 
Week 3 - Outcomes and Standards
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PROF JOHN S. CROUCHER
New South Wales, Australia
AT MACQUARIE UNIVERSITY in Sydney, NSW, there is a unit taught with the largest enrolment of any single subject in Australian universities. This unit in introductory statistics caters for around some 2600 students each year and serves the statistical needs of all first year subject areas across the campus. One might be forgiven for thinking that the reason for such an achievement is that the material involved in statistics is so fascinating that students simply can't resist it. On the contrary, with very few exceptions, those enrolled are there simply because it is a compulsory prerequisite to a great many popular fields of study such as business, economics, accounting, computing, behavioural sciences to name a few.
The fact is that almost no student comes to Macquarie to major in the area of statistics, and yet we have the largest Statistics Department in Australia. What happens after first year? For the department to survive as a viable entity, it was essential to convince at least a portion of the captive audience from first year that the subject of statistics could be interesting, challenging and relevant. Of course, this was no easy task.
In recent years the face of statistics has changed at Macquarie. The Department has repeatedly chosen to remain with the business school, despite desperate efforts on the part of some to transplant it into a school with mathematics. In hindsight, this appears to have been a wise decision with the number of tertiary mathematics students on the decline around the country.
To this end, since around 1995 the statistics department has systematically removed a number of compulsory mathematics prerequisites from its units, preferring to teach whatever mathematics is needed within the unit itself. It's fair to say that the introduction of a formal mathematics prerequisite on a statistics unit usually leads to a dramatic fall in numbers. The downgrading of assumed mathematical knowledge has been extremely beneficial in attracting more students to the Department.
It is always important to diversify and modernise the offerings in statistics and the department has also been very successful in this regard. Whether we like it or not, the word 'statistics' simply does not sound very exciting to the majority of students and so the term has been replaced where possible with another that might be more 'catchy', although the unit content is largely the same. Examples of these changes include replacing 'Applied Probability' with the name 'Risk and Chance' and 'Statistical Inference' with 'Modern Statistical Concepts'. The numbers in the units immediately doubled and tripled, respectively.
Perhaps the most significant departure from the way in which the department offered its units was a radical change of direction in an attempt to lure some of the huge number of business students enrolled in the business areas. To do this it was necessary to convince prospective customers that there were careers to be made in statistics and that employers were ready to embrace these skills. Although 'traditional' statistics had served reasonably well, the numbers of students had certainly levelled off and in some cases were falling.
The situation was turned around two years ago by the introduction of a Bachelor of Commerce degree with a major in statistics that concentrated in the field of operations research. This meant the introduction of new units in statistics that covered the subjects, in addition to operations research itself, of logistics, market research, quality management and, most recently, e-commerce. The interest from students was immediate with the numbers enrolling at third year level averaging over 100 per unit while the 'traditional' statistics units averaged around 30 students.
While some statistics staff have lamented the 'downgrading' of the tried and trusted subjects, there is no doubt that the survival of the department is now largely dependant on the continued success of the these operations research units that are firmly geared to the requirements of business and industry. This is a very important aspect as far as students are concerned since one of the most common questions asked is: ' Who will employ me if I get one of these degrees?'. There is now a much wider range of options in this respect.
Having an attractive program in statistics at the higher levels is important enough, but it is even more essential that the students have their appetite whetted from an early stage. The beginning introductory statistics unit covers the usual topics of descriptive techniques, hypothesis testing and linear regression. After having used Minitab as the computer package of choice, the department has now switched to the statistics module of Microsoft Excel for Windows. The rationale here is that this is a program that most students will have access to after graduation.
As has been mentioned, although this unit has some 2600 students each year, over 90% were still choosing not to proceed further with the study of statistics - either because they weren't interested or they could not fit it into their program. In addition, there were simply many hundreds of students across the university who did not do any statistics units at all because they had no compulsion or inclination to do so.
To remedy the situation, in 1998 the author made an informal survey of students to determine just what area of 'the real world' contained statistics that might be of interest to them. The overwhelming favourite topic was gambling, followed closely by sport, while medicine came in third. No other application of statistics seemed to spark any interest at all.
