SOME RESULTS ON THE EFFICACY OF METHODS OF REGULATING
MACHINE GAMBLING*
by
John Lepper and Stephen Creigh-Tyte#
ABSTRACT
This paper explores how far restrictions on the use of gambling machines can
restrict spending on them. Existing literature is reviewed. Existing controls on
ambient machine gambling are described and compared. A simple model of
machine gambling is presented and used to predict the likely relative
effectiveness of various types of regulation. Most commonly encountered
restrictions appear to work as expected and this result is robust in the presence
of expenditure determined by pathological gambling. Some suggestions for
further research are made.
INTRODUCTION
Gambling on machines is a repetitive form of gambling which offers players a
large number of completed wagers (i.e. staking of money followed by an
unequivocal result and immediate payment of winnings) in a short time. It is,
therefore, usually termed a continuous form of gambling (Abbott and Volberg
2000). It is also an example of a standard non-storable commodity which is
instantly consumed that is normally presumed by simple neo-classical economic
theory. One would expect, therefore, that gambling on machines would provide a
working example of theoretical economic processes.
But appearances are deceptive. There are few socio-economic studies of
machine gambling (Caswell 2005). Instead, psychologists have conducted most
of the empirical studies of this behaviour. However, while this approach has
*
The views expressed in this paper are those of the authors alone. They do not represent, and cannot be
construed as representing, the policy or views of Her Majesty's Government.
#
Respectively, Senior Adviser, National Lottery Commission, 101 Wigmore Street, London, W1U 1QU
and Head of Broadcasting and Gambling Economics, Department for Culture, Media and Sport, 2-4
Cockspur Street, London SW1Y 5DH. We are grateful to Phillida Bunkle, Jeffrey Derevensky, Elliot
Grant, Leighton Vaughan Williams, Rachel Volberg, two anonymous referees, and attendees at a workshop
at the 2005 EASG Conference in Malmo and the Southern Economic Journal Symposium at Nottingham
Trent University in 2008 for helpful comments on earlier drafts of parts of this paper. Any errors of fact,
logic or judgement which remain are our responsibility.
1
illuminated many of the individual motives which underlie machine gambling it is
largely silent on the relative effectiveness of policy instruments applied to a
population at large.
In this paper, we describe some of the recent empirical work into machine
gambling. We review some of the regulations which currently exist and propose a
method of comparing them. We then suggest reasons why some forms of
regulation are likely to prove more effective than others. Finally, we suggest
some possible ways in which the work could be refined.
PATTERNS OF MACHINE GAMBLING
In this section we review recently published investigations into machine
gambling. Machine gambling covers playing poker machines or electronic
gaming machines (EGMs in Australasia), slot machines and video lottery
terminals (VLTs in North America) and fruit machines and fixed odds betting
terminals (FOBTs in UK). In compiling such a review we implicitly assume that
the characteristics of all forms of machine gambling are similar enough to permit
findings about one type of machine to be applied to others. We also implicitly
assume that it is possible to make generalisations about gambling behaviour
across different types of machine and different cultures. Neither assumption may
prove to be valid.
Psychological Factors
Most studies of gambling behaviour concentrate on gambling which is associated
with problems. The most widely used definition of problem gambling describes it
as an impulse control disorder (APA 1994). Consequently, the majority of
investigations into the phenomenon have used a psychological approach. It is not
surprising, therefore, that studies which look predominantly for psychological and
demographic factors find that a complex web of psychological factors is
implicated in the causes of problem gambling.
Increasing intensity of mental disorders (Cunningham-Williams et al 1998),
depression (Shaffer and Hall 2002, Dickerson et al 2003, Wiebe et al 2003a and
2003b), impulsivity (Vitaro et al 1999) and risk-taking (Vitaro et al 2004) have all
been associated with higher levels of problem gambling. In addition, problem
gambling has been associated with control disorders (Kweitel and Allen 2000,
Schellinck et al 2001, Wiebe 2003a and 2003b) and control disorders have been
associated with depression, non-productive coping strategies and impulsivity
(Dickerson et al 2003). Chasing behaviour is strongly associated with impaired
control (O'Connor and Dickerson 2003).
2
Some investigators have attempted to test the hypothesis that machine gambling
represents a form of conditioned response. Some experiments have shown that
arousal measured by heart rate is higher when expectations are high (Ladouceur
et al 2003). Heart rate is also higher before, and changes more during, the
session among problem gamblers than among non-problem gamblers (Brown et
al 2004). By contrast, (Dickerson et al 1992) reported little variation in heart rate
or subjectively assessed excitement during a session.
