Chance News 11

Quotation

"Then there was the man who drowned crossing a stream with an average depth of six inches." - W.I.E. Gates

Forsooth

Here is a Forsooth from the December 2005 issue of RSS News.

The current rate of shrinkage they calculate at 8% per decade; at this rate there may be no ice at all during the summer of 2060

BBC News website

Investing in a poker player

Texas Hold'em poker is sweeping the globe as a favorite pastime of gamblers, young and old, novices and experts.

The following web site discusses a proposition from an amateur poker player to gain financial backing for entry into the 2006 World Series of Poker.

Pledgebank: Investment poker

Questions

Can playing tournament poker be legitimately described as an "investment" (one with medium risk and potentially high return)?

What factors would you look for to determine the attractiveness of this investment opportunity?

A game show for probabalists

A game show for the probability theorist in us all
New York Times, Dec. 14, A19
Gia Kourlas

This article describes the new NBC game show called "Deal or No Deal" The rules are described on the NBC website as:

The rules are simple. Choose a briefcase. Then as each round progresses, you must either stay with your original briefcase choice or make a "deal" with the bank to accept its cash offer in exchange for whatever dollar amount is in your chosen case. Once you decide to accept or decline the bank's offer, the decision is final.

To fully understand the game you should play it here. Choose "game" from the options and go to the bottom of the page that comes up and choose "Start game".

The Times article observes that it is not known how the bank determines its offers. Kourlas says that, at a meeting at his house to discuss the game, some thought the decisions my be based on probability concepts such as expected values and others thought that it had "psychological--but not logical--coherence.

Of course the game as played on the Internet the bank clearly has a strategy for determing the offers and if this were known we would have an optional stopping problem if we were ineresting only in the expected amount we win.

You can read more about this game including a discussion of the role of statistics in such a game here from Wikipedia.

Questions

(1) The amounts that are in the briefcases at the beginning of the game are:

$0.01
$1
$5
$10
$25
$50
$75
$100
$200
$300
$400
$500
$750

$1,000
$5,000
$10,000
$25,000
$50,000
$75,000
$100,000
$200,000
$300,000
$400,000
$500,000
$750,000
$1,000,000

(1) What is the expected amount in your initial suitcase?

(2) Assume that the banker always offers the expected value of the amounts in the remaining suitcases. Would any strategy give you a higher expected winning then just accepting the banker's first offer?

(3) If the bank does not offer the expected amount in the remaining suitcases, what is your optimal strategy to maximize your expected winning?

(4) Why might you not want to use expected value in deciding on your strategy for playing this game?

(5) Here is a remark from the Freakonomics Blog.

Guessing the banker's offer is fun to do. Interestingly, in the Australian and Dutch version, this task is relatively simple: the offer as a percentage of the average remaining prize increases with every round, starting from about 5% to finally 100%. This rule can explain about 95% of the variation in the offers. I wonder if the US bank uses the same rule?

Does this seem to fit what is done on the internet version of the game?

Sugested by Norton Starr and submitted by Laurie Snell.

New Form of Literary Criticism

Da Vincy novel breaks code for success
The Guardian, Dec. 28, 2005
John Ezard

The discipline of statistics suffers when it practitioners venture into fields without the aid of a content expert. There is a temptation to deal with something which has popular appeal; use of multiple comparisons of easily acquired computer data can lead to inane predictions. In the past, ludicrous forecasts related the winners of presidential elections to whether the American League or the National League won the World Series; or, the sexual orientation of an individual depends upon whether a forefinger is longer than the ring finger. According to the British newspaper, The Guardian, of December 28, 2005, statisticians are now into literary criticism, or at least what makes a book a bestseller.

The team of statisticians headed by Dr. Alvai Winkler, formerly of Middlesex University, "assumes that much of success lies in the title" of the work. "Comparing these with a control group of less successful novels by the same authors, they found that the winning books had three common features; they had metaphorical, or figurative titles instead of literal ones; the first word was a pronoun, a verb, an adjective or a greeting; and their grammar patterns took the form either of a possessive case with a noun, or of an adjective and noun or of the words The ... of ..."

Dr. Winkler states: "When we tested our model on 700 titles published over 50 years, it correctly predicted whether a book was a bestseller or not for nearly 70% of cases. This is 40% better than random guesswork [(70%-50%)/50% = 40%]. It is far from perfect but given the nature of the data and the way tastes change 70% accuracy is surprisingly good." However, despite the data dredging, the article points out that Harry Potter came in at 51% and The Da Vinci Code scored only 36%. The Winkler team, in an effort to avoid having its analysis look foolish, backpedals and predicts Dan Brown "will have a real bestseller next year with The Solomon Key. Though its title structure is identical to The Da Vinci Code, they count it as figurative 'due to its reference to the Greater and Lesser Keys of Solomon, medieval books about black magic.'" In other words, for "yes," read "no."