Teaching Statistics Using Gambling
Catering to the market, in 1999 a new unit called 'Gambling, Sport and Medicine' was introduced at first year level with no pre-requisites, but with a STAT prefix so that there could be no mistake that it was indeed a statistics unit. The response was overwhelming to say the least with nearly 400 students enrolling from across twenty-six different study areas across the campus. In the year 2000, not only have similar numbers enrolled in this unit, but our numbers in second year units have noticeably increased as well.
To teach a unit in gambling takes a great deal of planning since it is a sensitive issue with associated social problems and, moreover, a number of the students had not yet reached the legal gambling age of 18 years. As well as teaching from a statistical point of view, it was also necessary to talk about the negative side of gambling and the devastating impact it can have on those who do not gamble wisely. This task was made easier by the fact that the author of this paper, who designed and teaches the unit, is also Chairman of the Responsible Gaming Committee of NSW. This committee has members from all areas of the gaming industry with the aim of forming a unified approach to the area of problem gambling.
But the unit was also to provide innovations in a number of key areas. Firstly, when news of the unit reached the media there was an immediate positive response, including television, radio and press coverage that an educational unit on gambling was being taught at an Australian university - this was undoubtedly a first. It was also clear that this was not a unit that teaches you how to win at gambling - on the contrary, its aim is to present statistical principles in a way that captures the imagination but at the same time is challenging and informative.
One of the best ways of achieving this goal is by the use of visual aids or 'props', and there is no shortage of these when it comes to gambling. The department was fortunate enough to receive a donation from Penrith Panthers Club in the west of Sydney of two working poker machines. These have been a highlight of the teaching of probability and expected returns and added a new dimension of excitement to the learning process.
Other devices that were purchased inexpensively included a two-up kip and coins, dice and packs of cards. A roulette wheel was more difficult since they cost around $20,000 for a new one and around $3500 for one that is reconditioned. Since both were beyond the budget, a plastic one costing around $100 did the job nicely, although smaller than would have been liked.
Gambling topics covered in the unit include:
- History;
- Lotteries, Lotto;
- Keno;
- Keno Heads or Tails;
- Roulette;
- Two-up;
- Craps;
- Horse racing;
- Sports betting; and,
- Poker machines.
As can be seen, before launching into the statistics of any topic, it is essential to provide some background information of the history or any special happenings of note. As an example, relevant statistics on gambling include the information of the type shown in the next section.
The History of Gambling
The amount of money gambled in the world is quite staggering and Australia is no exception. According to the Australian Bureau of Statistics, in 1997/98 a total of $94.5 billion was wagered in Australia on all types of legal gambling and, of this, $11.33 billion (or 12%) was lost. Since the total population of Australia aged 18 years or over is around 14 million people, this amounts to an average loss of around $800 for each adult.
The 1999 Productivity Commission report into gambling in Australia found that around 80% of Australians reportedly gamble 'sometimes' while 40% gamble 'regularly'. Although 38% of people admit to playing poker machines, nearly two-thirds of these only do so less than once a month. The highest participation gambling activities, with the percentage of the population who play them are Lotto/lotteries (60%), Instant scratch tickets (47%), poker/gaming machines (38%), racing (35%), Keno(16%), Casino game tables(10%), Sports betting(6%), Bingo(5%) and private gambling(5%).
Gambling takings are growing three times faster than the economy with a rise of 42% since 1995. There are 7,972 gambling venues in NSW with the Australian gambling industry providing 37,035 jobs in 1,776 businesses as at June 1998. Nationwide, gambling nets governments $3.72 billion a year in taxes of which $1.72 billion comes from poker and gaming machines.
People in Victoria bet more than those in any other state, wagering an average of $9357 per person during 1997/8 while NSW fed $6498 a head into gaming machines. The number of gaming machines in the nation's casinos, who employ 22,500 staff, has increased to 10,733. Revenue for the top ten clubs in NSW during 1997/8 was around $240 million while total poker machine profits for all venues increased to $2.5 billion. In NSW there are currently 72,584 gaming machines in clubs and 23,895 machines in hotels.