Some have found that near wins are an encouragement to continued gambling
(Cote et al 2003) although others have shown that the relationship between
proportion of near-wins and number of wagers is an inverted U shape peaking at
about 35% (Kassinove and Schare 2001). It has been found that sequentially
presented near-wins are more effective in prolonging play than those presented
simultaneously (Ladouceur and Sevigny 2002).
Finally, it has been shown that small wins lead to faster play but large wins
interrupt the previously established rhythm of play (Dickerson et al 1992). Later
work suggests that pause length is related to the size of win (Delfabbro and
Winefield 1999, Dixon and Schreiber 2004). However, for most people losses
and near-wins increase the speed of play (Dixon and Schreiber 2004).
Other Factors
The problem with psychological factors is that they explain relatively small
proportions of the variation in problem gambling behaviours when tested
alongside other factors (Kweitel and Allen 2000, Vaughan Williams et al 2008).
Mood and, when age is taken into account, sensation seeking are not related to
persistent gambling (Dickerson et al 1991). Indeed, some have found that
psychological distress is not implicated in problem gambling (Abbott et al 1999,
2004, Doiron and Nicki 2001, Winters et al 2002). Others have argued that
repeated playing of gambling machines or chasing losses involves considerable
cognition and is not evidence of automated behaviour or conditioned response
(Dickerson et al 1992).
Problem gambling and impaired control over gambling are both associated with
alcohol consumption and/or substance abuse (Cunningham-Williams et al 1998,
Abbott et al 1999, 2004, Doiron and Nicki 2001, Shaffer and Hall 2002, Winters
et al 2003).
Some 71% of the variance in session length is explained by the size of wins and
age (Dickerson et al 1991). Chasing both within and between sessions is related
to the proportion of income spent on gambling (O'Connor and Dickerson 2003).
Nevertheless, there is also evidence that a number of gambling behaviours
display varying degrees of irrationality. A majority of machine players have been
found to switch from rationality to irrationality in a laboratory situation (Sevigny
3
and Ladouceur 2003). In addition, favourite-longshot bias is well-known
(Vaughan Williams 2003). Some have even accounted for this phenomenon in
the case of lotteries by postulating that a value is attached to the life chance
represented by a very large win (Forrest et al 2001, Nyman 2004) although this
may be less than appears at first sight (Casey 2007, Slater 2007).
Finally, it has been shown that expenditure per head on EGMs is closely related
to the availability of EGMs in the community (Marshall 2005). This appears to be
related to variations in the constraints placed upon such gambling by geography,
society and regulation. On the basis of individual data the proportion of the
population playing EGMs, the median expenditure on EGMs, the frequency of
use of EGMs and the duration of use of EGMs are all positive related to the
density of EGMs in the local population (Marshall 2005).
AMBIENT MACHINE GAMBLING
In the developed English-speaking world very few jurisdictions allow ambient
(Gambling Review Body 2001) or convenience (GAO 2000) machine gambling.
Here ambient machine gambling is taken to mean machine gambling provided in
locations that afford ready access to opportunities for machine gambling in the
course of everyday life. Those that do, generally impose limitations on machine
gambling. These limitations are usually combinations of four factors; namely, the
maximum than can be wagered on each game, the number of machines in each
location, the maximum prize and the minimum return to players.
This note reports on the current state of regulation of ambient machine gambling
in five developed countries and shows that the there is little uniformity of
regulation internationally. A measure of maximum loss is developed and a
comparison made between different jurisdictions. Finally, some inferences are
drawn about the likely relative effectiveness of the four limitations listed above.
CURRENT REGULATION OF AMBIENT GAMBLING
This note is confined to an examination of regulations in those jurisdictions,
which allow random, non-lottery-based machine gambling in convenience
locations. The games are generally related to poker, roulette or some other nonlottery game based on random numbers. In some places, their availability is
limited to premises licensed to sell alcohol or to provide other types of gambling.
Hence, the locations include hotels (pubs), clubs, arcades, restaurants, cafes,
truck stops, licensed betting offices (LBOs) and bingo halls.
Very few jurisdictions allow this form of gambling. For example, it is allowed in
only six States of the USA while a further 6 States confine it to racetracks or
casinos. It should also be recalled that machine bingo and machine-based lottery
games are also run in many States. One State, South Carolina abandoned
4
ambient machine gambling on 1st July 2000 and in Louisiana 33 parishes voted
to abandon this form of machine gambling by the end of June 1999.
Such gambling (the pokies) is widely available in Australia and New Zealand.
