Introduction
Many researchers recommend treating gambling as a public health issue, a perspective that encompasses a wide spectrum of interventions to reduce the population's exposure to the risk of gambling-related harm (Browne et al., Reference Browne, Langham, Rawat, Greer, Li, Rose and Best2016; Bowden-Jones et al., Reference Bowden-Jones, Dickson, Dunand and Simon2019; Orford, Reference Orford2019; van Schalkwyk et al., Reference van Schalkwyk, Cassidy, McKee and Petticrew2019; Wardle et al., Reference Wardle, Reith, Langham and Rogers2019). Warning labels are a class of intervention that have been used across several public health domains, such as warnings about alcohol content and safe consumption limits and calorie labelling on food packaging. In both of these other domains, warning labels are combined with other public health interventions, including restrictions on price and product availability (Nuffield Council on Bioethics, 2007). For example, in 2018, the UK introduced a tax on sugary beverages (Thornton, Reference Thornton2018), which aimed to increase the price and discourage the consumption of drinks with the highest sugar content levels. In gambling, a recent example of a restrictive public health intervention is a reduction of the maximum bet on UK electronic gambling machines from £100 to £2 a spin (Casey, Reference Casey2018).
By comparison, warning labels represent a public health intervention that does not restrict consumer choice (Nuffield Council on Bioethics, 2007). Better product-relevant information, such as a red traffic light label indicating that a food product is high in calories (VanEpps et al., Reference VanEpps, Downs and Loewenstein2016a) or has poor nutritional content (Kanter et al., Reference Kanter, Vanderlee and Vandevijvere2018), can inform and guide consumer choice towards relatively safer options. Better consumer information can also potentially shape product development, as it encourages firms to provide products that will look attractive under the labelling system, such as healthy salads. For example, the introduction of colour-coded energy performance certificates for UK homes has provided sellers with a greater incentive to invest in energy improvements (Comerford et al., Reference Comerford, Lange and Moro2016). In UK gambling, the academic advisory board to the industry regulator, the Gambling Commission, has recently advised that the clear and consistent provision of warning labels could form one key metric in a proposed safer gambling operator league table (Advisory Board for Safer Gambling, 2020).
By comparison to the examples from the previous paragraph, many current gambling warning labels do not provide consumers with information that can yield an informed comparison of relevant products. Some warning labels are extremely generic (e.g., in Australia, ‘Gamble responsibly’; in the UK, ‘When the fun stops, stop’; or in Ontario, ‘Play smart’). These labels provide little information to meaningfully guide consumers (Newall et al., Reference Newall, Walasek, Singmann and Ludvig2019c) and might be ignored due to sheer repetition of content (Lole et al., Reference Lole, Li, Russell, Greer, Thorne and Hing2019). Other gambling warning labels warn gamblers only about the product they are currently using, an approach that has been most consistently applied to electronic gambling machines (Wohl et al., Reference Wohl, Parush, Kim and Warren2014; Ginley et al., Reference Ginley, Whelan, Pfund, Peter and Meyers2017; McGivern et al., Reference McGivern, Hussain, Lipka and Stupple2019). This product-specific approach fails to enable informed comparisons of relevant products by not providing comparable cross-product information.
The rest of this article considers the issue of statistical risk warnings in gambling, an approach specifically designed to enable cross-product comparisons of product risk. First, underlying conceptual similarities between the approach suggested and current public health approaches towards alcohol and food will be compared. The next section introduces the conceptual similarity between standard drink and calorie labelling with the theoretical loss in gambling, while emphasizing issues unique to gambling. The rest of the article reviews theoretical loss in gambling, using two economically significant products of electronic gambling machines and sports betting as examples of a distinction that has previously been made between non-skilled and skilled gambling (Turner et al., Reference Turner, Fritz and Mackenzie2003). In each case, we will begin with current knowledge regarding statistical risks and their communication through warning labels. We will then move on to a discussion of product-specific issues, as the given gambling products do raise unique issues regarding the communication of theoretical loss. Each section then provides recommendations for further product-specific research. A discussion section then concludes with the argument that a consistent and behaviourally informed approach to statistical risk warnings in gambling can provide one input to a multidimensional public health approach to gambling (Browne et al., Reference Browne, Langham, Rawat, Greer, Li, Rose and Best2016; Bowden-Jones et al., Reference Bowden-Jones, Dickson, Dunand and Simon2019; Orford, Reference Orford2019; van Schalkwyk et al., Reference van Schalkwyk, Cassidy, McKee and Petticrew2019; Wardle et al., Reference Wardle, Reith, Langham and Rogers2019).