Whether or not Dan Brown's new book approaches the financial and literary success of The Da Vinci Code will, of course, depend on The Da Vinci Code. And one hopes, at least to some extent on what is inside the covers and presumably to chance as well (state of the economy, natural disasters, the phases of the moon, etc.). Titles come and titles go as in Hemingway's identical Fiesta and The Sun Also Rises, not to mention Agatha Christie's penchant for multiple naming of the same book. The reader is encouraged to look up the original title of her brilliant novel, And Then There Were None, to see how unconsciously prejudiced we used to be. Her last book, Sleeping Murder, scored 83% and was deemed "the most perfect title." Nevertheless, this Agatha Christie fan claims it can't compare with some of her earlier novels when she was in her prime, regardless of the subsequent rechristenings of the titles.

Unquestionably, under any conceivable criterion, a candidate for the dullest book title in creation would be Statistics in Britain, 1865-1930: The Social Construction of Scientific Knowledge by Donald MacKenzie. Never judge a book by its title; MacKenzie gives a fascinating presentation of the political and social mindset of the pioneers of statistics who invented, among other concepts, regression, correlation, and the t-test in order to advance a particular agenda which, embarrassingly enough, had eugenics in the forefront. Every practitioner of statistics needs to read this book.

Discussion

Do you think Winkler's claim that 70% correct is 40% better than random guesswork makes sense? If not how might you compare 70% correct to guesswork?

Submitted by Paul Alper.

Mothers Know Best. Or Do They?

Pestering a busy statistican
Wall Street Journal, Dec. 27, 2005, A1
Anna Wilde Mathews in London and Peter Wonacott in Moradbad India.

In a sense, we--statisticians and lay people--were spoiled by the famous study some 50 years ago relating lung cancer to cigarette smoking. Spoiled because the connection was so blatantly obvious in that smokers had a five to ten-fold increase in lung cancer over nonsmokers. Since then, most studies which tried to find culprits or saviors have produced far less striking results. A, let us say, mere 20%, as opposed to a 500 or 1000%, difference between a treatment and a placebo would be regarded nowadays as an achievement. Too many things which ought to promote health just don't seem to pan out when a careful experiment is done.

One exception would seem to be the one our mothers drilled into us: eat your vegetables! According to the Wall Street Journal article, a 1992 article in the British Medical Journal by Ram Singh claims, "Heart attack victims who ate more fiber, fruits and vegetables for a year cut their risk of death during that period by almost half." The WMJ reports that "Singh's study has been cited more than 200 times in other scientific articles and guidelines for doctors." The newspaper further states that in other journals Singh "offered eye-popping evidence about the cardiac-health benefits of a good diet" which should include "fish oil, mustard oil, zinc, magnesium," and, of course those old standbys, "fruits and vegetables." Patients at his hospital are handed a card which advises in addition to the usual fruits and vegetables, "eating papaya, walnuts, lentils" and "a glass of whiskey every other day and about 15 minutes of yoga daily."

Except perhaps for the whiskey, most of us would automatically nod our heads in agreement because it makes such good intuitive sense. Unfortunately, intuitively sensible though the advice may be, the WSJ article points out there is considerable reason to believe that Singh's results are bogus. By 1993 critics doubted that he could have conducted five distinct trials involving so many patients in such a short period. Furthermore, there were allegations that he "had tried multiple treatments simultaneously on patients and then written articles as if only one treatment was being used at a time." In addition, "He used some of the same patients in more that one study." Moreover, another paper of his to the BMJ had improper randomization with only the younger patients getting--you guessed it--the fruits and vegetables

When the BMJ editor asked for the raw data, Singh who works in India, apologized because "termites had eaten crucial data." A British statistician was asked to review Singh's work and eventually concluded it was "either fabricated or falsified," and "was full of basic statistical errors and contradictions." The strangest aspect of the whole affair is the length of time the BMJ editor took to unravel the assertions made by Singh's original paper. When the editor was alerted to the alleged problems in 1993, a comedy of errors ensued. The statistician tapped to do the checking changed jobs and thus, several years went by. All the while, the editor was trying to hide his detective work from Singh. In 2002--ten years after publication--Singh "sent a copy of one of his articles with a serrated edge that he said had been gnawed by termites." Three further years go by--we are then half way through 2005--before "the BMJ carried a headline: 'Suspicions of fraud in medical research--Who should investigate?' along with a photo of a list of Dr. Singh's publications."

Whether or not mothers know best, the mother of my child continues to believe that fruits and vegetables must be good for you despite the lack of statistical evidence. If she is typical, the public consequently feels it is a shortcoming of statistics if it can't verify the obvious. Fortunately for family harmony, unlike former President H.W. Bush, our daughter likes broccoli. As far as we know, she isn't into whiskey or fish oil.

Submitted by Paul Alper.