Newly opened locations are allowed fewer machines than older established
ones. It is available in 7 Provinces of Canada as an adjunct to the provision of
lottery games by video terminal (VLTs). However, Loto Quebec is in the process
of reducing by 2,500 the number of its machines in bars, brasseries and taverns.
In England, Wales and Scotland so-called jackpot fruit machines are located in
bingo halls and Adult Entertainment Centres (inland arcades) and Fixed Odds
Betting Terminals are available in many LBOs. Elsewhere in Europe machine
gambling of this type is largely confined to casinos, which means it does not
qualify as ambient gambling.
Apart from Nevada, Queensland, South Dakota and Washington all jurisdictions
set maximum prizes. Nevada and South Carolina before July 2000 are alone in
not setting limits on the wager per game. Only Nevada, South Carolina before
July 2000 and Great Britain do not set minimum returns to players. All locations
set limits of the number of machines in each location.
It is clear that, apart from the so-called restricted locations of Nevada, Australia
has by far the most liberal regime of those surveyed. There a maximum prize of
over £4,000 and maximum wager per game of over £4 is allowed. Elsewhere,
maximum prizes are uniformly less than £500 and maximum wagers are a little
over £1. It is clear that the current limits of £UK100 on FOBT wagers in Great
Britain and $US100 on slots in South Dakota are significantly larger than allowed
in other comparable jurisdictions
5
TABLE 1
RESTRICTIONS ON MACHINE GAMBLING:
AMBIENT GAMBLING IN SELECTED COUNTRIES
Maximum
win
AUSTRALIA(1):
NSW
Victoria hotels and clubs
Queensland hotels and clubs
South Australia hotels and
clubs
CANADA(21):
Alberta(6)
Nova Scotia(7)
Quebec(8)
GREAT BRITAIN (9):
Fixed Odds Betting
Terminals (10)
Jackpot Fruit Machines
Fruit Machines
NEW ZEALAND
Jackpot Machines(1)(11)
USA (14)(17)(20)(21):
Louisiana(22)
Montana(18)
Nevada(16)
Oregon(19)
South Carolina before July
2000(15)
South Dakota(23)
Washington
Maximum
wager per
game
Minimum
Return to
Player
$A10,000
$A10
85%
$A10,000
$A10
87.5%
No limit
$A5
85%
$A10,000
$A10
87.5%
$C1,000
$C2.50
$C1,000
$C2.50
92%
average
80%
$C500
$C2.50
92%
£UK500
Number per location
Clubs no limit; hotels 30;
104,000 in State.(2)(3)
Clubs 105, hotels 105 (2);
27,500 in State (4)(5)
Clubs 280;Hotels 35; no
State limit(2)
.Clubs 40; hotels 40; no
State limit(2)
Variable up to 10 set in
licence; 6,000 in province
Variable, set in licence;
3,234 in province.
5
No limit
4 per LBO
£UK500
£UK35
£UK100
£UK1
£UK0.50
No limit
No limit
4 per bingo hall
2 per pub
$NZ1,000
$NZ2.50
78%-92%.
18(12)
9(13)
$US1000
$US800
No limit
$US600
$US4
$US2
No limit
No limit
Variable, set in licence
20
15
20
$US125
per day.
Unlimited
jackpots.
No limit
No limit
No limit
No limit
80%
No Limit
96%
maximum
No limit
$US100
$US5
80%
75%
6
5
30
5
Sources:
1. Australian/New Zealand Gaming Machine National Standard, Revision 9.0, 23 March 2007,
Section 8.3 http://www.olgr.nsw.gov.au//pdfs/gmns_v9.pdf.
2. Institute for Primary Care (AIPC): “The Changing Electronic Gaming Machine (EGM) industry
and Technology”, Gambling Research Panel, Victoria, August 2004, Table 4.4, p.63.
3. Commonwealth Grants Commission: "The Gambling Assessment", Discussion Paper CGC
2002/16, Commonwealth Grants Commission, Canberra, September 2002.
4. Non casino only. Casino EGMs limited to 1,500.
5. In non-casino locations only. In addition, Crown Casino is limited to 2,500.
6. http://www.aglc.gov.ab.ca/gaming/
7. www.gov.ns.ca/aga/legislation.htm Video Lottery Regulations under Sec 127 of the Gaming
Control Act 1994-95.
8. www.loto-quebec.com
9. By agreement with the Gambling Commission minimum payout of non-casino, non-FBOT
machines is expected to be over 70% and the actual payout ratio has to be stated on the machine.
FOBT payout rates are around 97%
10. .By agreement with the Gambling Commission each game on an FOBT takes 20 seconds.