In 1997/98, NSW gamblers lost a total of $3.6 billion, mainly by playing gaming machines, this corresponding to a loss of $720 for every person in the State. In fact, 20% of the world's poker machines are in Australia, even though we have less than 1% of the world's population. Indeed, over 10% of the world's poker machines are in NSW alone, which now has around 100,000 of them.
It is reported that gaming and betting revenue in NSW is expected to increase by almost $400 million over the next four years with revenue from hotel gaming devices expected to climb by about 25 percent in 1999-2000. Also in this year, gambling revenue in NSW is expected to rise by $139 million to $1.55 billion. In the past 10 years, the States' total revenue from gambling taxes has grown from $500 million a year to almost $4 billion.
These statistics make gambling one of the hottest issues of the day and one that is of interest not only to students but the public at large. To some extent, there are very few adults who are not affected in some way by a gambling activity. If we only considered legal gambling in NSW alone, the gambling turnover and amount lost in a variety of activities in 1997/98 is shown in Table 1.
Table 1 Gambling turnover and losses in NSW 1997/98
|
Type of gambling |
Amount gambled ($) |
Amount lost ($) |
% lost |
|
Poker and card machines |
30,540,143,000 |
2,989,084,000 |
9.8 |
|
TAB |
3,554,474,000 |
533,852,000 |
15.0 |
|
Casino gambling |
2,635,039,000 |
446,200,000 |
16.9 |
|
Lotto, Tattslotto |
626,544,000 |
250,285,000 |
39.9 |
|
On-course bookmaker |
610,658,000 |
33,586,000 |
5.5 |
|
On-course totalisator |
394,923,000 |
59,896,000 |
15.2 |
|
Keno |
384,400,000 |
96,100,000 |
25.0 |
|
Instant lottery |
171,288,000 |
62,691,000 |
36.6 |
|
Lottery |
134,338,000 |
46,554,000 |
34.7 |
|
Sports betting (Racing) |
50,625,000 |
5,069,000 |
10.0 |
|
Pools |
7,145,000 |
3,573,000 |
50.0 |
|
TOTAL |
39,109,577,000 |
4,526,890,000 |
11.6 |
Source: Australian Gambling Statistics, Tasmanian Gaming Commission
It is clearly evident from Table 1 that the losses on gaming machines swamp everything else, and for this reason the unit at Macquarie spends a considerable amount of time discussing the statistics of how these devices operate. Gamblers are often lured by the attraction of big prizes, and the more publicity these receive the more tempting it becomes to gamble. In the USA version of Powerball in 1998, thirteen factory workers won $161.5 million, the largest cash win in the history of the game.
In late 1998 a woman gambled $470 on poker machines at the Palace Station Hotel and Casino in Las Vegas, USA. As a result, she won a record $43.5 million, which will be paid to her in annual instalments of $1.73 million over the next 25 years.
Also, in the 1998 World Soccer Cup one gambler considered backing England to beat Colombia. He was offered odds of 5-4 on (that is, for every $5 bet he would win $4) for an English victory and decided to wager £200,000 (AUD$554,640). Luckily for him, England won the match 2-0 and the bookmakers suffered their biggest payout to a single punter of £360,000 (AUD$998,352) in over 30 years.
Sports betting in Australia, which first became legal in the Northern Territory in 1982, grew by over 1000 percent between 1991 and 1999 with annual turnover now exceeding $400 million. Legalised sports betting came to NSW in 1991 and there are around 30 sports betting operations in Australia. In order of popularity, punters like to gamble on AFL, cricket, soccer and rugby league.
Poker machines have been a huge success for Australian casinos with takings jumping by a record 24 percent in 1998/9 to $867 million. While takings from gaming tables dropped seven percent, casinos still managed to win $1.32 billion from gamblers. Casinos now have a total of 10,733 poker machines and 1129 gaming tables and annual casino takings from gambling now total $2.218 billion.
