, it wasn't the best thing to do.... But it was what they had to do emotionally. Math and the mind don't always add up.

1. What do you think about the "two-Ambien" test?
2. People frequently base quantitative decisions on calculations that are incorrect or inappropriate; they simply have weak quantitative skills. Do you think that the "math" behind financial decision-making provides a sufficient basis, by itself, for investment decisions?

Submitted by Margaret Cibes

Infuse and Kuklo

J. Scott, editor of the Journal of Bone and Joint Surgery writes about a paper, “Recombinant human morphogenetic protein-2 for type grade III open segmental tibial fractures from combat injuries in Iraq” by Timothy Kuklo, et al, which appeared in the JBJS in August, 2008:

“The paper described the management of 138 Gustillo Type IIIB and C tibial fractures in soldiers injured in Iraq. It was a retrospective study with some randomization of these patients into two groups, one of which received bone morphogenetic protein-2 (rhBMP-2) as part of the management and the other did not. The authors reported a significantly higher union rate in the group treated with rhBMP-2 (92% vs 76%). There was also a higher rate of further surgery required in the patients who did not receive BMP.”

For the non-specialist, rhBMP-2 is sold commercially as “Infuse” and is marketed by Medtronics. And, the paper “clearly seemed to represent a major contribution to the treatment of these severe complicated fractures which are difficult to manage and usually require several surgical procedures, careful wound management and extensive rehabilitation.”

However, you won’t be able to read the Kuklo paper to find out what is meant by “a significantly higher union rate in the group treated with rhBMP-2 (92% vs 76%)” because the paper has been withdrawn by Scott and the JBJS. The reasons may be found in Wilson and Meier’s reporting in The New York Times. The headline is “Doctor Falsified Study on Injured G.I.’s, Army says.” Not only did he “not obtain the Army’s required permission to conduct the study” but also “Army investigators found that Dr. Kuklo forged the signatures of four Walter Reed doctors on the article before submitting it last year to a British medical journal, falsely claiming them as co-authors.” In addition, “the total number of patients Dr. Kuklo reported as having been treated for extensive lower leg wounds at Walter Reed during the study period—138 soldiers—was greater than the number for which the hospital could find records.”

Further, according to Scott, the forgery came to light because “Shortly after the paper was published we received correspondence from one of the persons identified as a co-author indicating than the alleged co-authors had not seen the manuscript prior to publication and they had not signed the letter of transmittal. It was further disclosed that much of the paper was essentially false.”


1. The NYT article states “During the six-month period ending last October, sales of Medtronic’s bioengineered products, principally Infuse, reached $419 million, according to a company filing.” A Medtronics spokesperson “confirmed that Dr. Kuklo was a paid consultant to the company and that the company financially supported some of his research at Walter Reed.”

A subsequent NYT article reveals that “Army doctors can accept money to consult for medical product companies if they are given approval. Military officials said Wednesday that they had not found records that Dr. Kuklo sought or received such permission.” A “consultants list shows that Medtronic paid about $943,000 from 2003 to 2008 to 22 doctors for consulting specifically about Infuse.” Kuklo’s name is not on that list “because he had a general consulting contract with Medtronic, rather than one specific to Infuse.”

2. Kuklo is now an associate professor at Washington University. Here we have this commentary from someone from St. Xavier University whose father “served on the medical school faculty for over 30 years”: “Dr Dan Riew, the Mildred B. Simon Distinguished Professor and Chief of Cervical Spine Surgery in the Department of Orthopedic Surgery, alleged that his colleague’s forging signatures of four phantom co-authors may have been subsequent to oral authorisation. Astonishingly, Dr Riew claimed that when a researcher is without a fax machine or is abroad, the forging of signatures may be the only alternative.” From the St. Louis Post-Dispatch is the headline, “WU colleagues say surgeon accused of fraud is honest, hardworking.” The university’s chief of orthopedic spine surgery writes, “The claims are largely false. Dr. Kuklo is a very honest investigator.”

3. Forging co-authors, although bizarre, is not unique to this instance. Another example may be found a short time ago in Chance News. An interesting book to read is Why Smart People do Dumb Things by Feinberg and Durant. The section on Cyril Burt focuses on his putative co-authors, sometimes known as “the ladies,” Ms. Howard and Ms. Conway. Then use Google to find assertions that Howard and Conway did exist and were not inventions of Burt.

4. Speculate on what motivates highly respected medical and scientific researchers to commit fraud.