11. Department of Internal Affairs, Wellington.
12. Prior to October 17th 2001.
13. Venues opened after October 17th 2001 subject to local authority permission.
14. United States General Accounting Office: “Convenience Gambling: Information on Economic and
Social Effects in Selected Locations”, GAO-01-108, October 2000.
15. David Plotz “Busted Flush- gambling laws of South Carolina”, Harper’s Magazine, August 1999.
16. Nevada Gaming Commission and State Gaming Board.
17. http://www.winneronline.com/articles/december2001/rose_status/htm
18. http://data.opi.state.mt.us/bills/mca_loc/23_5_6.htm
19. http://arcweb.sos.state.or.us/rules/OARS_100/OAR_177/177_200.html
20. www.gambling-in-us.com.
21. www.nagra.org.
22. www.state.la.us/osr/lac.
23. http://legis.state.sd.us/statutes/DispalyStatute
.
CALCULATION OF MAXIMUM LOSS
In 1999, the Australian Productivity Commission (Australian Productivity
Commission 1999) published comparative estimates of the maximum loss that a
player could incur during an hour’s play in different jurisdictions. This estimate is
based on a simple model of the technical characteristics of machines and the
regulations which constrain their use. We adopt this kind of calculation here.
We assume that each player wagers at the maximum permissible level on each
game played (MW). We also assume that the player receives the minimum return
specified in regulations (MR). Let us now assume that the player plays
continuously for a period of time (T) on the machine which repeats games with a
known frequency (F). This means that the maximum number (MN) of games
played is T/F:
MN = T/F
7
The maximum session wager (MSW) is then given by the number of games
multiplied by the maximum wager per game:
MSW = MN * MW = (T/F) * MW
However, the machine makes a minimum return to the player during the session
(MSR). This is the minimum percentage stake returned (MR) multiplied by the
amount wagered in the session. Hence:
MSR = MSW * MR
The maximum loss that the player will make during a given time (MSL) is then
the difference between the maximum session wager and the minimum session
return:
MSL = MSW – MSR = MSW * (1 – MR)
Hence:
MSL = MW * (T/F) * (1 – MR)
(1)
The MSL for many different jurisdictions can be calculated from the data
contained in Table 1. For this purpose we assume that a gambling session lasts
one hour or 3,600 seconds and that typically a gambling machine repeats games
every 5 seconds. This means that for the present purposes each gambling
session consists of 720 games.
Great care should be taken in making translations of stakes and prizes between
currencies. In theory, both should be translated in terms of the respective
purchasing power current in the jurisdictions concerned. Account should also be
taken of the role that particular denominations play in the life of respective
countries. If exchange rates reflected these factors then it would be appropriate
to merely rework the above levels into a common currency using marketdetermined exchange rates. However, exchange rates are largely dictated by the
movement of capital around the world and bear very little relation to relative
purchasing power or the way of life in the countries concerned. For these
reasons, simple translation of the above into a common currency may be
misleading.
8
TABLE 2
MAXIMUM SESSION LOSSES IN LOCAL CURRENCY:
SELECTED JURISDICTIONS
JURISDICTION
Local
Currency
Units
AUSTRALIA:
NSW and Queensland
Victoria and South Australia
1,080
900
CANADA:
Alberta
Nova Scotia
Quebec
144
360
86
GREAT BRITAIN:
FOBTs
Bingo Halls
Pubs
540
72
27
NEW ZEALAND
Minimum
Maximum
144
360
USA:
Montana
Oregon
South Dakota
Washington
Source: Table 1 above .
288
86
14,400
900
BEHAVIOURAL AND POLICY ISSUES
The above model is based upon a series of identities and exogenously
determined factors. In practice, it is likely that the time spent gambling, the
technical characteristics of the machines, the return to players and the amount
staked will be determined by the choices of players and providers. The choices
arrived at may be different from the parameters set by regulation. In a
competitive environment providers may set the payout above the minimum to
attract customers. For example, in Nevada payout ratios range between 88% and
95% even in the absence of a minimum return specified by the authorities with
frequent advertising of the tightness of the odds in slots in the various casinos.
In general, we should expect three sets of behavioural factors to modify the
regulatory framework. First, the more the competitive the market the higher the
return to players and the greater the range of wagering options. Second, we
would expect the actual maximum possible speed of play to be set by providers
9
in response to player demand. Third, we should expect the time spent machine
gambling to be determined by the costs and benefits to players. It follows that all
aspects of the relationship described above are potentially determined by
behavioural factors. This means that even when no limits are specified in
regulation the maximum session loss is never infinite although it may be
potentially very large.