Problem Gambling
The down side of gambling is also emphasised to the lecture group who learn that at least 115 calls are made each day to a State Government hotline (G-line) for people with gambling problems. This is a 24-hour telephone service on 1800-622-112. Figures show that fifty-five percent of these callers were male and about eighty percent of all callers are referred to counselling services such as St Vincent de Paul, Creditline or Lifeline.
It is estimated that about 70 percent of people who develop gambling problems play poker machines, with NSW having at least 74,000 problem gamblers. There were six percent who had problems with Casino gambling. However, it is also felt that the total number of people who are adversely affected by either their own or someone else's gambling problem in NSW could be as high as 750,000. To this end, the Australian Medical Association (AMA) has recently sent information kits to the State's 7500 general practitioners in a bid to curb the growth of gambling related problems.
The Productivity Commission report into gaming in 1999 found that Australia's 290,000 problem gamblers each lose $12,000 a year or $3.5 billion in total. In contrast, recreational gamblers spent an average of $625 each year. While problem gamblers have no special characteristics, the report said that they often tend to be younger than average, often in their early twenties. Problem gamblers tend to spend their money on electronic gaming machines such as poker machines, casino tables and the TAB rather than on the lotteries. In fact, seventy percent of problem gamblers blame poker machines.
One interesting example provided in the report involved the poker machine Black Rhino. It was found to require 6.7 million button pushes or 391 days non-stop continuos play just for a 50% chance to win the jackpot.
Calculating the Chance of Success
Being a unit in statistics, one of the primary purposes is the calculation of the probability that a gambler is successful if they choose to undertake a particular gambling activity. This is determined not only for a single play of the game but also if it is played many times over. It is interesting to compare the odds against winning a prize with a single entry and the percentage of the amount wagered, this being called the Percentage House Margin, kept by the operators in various forms of gambling. Table 2 lists the probability of winning the major prize for a variety of popular games with a single entry. However, the cost of that entry can itself vary markedly, such as 25 cents for NSW Lotto and $1 for OZLotto.
Table 3 gives an indication of the percentage House margins for a number of games and it is interesting to note the vast differences between them with the smallest being for the card games Blackjack and Baccarat, the former requiring skill to play effectively. The other games rely on machines and physical devices and so their House margins are larger with the lowest being 1.4% for certain bets in Craps to 62% for Scratch Lottery tickets. The types of calculation required to obtain these figures are discussed throughout the unit.
Whether or not an individual is prepared to risk their hard-earned money, gambling still provides a fascinating study from many points of view. These include the mathematical calculations involved with finding the chance of success, the formulation of winning strategies and discovering how to make your winnings go further.
On the other hand, the gaming operators are always on the lookout for methods to try and induce their prospective clients to be tempted to play a particular game. There is much psychology involved in being able to have a gambler part with their cash, such as the determination of exactly what attracts people to play certain poker machines. It is often said that many gamblers are lured by the prospect of obtaining 'free games', although in the long run such machines may have a relatively poor payout. It is no wonder that the gambling section of the unit has enjoyed the success it is currently experiencing.