Product labelling on alcohol and food packaging
Alcohol labelling is one closely related approach from related public health domains to the statistical risk warnings proposed here for gambling products. All alcohol products contain some amount of pure ethanol. A higher total consumption of pure ethanol exposes the consumer to greater risk of alcohol-related harm. In some jurisdictions, this is communicated primarily through the percentage concentration of alcohol, called alcohol by volume (ABV). In theory, a consumer could multiply the ABV of what they are drinking by the total amount drunk to derive an estimate of their consumption of pure ethanol.
However, some metrics aim to perform this concentration by volume calculation for consumers. A given amount of pure ethanol is communicated as a given number of ‘standard drinks’ in the USA and Australia or as a ‘unit’ of alcohol in the UK. These metrics allow consumers to easily compare the consumption of a glass of wine with a larger but less concentrated glass of beer – products varying both in terms of concentration and volume of ethanol (Hobin et al., Reference Hobin, Vallance, Zuo, Stockwell, Rosella, Simniceanu and Hammond2017). Effective communication of product risk always involves elements of consumer psychology. The field of alcohol research continues to debate how to best communicate product risk by providing simple and effective heuristics that are consistent with medical evidence underlying healthy drinking ranges. As in risk communication more broadly (Garcia-Retamero & Cokely, Reference Garcia-Retamero and Cokely2017), it has been argued that graphical aids could help drinkers to better comprehend this information than the ABV and standard drink information in current use (Blackwell et al., Reference Blackwell, Drax, Attwood, Munafò and Maynard2018).
Front-of-pack food labels inform customers about the overall energy content (calories) and the nutritional composition of food products. Early reviews of food labelling observed that many consumers feel confused and overwhelmed by the wealth of information found on nutrition labels (Cowburn & Stockley, Reference Cowburn and Stockley2005; Campos et al., Reference Campos, Doxey and Hammond2011). In an attempt to improve people's understanding of the healthiness of different foods, the UK has adopted ‘traffic light’ warning labels, which use green, amber and red colours to highlight the relative amount of fat, saturates, sugars and salt in 100 g of a given food product (Kanter et al., Reference Kanter, Vanderlee and Vandevijvere2018). Some experimental research has indicated that summarizing calorie information via a traffic light system can nudge consumers towards healthier food choices (VanEpps et al., Reference VanEpps, Downs and Loewenstein2016a) in an effect that is not substantively improved via the added provision of numerical calorie counts (Downs et al., Reference Downs, Wisdom and Loewenstein2015). Overall, the weight of evidence across restaurant and supermarket settings (VanEpps et al., Reference VanEpps, Roberto, Park, Economos and Bleich2016b; Bleich et al., Reference Bleich, Economos, Spiker, Vercammen, VanEpps, Block and Roberto2017; Dubois et al., Reference Dubois, Albuquerque, Allais, Bonnet, Bertail, Combris and Chandon2020) suggests that food labelling, either graphic or numeric, can have some beneficial effects on food choices. Although measurable, these effects are also limited, suggesting that other approaches are needed in conjunction in a public health approach towards obesity (Nuffield Council on Bioethics, 2007).
Theoretical loss in gambling
Theoretical loss is the statistical average result that occurs from any given gambling scenario. Different gambling products can present unique challenges with respect to the calculation and communication of theoretical loss, but all gambling products are sold to the vast majority of gamblers with some implied theoretical loss embedded. Roulette is a relatively simple gambling game that can be used to demonstrate the principle of theoretical loss. European roulette wheels have 18 black slots, 18 red slots and 1 green slot. A $10 bet on either black or red will win $10 profit if the roulette ball ends up in a slot of that colour and will otherwise return nothing. Theoretical loss is calculated by multiplying the payoff of each outcome by its probability. Since each slot is equally likely, a $10 bet will on average lose the gambler (18/37 × $10) + (19/37 × –$10) = –$0.27. Over time, gamblers’ losses on European roulette will converge towards 2.7% of all money bet, which is known as the ‘house edge’. If they make 50 such bets over the course of an hour, then the average cost of this entertainment activity is $13.50 per hour.