For the purposes of illustration we explore the relationship between session time
and the expected net return to play. Forrest (2003) argued that the price of
gambling is the expected net return from a given stake. If we denote behavioural
variables in italics then in our terminology expected return to a wager in a
particular game is:
ER = ((H - P probW)/ H) = (1 - P probW)
(2)
where P is the prize, probW is the probability of winning and H (or hazard) is
amount wagered. If ER is averaged across all games in a session then the price
per session can be calculated. If prizes P are raised in relation to H then ER rises
and the price of the gamble falls.
It is likely that a person faced with reduced prices will want to prolong the session
or to increase their expenditure on it. Thus we would expect that:
T = a0 + a1ER
(3A)
and
H = b0 + b1ER
(3B)
Normal and Pathological Demand
We would normally expect that as the price of gambling falls relative to other
competing products both T and H would rise as a person seeks to raise
expenditure on gambling. Hence, in the case of “normal” gambling behaviour:
a1, b1 > 0
Contrast this with pathological gambling. In that case, a gambler seeks to recoup
losses by further gambling or to increase her gambling whatever the movements
in price or expected return. Hence, as the price of gambling rises or ER falls a
pathological gambler will seek to try to increase gambling expenditure by
increasing the time spent and the amount wagered. In that case:
a1, b1 < 0
10
Minimum Returns
If the above behavioural relationships are inserted into equation 1 we obtain a
behavioural estimate of the maximum session loss MSL.
MSL = H (T/F)(1 – ER)
(4)
= (b0 + b1 ER )((a0 + a1 ER )/F)(1 – ER )
Expansion and manipulation produces:
MSL = (1/F){a0b0 + (a1b0 + a0b1 - a0b0)ER + (a1b1 - a1b0 - a0b1) ER2 - a1b1ER 3}
If we assume that a0 and b0 are zero then:
MSL = (1/F){a1b1(ER2 - ER 3)}
(4A)
and
dMSL/dER = 2(a1b1/F)ER - 3(a1b1/F)ER2
(5)
or:
dMSL/dER = (a1b1/F){2((H - P probW)/ H) – 3((H - P probW)/ H)2}
This result holds whether demand is normal or pathological.
Equation 5 presents an equivocal conclusion. Provided ER > 2/3 then a rise in
ER (a fall in price) will lead to a rise in MSL. It follows that, in those
circumstances, if:
MR = f(ER) s.t. f/ > 0
then imposition of a raised minimum average return to a gamble will tend to raise
session losses. However, if ER < 2/3 the opposite is the case. This suggests that
if controls on payouts are to be used to control player losses they should take the
form of a maximum, not a minimum, and be set somewhat below the prevailing
level of ER at no lower than 66%.
Maximum Wager
Alternatively we can define MSL in terms of H. If we substitute equation 2 into
equations 3A and 4 and assume “normal” demand we obtain:
MSL = H [a0 + a1((H - P probW)/ H)][1/F][1 - ((H - P probW)/ H)]
11
When a1 > 0, i.e. “normal demand, this simplifies to:
MSL* = (1/F){a0 P probW + a1 P probW - a1 ((P probW)2 /H)}
Hence:
dMSL/dH =- -(a1/F)((PprobW)2/H2) > 0
(6)
When a1 < 0, i.e. pathological demand:
MSL* = (1/F){a0 P probW - a1 P probW + a1 ((P probW)2 /H)}
and
dMSL/dH = -(a1/F)((PprobW)2/H2) > 0
(6A)
Equations 6 and 6A show unequivocally that a rise in H raises MSL and a fall
engineered either by regulation or by the gamblers themselves leads to the
opposite effect. It therefore provides the reason why binding limitations on
wagers can limit the maximum session losses suffered by punters. The effect
tends to be greater the higher the prize and the larger the probability of winning
and the lower the time taken by each game. It also seems to be most effective
when the level of wagers H is relatively small and a1 high so that behaviour is
highly influenced by the effective price of gambling.
This finding is in line with the findings of Blazsczynski et al (Blaszcynzski et al
2001) and Dickerson et al (Dickerson et al 2003) in NSW. Blaszcynzski et al
found that there was a large reduction on time played, number of bets, money
lost and consumption of alcohol and tobacco among players of machines the
stake of which was limited to $1 compared with those who played machines with
maximum stakes of $10. Dickerson et al also found that regular players who
limited their budget for gambling were far less likely to encounter problems with
gambling than those who did not set a limit to gambling expenditure. However,
even these players were found to encounter problems from time to time.