Table 2 Chance of success in various types of gambling
|
Type of game |
Chance of success |
|
NSW Lotto |
1 in 7,059,052 |
|
OZ Lotto |
1 in 8,145,060 |
|
Powerball |
1 in 54,979,155 |
|
6 from 38 Pools |
1 in 2,760,681 |
|
Lucky Seven |
1 in 1,000,000
(reduced to 1 in 200,000 since one ticket lasts 5 draws) |
|
Lotto Strike |
1 in 3,258,024 |
|
$2 Lottery |
1 in 180,000 |
|
$5 Lottery |
1 in 140,000 |
|
$2 Scratch Lottery |
1 in 4.9
(of winning something, up to $100,000) |
|
$5 Scratch Lottery |
1 in 3.3
(of winning something, up to $250,000)
|
Table 3 Percentage House margins for various gambling opportunities
|
Blackjack |
Between 0% and 8% |
|
Baccarat |
Between 1.2% and 14.1% |
|
Craps |
Between 1.4% and 16.7% |
|
Roulette |
2.7% |
|
Poker machines (Casino) |
8% |
|
Poker machines (clubs and hotels) |
Between 8% and 15% |
|
On?course bookmakers |
5.5% |
|
NSW TAB (win and place) |
14.25% |
|
Quinella |
15% |
|
Trifectas, doubles, exacta |
17% |
|
Superfecta |
20% |
|
FootyTAB |
25% |
|
Keno |
25% |
|
NSW Lotto |
40% |
|
Pools |
50% |
|
Instant scratchies |
62% |
Sport
It is quite timely that Sydney hosts the Olympic Games in the Year 2000 since this provides a golden opportunity to demonstrate statistical techniques using sporting data. In particular, one lively topic of discussion is the times and distances that athletes and swimmers will have to achieve in order to win a gold medal. With an abundance of historical data, students are able to come up with various intervals within which they feel the winning performance will lie. They will be able to check themselves soon enough whether they were correct!
Apart from the Olympics, there are a number of popular sports including football, cricket and basketball that are all covered in some aspect. Some of these are along the lines of developing or testing of strategies for play, while for others it is considering the effect of rule changes. One of the beauties of teaching statistical principles using sport is that there is never any shortage of information to analyse and it is always topical. In all, after seven weeks of learning about the statistics of gambling, the next three weeks is spent on the statistics of sport.
Medicine
The medical statistics component of the unit is the shortest with usually only two or three weeks spent discussing the statistics of medicine. Although well liked by the students, it does not enjoy the popularity of the gambling or sport sections. The topics considered include clinical trials, medical research that involves statistical principles and the statistical controversies surrounding DNA evidence in law. For those students who are keen to undertake further studies in this area, at third year level the department offers a complete unit in epidemiology. A number of our graduates have gone on to find employment in the medical area.
Flexible Learning
During 1999 and 2000 the author spent considerable time developing a version of the Gambling, Sport and Medicine unit that can be taught by distance education. It is expected to be ready sometime in 2001 and will allow those enrolled to have a bulletin board, access to unit information, FAQs, weekly exercises, practice examinations and solutions. The actual lecture notes will not be placed on the Web but will be mailed out. Another exciting feature of this presentation is the introduction of an animated simulation component in which students can play games such as two-up, Keno and even poker machines in order to test strategies and the verify the theoretical statistical results.
This flexible learning approach is also expected to be very popular among the internal students who will also have access to the same information. The only difference is that they have the opportunity to attend the lectures on campus.
Remarks
Undoubtedly this unit, which prominently features gambling, has been an outstanding success and has, in a short space of time, attracted many hundreds of students along with hundreds of thousands of dollars in funds to the department. The media has been very supportive, as has the gaming industry itself in assisting a venture that provides an essential public education program in this controversial area.
The onus on academics is to be able to present their material in a way that is relevant, challenging and interesting. Although this may be easier to do in some areas of study than others, the results are well worth the effort involved, as evidenced by the Macquarie experience. The hunt is now on to repeat this success by offering other types of units that will also attract the attention of students who otherwise would not have dreamt of studying statistics. Already there are plans to offer postgraduate degrees in the field of gaming and hopes are high of a very successful outcome.
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ABOUT THE AUTHOR
Professor John Croucher is Professor of Statistics at Macquarie University in Sydney where he leads the department in the fields of operations research and gaming studies. His first year unit in gambling attracts over 350 students annually from over twenty-five different study areas across campus and he is the Chairman of the Committee on Responsible Gaming in NSW. John is also the author of ten books covering areas such as mathematics, statistics, fraud, management and humour along with publishing over fifty research articles in scientific journals. For seven years he was a television presenter as the statistician on football telecasts and is much sought after as a public speaker, giving hundreds of media interviews and invited talks to professional societies and universities around the world, including Oxford and Cambridge.
John Croucher can be contacted by email at:
john.croucher@efs.mq.edu.au
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