Theoretical loss can therefore be expressed as follows:
$${\rm Theoretical}\,{\rm loss} = {\rm house}\,{\rm edge} \times {\rm total}\,{\rm amount}\,{\rm bet}$$Although much gambling is motivated by the thrill of the potential of winning, in the long run all gamblers exposed to a positive house edge will lose money, due to the statistical law of large numbers (Dekking et al., Reference Dekking, Kraaikamp, Lopuhaä and Meester2005). Of relevance to statistical risk warnings in gambling, theoretical loss can therefore be applied to all gambling products, and it is a useful metric for product harm, given that actual losses represent a reliable predictor of gambling-related harm (Markham et al., Reference Markham, Young and Doran2014, Reference Markham, Young and Doran2016). Furthermore, the provision of transparent pricing information could foster competition in product offerings with potential longer-term benefits to gamblers. The theoretical loss of any gambling transaction represents the expected ‘price’ that is paid by the gambler over the long term. Currently, the true cost of gambling is obscured to gamblers, who naturally attend to the ‘noisy’ short-run sequences of their wins and losses. Making theoretical loss more salient to gamblers has the knock-on effect of providing gambling operators with more incentive to compete on price. However, there are at least two major challenges to employing theoretical loss for gambling product warnings.
First, some gambling forms, such as electronic gambling machines, are not consumed in discrete units of consumption, like a bottle of beer, but can be gambled on continuously, with re-staking of winnings. This can make theoretical loss difficult to calculate, which also depends on the speed, stakes and time spent gambling. These challenges may make it simpler to communicate statistical gambling risk via the house edge, which is conceptually related to the ABV in alcohol.
Second, the volatility of gambling means that theoretical loss is only a relevant statistic in the long run, and short-run results may differ from this statistic. Gambling products with a highly skewed payoff schedule converge surprisingly slowly to their average expected return (Browne et al., Reference Browne, Rockloff, Blaszcynski, Allcock and Windross2015). By comparison, the calories in a cheeseburger are consumed with certainty. Gamblers may simply be paying more attention to their short-run wins and losses than the long-run implications of their bets. Some preliminary data suggest that a qualitative warning about the volatility of gambling may serve as a useful addition to a numerical statistical risk warning (Newall et al., Reference Newall, Walasek and Ludvig2020c).
Theoretical loss in non-skilled gambling
A non-skilled gambling game is one in which chance is the only determinant of long-term outcomes, where gamblers do not have any real ability to learn a better strategy over time or to apply skill (Turner et al., Reference Turner, Fritz and Mackenzie2003). The house edge input to theoretical loss can therefore be calculated with precision in non-skilled gambling games, making these an easier introduction to the topic of statistical risk warnings than skilled gambling games. Roulette, scratch cards, lotteries, craps, bingo and traditional slot and electronic gambling machines are all non-skilled games (Turner et al., Reference Turner, Fritz and Mackenzie2003), although some electronic gambling machines that introduce a small element of skill are being brought to market (Delfabbro et al., Reference Delfabbro, King and Gainsbury2019).
Current knowledge
The house edge of electronic gambling machine games can be altered in a way that is not immediately obvious to gamblers (Schüll, Reference Schüll2012). A natural question therefore is whether gamblers can by themselves detect differences in the house edge across seemingly identical games. A laboratory study involving a long period of 60 hours of play found that gamblers could discriminate between two identical games with radically different house edges of 2% and 15% (Dixon et al., Reference Dixon, Fugelsang, MacLaren and Harrigan2013). However, in most electronic gambling machine environments there will be many potential games on offer, and so 60 hours of play across two games may not correspond to the typical gambler's experience. Indeed, field studies conducted on casino floors suggest that gamblers cannot differentiate between differences of up to 8.9% in the house edge on seemingly identical games, a differential that can have a marked impact on the actual long-term losses experienced by players (Lucas & Spilde, Reference Lucas and Spilde2019). This suggests that electronic machine gamblers may benefit from well-designed statistical risk warnings.
In the UK, statistical risk information is provided for electronic gambling machines (Gambling Commission, 2012), albeit hidden far down on help screens that most regular machine gamblers have never even seen (Collins et al., Reference Collins, Green, d'Ardenne, Wardle and Williams2014). In addition, the information is communicated in both the UK and other jurisdictions, such as Australia (Beresford & Blaszczynski, Reference Beresford and Blaszczynski2019), via the ‘return-to-player’ percentage, which represents the average percentage of money returned per gamble. However, as has been suggested (Eggert, Reference Eggert2004), the return-to-player percentage is an inefficient risk communication metric compared to the house edge.