Hence, it seems likely that, in reality, the actual relationship between T, ER and
MR and between H, ER and MR takes a similar form to that suggested above. In
the nature of those relationships lies the importance of controls over levels of
wagers, prizes and payout rates in minimizing session losses. Until they are
explored with greater precision little more can be said about the likely effect on
gambling problems of restrictions on machine gambling wagers.
Limitations on Time
If we differentiate equation 4 with respect to time spent gambling we obtain:
12
dMSL/dT = 1/F {H(1 – ((H - P probW)/ H)}
(7)
or:
dMSL/dT = 1/F{PprobW} > 0 whatever the sign of a1 or b1.
This shows that limitations on time spent gambling unequivocally reduce session
losses. The effect is likely to be larger the higher the prize and chance of winning
and the faster the speed of games.
Frequency
Slowing the speed of games involves raising F which is the number of seconds
that it takes for each game to occur. We can obtain the effect of reducing the
speed of games by differentiating equation 4 with respect to F:
dMSL/dF = -(1/F2){a1b1(ER2 - ER3)}
(8)
or:
dMSL/dF = -(a1b1/F2){((H - PprobW)/H)2 - ((H - PprobW)/H)3} < 0
This gives an unequivocal result because a1b1 >0 whether “normal” or
pathological demand is present in the marketplace and 1 > ER > 0. It shows that
raising the number of seconds it takes to complete a game will reduce maximum
session losses. However, the effect will be greater the lower the prize and the
higher the maximum wager and will be less the greater the minimum return to
players and the greater the time taken for each game.
COMPARISONS OF EFFECTIVENESS
This section compares the results obtained in the previous section to determine
the likely relative effectiveness of different policy measures.
Minimum Return and Maximum Wager
For:
dMSL/dER > dMSL/dH
then:
dMSL/dER – K = dMSL/dH s.t. K > 0.
Hence when a1 > 0:
13
(a1b1/F){2((1 – (P probW)/ H) – 3(1 - (P probW)/H)2} - K
= - -(a1/F)((PprobW)2/H2)
and when a1 < 0:
(a1b1/F){2((1 – (P probW)/ H) – 3(1 - (P probW)/H)2} - K
= -(a1/F)((PprobW)2/H2)
Hence if a1, b1 > 0:
K = (a1/F){-b1 - 2b1(P probW)/ H) – (3 b1 + 1)(P probW)/H)2}
or if a1, b1 < 0:
K = (a1/F){-b1 - 2b1((P probW)/ H) + (3 b1 - 1)((P probW)/H)2}
Hence:
K > 0 iff:
((P probW)/H)2 > b1 + 2b1((P probW)/ H) + 3b1 ((P probW)/H)2 if a1, b1 > 0
and:
3 b1((P probW)/H)2 > b1 + (2b1 + 1)((P probW)/ H) if a1, b1 < 0
When a1, b1 > 0, K is positive only when very low values for b1 are encountered.
By contrast, when a1, b1 < 0, K is never positive. Hence, for all likely values of a1
and b1 restrictions on size the of wagers is likely to prove more effective in
restricting session losses than controls over expected returns.
Maximum Time and Maximum Wager
For:
dMSL/dT > dMSL/dH
then:
1/F{PprobW} > - -(a1/F)((PprobW)2/H2) when a1 > 0
(9A)
and:
1/F{PprobW} > -(a1/F)((PprobW)2/H2) when a1 < 0
14
(9B)
Note that the right hand term in both equation 9A and 9B is always positive. It
follows that if the price of the gamble is greater than the square of the payout
ratio multiplied by a1 then limiting time played is likely to be a more effective way
of reducing player losses than limiting the size of wagers. The likelihood of
equation 2 being satisfied can be judged from the following table.
PprobW
0.2
0.5
0.8
0.9
((PprobW)/H)2
0.04
0.25
0.64
0.81
a1
<5
<2
<1.2
<1.11
The above table gives the values of a1 required to satisfy equations 9A and 9B
for different selected values of PprobW when a unit wager is assumed. It shows,
for example, that when the payout ratio is 50% then provided a 1 < 2 the condition
in equations 9A and 9B is satisfied. It follows that when the payout ratio is close
to 1 then it is likely that limiting the size of wagers will be more effective in
restricting player losses than placing limitations on playing time. If there is any
uncertainty over the value of a1 then there may be a case for simultaneously
imposing limits on wagers and session times.
Frequency and Maximum Wager
For:
dMSL/dF > dMSL/dH
(10)
and irrespective of the sign of a1:
|(a1b1/F2){((H - PprobW)/H)2 - ((H - PprobW)/H)3}| >
|(a1/F)((PprobW)2/H2)|
Divide both sides by the RHS.
Hence, if:
| b1(1 - (PprobW)/H))| > 1
(11)
then equation 10 is satisfied.
We can judge the likely effectiveness of the regulatory measures by evaluating
equation 11 as follows:
15
(P prob
W)/H
0.5
0.5
1
2.5
5
b1
1
2
5
10
0.6
0.7
0.4
0.8
2
4
0.8
0.3
0.6
1.5
3
0.9
0.2
0.4
1
2
0.1
0.2
0.5
1
The above table shows the value of the LHS equation 11 for selected values of
b1 and (P prob W)/H . It shows that as the rate of payout rises the value of b1
must rise to high levels if regulation of frequency is to remain more effective than
regulation of maximum wager in limiting player losses. This suggests that where
the returns to players are high, regulation of wagers is likely to be more effective
than regulation of game frequency in limiting player losses. However, the
opposite is the case when returns to players are relatively low.
OTHER POSSIBLE HYPOTHESES
The above discussion focuses on little more than behavioural version of a
tautology. In order to capture the dynamic nature of machine gambling behaviour
it is necessary to extend the analysis to models of choices taken over time. The
psychometric analysis considered earlier suggests at least three possible
models. These postulate that a machine gambler:



tries to maximize time on the machine;
earn the maximum return from the session; or
change life chances.
In addition, a more recent suggestion has been made by Bunkle (2007 and
2008).
These are now discussed briefly and some implications for policy drawn.
Maximize Time
In practice, individual players, once they decide on a session of machine
gambling, try to maximize the time they spend on the machines subject to the
amount of money and/or time they wish to devote to the session. In other words,
they want no more than a good run for their money (see Griffiths 1993a and
1993b for a case study ). Some players claim to exercise considerable skill in
attaining that end including believing that they can influence the outcome of the
game (Sevigny and Ladouceur 2003) and even claiming to know when particular
machines will pay out (Fisher 1993).
16
A punter will approach a machine willing to spend a certain amount gambling.
She will expect to obtain a stream of benefits (measured by the number of games
played) for that level of expenditure. The session will be planned to last until the
expected additional welfare of the last game expected to be played in the session
will be the same as the additional welfare obtained from the same time spent on
the next most worthwhile activity. Perhaps normally a certain amount will buy a
given time on the machine. This expectation may include a presumption (no
doubt implicit) about the average payout per machine. However, that expectation
may be less or more than fulfilled depending on the random distribution of wins
actually encountered in the particular session. It follows that if actual wins are
greater than the expected rate of payout the session will be longer and stakes
higher than expected for a given planned expenditure.
For such players a big win comes as a surprise. It poses an unexpected choice
problem for many gamblers because it forces gamblers to choose between
cashing in the credits and playing for longer than expected. The existence of the
choice means that the punter hesitates until the choice is made either to end the
session or to continue wagering as before. This hesitation is why punters pause
after a big win. A big win has another effect. It makes the punter richer than
before. Hence, wagers rise after a big win because the punter's wealth has risen.
The opposite occurs when a string of losses reinforces the belief that a win is
imminent and so play speeds up. The losses also reduce the punter's wealth.
This, in turn, reduces the chance that the punter will achieve her target time on
the machine with the result that the size of each wager is reduced during a losing
streak in order to make the remaining budget purchase a larger number of
games.
If punters are rational in this way there may be no reason for a policy maker to try
to influence the process of decision-taking. If, however, the rationally taken
choices of punters leads to harms for example in the form of neglect of children
then it may be appropriate to require punters with children to demonstrate that
care has been provided while the machine is played.
Maximum Return
The existence of a motivation to play for money is confirmed in a number of
survey-based studies (Productivity Commission 1999, Abbott et al 2000). If a
punter enters into a session in order to maximize the monetary return a different
dynamic takes shape. In this case, the player plays until the difference between
expected wins and expected stakes is at a maximum subject to a budget or time
constraint.
However, this raises the question of how a decision rule can assist in achieving
this aim , given that actual wins cannot be known. In effect, at each game the
17
player must make the choice between carrying on with the session in the hope or
expectation of a further increase (decrease) in net gains (losses) or stop playing.
It is clear that some base this choice on past experience and talk of "learning the
reels" (Fisher 1993). Clearly, expectations based on such information are
grounded in the belief that the events produced by the machine are independent
of each other. If, for example, players believe that either the sequence of results
such as "near wins" (Kassinove and Schare 2001, Cote et al 2003) or the sounds
made by the machine (Fisher 1993) indicates that a win is imminent then it
follows that if decisions are constrained by time the speed of play will be
increased to bring the expected win closer in time. If, however, sessions are
constrained by a budget stakes will be reduced in order to ensure that the
session is still in progress when the win occurs and so people who expect to win
play longer than those who do not.