A return-to-player percentage of 90% is equivalent to a house edge of 10%, since in both cases 10% of all money bet is lost on average (Parke et al., Reference Parke, Parke and Blaszczynski2016). In practice, return-to-player information might be communicated via the label, ‘This game has an average percentage pay-out of 90%’, a statement that only 6 out of 20 regular gamblers could interpret correctly in one study: ‘For every £100 bet on this game about £90 is paid out in prizes’ (Collins et al., Reference Collins, Green, d'Ardenne, Wardle and Williams2014). Some results show that gamblers display a better understanding of this information when it is given in terms of the house edge. Specifically, 66.5% of gamblers correctly understood a house edge statement of, ‘This game keeps 10% of all money bet on average’, compared to 45.6% of those given a return-to-player statement (Newall et al., Reference Newall, Walasek and Ludvig2020a). Furthermore, gamblers perceived a lower chance of winning when given house edges of between 5% and 15% than when given equivalent return-to-player statements ranging from 95% to 85% (Newall et al., Reference Newall, Walasek and Ludvig2020a). Taken together, these results imply that gamblers have a more informed and less optimistic interpretation of the winning chances when given house edge information compared to the more widely used return-to-player information.
However, these results pertain only to the house edge rather than the theoretical loss, which is the product of the house edge and the total amount bet. Some preliminary evidence suggests that gamblers’ perceived chances of winning in a hypothetical scenario do not differ when the house edge is instead restated in terms of the theoretical loss (e.g., ‘This game keeps £10 for every £100 bet on average; Newall et al., Reference Newall, Walasek and Ludvig2020b). Personalized theoretical loss information, however, which reflects a gambler's stakes and speed of play, may be able to improve upon this result.
Some results suggest that numerical statistical risk warnings could be improved via qualitative information about the volatility of gambling. Specifically, a study has investigated the effects of adding the following ‘volatility statement’ information to return-to-player or house edge percentages (Newall et al., Reference Newall, Walasek and Ludvig2020c):
It takes millions of plays for a gambling game to tend towards its average return. A gambling game will not return a minimum value of prizes in any given period of gambling.
This additional text reduced gamblers’ perceived chances of winning in both the house edge and return-to-player conditions, with the lowest perceptions occurring in the house edge and volatility statement condition. House edge information was again correctly understood better than return-to-player percentages (Newall et al., Reference Newall, Walasek and Ludvig2020c). This study suggests that improved statistical risk warnings in gambling could be constructed that communicate both the mean (house edge) and variance (volatility) of the relevant distribution of payoffs.
Graphs can often communicate risk better than numbers (Garcia-Retamero & Cokely, Reference Garcia-Retamero and Cokely2017). Some research has explored the possibility of proxying variations in return-to-player information on scratch cards with a star rating system (Walker et al., Reference Walker, Stange, Dixon, Koehler and Fugelsang2019). The study by Walker and colleagues found that participants put more weight on a star rating system of 1–5 stars when it was used instead of return-to-player percentages of 67.89–68.39% (with the 67.89% scratch card given one star and the 68.39% card given five stars). However, it is unclear as of yet how such a graphical rating system could be consistently applied across all non-skilled gambling games, given that a variation of 0.5% in the house edge is relatively small, and in the abovementioned study was represented by a difference of four stars in the graphical display.
Product-specific issues
It has been argued that regulations intended to help inform consumers may be interpreted by firms in ways that do not genuinely help consumers (Page, Reference Page2019). Evidence from UK online casinos is consistent with this view. The UK gambling regulator requires online casinos to make ‘information that may reasonably be expected to enable the customer to make an informed decision about his or her chances of winning must be easily available’ (Gambling Commission, 2017, emphasis added). The return-to-player percentage and the house edge are two of the four allowed formats for providing this statistical risk information. As previously discussed, of these two, the house edge is better for consumers, although not necessarily the best of all statistical risk communication formats (Newall et al., Reference Newall, Walasek and Ludvig2020a). A field study of 363 online roulette games across 26 major UK online operators found that none used the house edge, while a return-to-player warning label was found on 98.3% of games. Furthermore, 95.5% of return-to-player statements used the smallest font size on the screen, 99.7% used the lowest level of text boldness from the screen and 16.8% used acronyms in place of the term ‘return-to-player’ (e.g., ‘RTP is 97.2973%’; (Newall et al., Reference Newall, Walasek, Ludvig and Rockloff2020d). This suggests that current UK regulations are insufficient to ensure that statistical risk information is made sufficiently prominent and understandable to gamblers.