It is conceivable that for such people limiting stakes or prizes could merely serve
to reinforce a false expectation about the machine and extend playing sessions.
A more appropriate policy response may be to provide education about the
workings of gambling machines and to ban non-random programming of graphics
on machines which suggest near misses.
Change Life Chances
Some may play machines because they seek to fundamentally increase their
stock of wealth (Forrest et al 2001, Nyman 2004). The windfall gain necessary to
be classed as life-changing probably varies between people and will depend on
their marginal valuation of money. Hence, those with a large stock of wealth (and
so a relatively low marginal utility of money) are less likely to gamble for this
reason than those with relatively little wealth. Nevertheless, if prizes are large
enough, as in some lotteries, rich people are attracted to them. Moreover, the
strength of the expectation of achieving a life changing windfall gain is likely to
vary inversely with the size of that windfall gain. In other words, the involvement
in the session is an input into a consumption technology (Becker and Murphy
1988) which has a dream as an output.
The value of the session then lies not in the achievement of the windfall gain.
Rather, its worth rests upon the entertainment of hope while the session is in
progress. This means that the session produces a period of hope and in this
period lies its value to the player. This is especially so for those with limited hope
in the rest of their lives (Bunkle 2007, 2008).
It follows that the longer the session lasts the longer the hope can be sustained
and so the more value it amasses. (This is perhaps the fundamental motivation
for trying to maximise time spent on the machines.) However, it is also true that
the longer the hope is sustained the larger the dissonance between the hopes
that are sustained by participating in the session and the real losses of time and
18
money that result. That dissonance causes shock as the session ends and the
actual expenditure of time and money on the session are confronted. Hence, the
punter will not prolong the session beyond the point at which the shock of that
dissonance overwhelms the value of the hope created.
In addition to dissonance are the costs of winning perceived by players (Casey
2007, Lepper and Hawkes 2007). Some players fear that the relationships that
they value in life will be disrupted by a big win. Hence, many entertain limited
hopes which will enhance rather than overwhelm existing lifestyles.
Inappropriate Heuristics
Bunkle has recently suggested that players want to experience winning even if
this means that they lose money overall (Bunkle and Lepper 2002, Bunkle 2007,
2008, Livingstone and Wooley 2007). This means that players’ measure of
benefit is the sequence of winning occasions contained in session. This is true
even if the money won on those occasions is considerably less than the amount
lost in the remainder of the session.
The effect is that players have a false sense of the monetary losses suffered. As
a consequence, many express surprise at the money that has been spent in a
session. This may result from the inappropriate use of a heuristic developed to
guide decision-making in non-gambling situations. It is possible to argue that
either players adopt false beliefs about their actions or the characteristics of the
machine encourage the use of inappropriate heuristics. In either case, the
information normally employed to determine marginal utility is misleading when
applied to machine gambling and so may lead to perverse consumption patterns.
It may, for example, account for some of the results obtained by prospect theory
in this context (Cain et al 2008, Peel et al 2008). It may also lead to lack of
effectiveness of control mechanisms (Zangeneh and Haydon 2004).
CONCLUSION
Ambient machine gambling is a relatively unusual phenomenon. Where it is
permitted a wide variety of regulations control its use. It is likely that controls over
maximum wagers are more effective than the imposition of maximum payouts in
limiting losses to patrons. Depending on the actual values observed limiting
player time or the frequency of games may also reduce maximum session
losses. However, these, too, appear less effective in reducing session losses
than limiting the size of wagers.
Within the confines of the model presented above, this result holds even in the
presence of pathological gambling.
These conclusions must necessarily be treated with caution for two reasons.
First, there is no attempt to estimate the welfare implications of the measures
19
discussed. Hence, it may be that the loss of enjoyment by all players that results
from imposing blanket restrictions on machine gambling may outweigh the
regulatory benefits to the few for whom the activity is source of compulsion.
Second, restricting one form of gambling (in this case machine gambling) may
encourage greater use of other less fettered forms of hazard. The above analysis
makes not attempt to estimate the diversion effects of the measures discussed
above. A robust causal model of gambling behaviour is required before such
estimates can be attempted. Until such a model is available it is not possible to
estimate which of the alternative policy instruments or combinations of
instruments is likely to prove most effective in reducing overall gambling
problems.
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