There are two distinct ways that a gambler can be exposed to a high theoretical loss. The first way is to make bets at high house edges. The second way is to bet at a lower house edge, but to bet so much money that the total amount of theoretical loss is still substantial. This second reason is why high-speed electronic gambling machines are considered a dangerous form of gambling (Schüll, Reference Schüll2012). Furthermore, electronic gambling machines involve the automatic reinvestment of winnings. In these games, say $100 could be inserted by the gambler, who could then easily bet much more than $100 total before losing everything, since intermediate wins are automatically reinvested into the account total. Electronic gambling machine gamblers in particular seem to misunderstand that house edges apply to the total amount bet, rather than the amount of money inserted (Harrigan et al., Reference Harrigan, Brown and Barton2017). This unique danger of repeat gambling games raises unique concerns for statistical risk warnings.
Multiple possible interventions exist for electronic gaming machines. The UK government chose to reduce the maximum bet amounts on UK electronic gambling machines from £100 to £2 from April 2019, which might be effective, but does also reduce consumer freedoms (Casey, Reference Casey2018). One possible freedom-preserving intervention would be to prevent the automatic reinvestment of winnings (Byrne & Russell, Reference Byrne and Russell2019) in order to reduce confusion about the relationship between theoretical loss and amount bet versus the amount of money inserted. This cash pay-out of winnings by default may further act as a potential nudge for gamblers to consider stopping gambling.
In theory, an interactive display could be created for electronic gambling machines that dynamically calculates the entire statistical distribution of potential outcomes. This display could, for example, use data of the game's house edge, the gambler's current bet size and their betting frequency to forecast theoretical loss over different hypothetical session lengths. Furthermore, the display could be augmented to show the 95% confidence interval of possible results over this forecasted sequence of gambling, therefore providing a graphical measure of statistical volatility.
Recommendations for future research
One further remaining issue is the extent to which statistical risk warnings can modify gambling behaviour, rather than mere perceptions of winning. One Canadian study showed that the provision of more information on slot machines, including a categorical label for the house edge (represented as ‘Hold %: very low/low/high/very high’), had little effect on gambling behaviour (Harrigan et al., Reference Harrigan, Brown and Barton2017). However, the efficacy of this intervention may have been affected by how this information was presented, including the usage of categorical groupings and the term ‘hold percentage’, which may not have been the clearest way of describing the underlying concept. Additional interventions, such as an interactive display, may have enhanced the efficacy of this warning label.
Theoretical loss in skilled gambling
The provision of statistical risk information is more complicated in skilled gambling games, where theoretical loss is also influenced by the gambler's choices (Turner et al., Reference Turner, Fritz and Mackenzie2003). However, this added level of complexity also introduces an additional avenue via which gamblers can be directed towards lowering their theoretical loss. For example, the game of blackjack has a known ‘basic strategy’, which provides the lowest-loss play for any of the game's potential states. This basic strategy is simple enough to be printed on a small card or leaflet, yet many regular blackjack players deviate from the basic strategy suboptimally. These deviations may cost regular gamblers large sums of money over time, and yet these gamblers can appear unwilling on their own to learn a simple and demonstrably better strategy (Wagenaar, Reference Wagenaar1988). Some gamblers in skilled games such as poker can in fact also produce theoretical gains (Sklansky & Malmuth, Reference Sklansky and Malmuth1998). These skilled gamblers are not the intended subjects of statistical risk warnings, as they have likely already mastered the underlying concepts.
Given that each skilled gambling game has its own unique strategic considerations, the remainder of this section will focus on the economically important ‘fixed-odds’ sports betting market. In fixed-odds sports betting, a gambling operator (the bookmaker) posts a set of odds for an upcoming sports event ahead of time, setting the terms at which gamblers bet against the bookmaker (Buchdahl, Reference Buchdahl2003). Sports betting is a skilled gambling form, where the judicious selection of bets has the potential to earn long-run profits, albeit this potential is not always tolerated by gambling operators, who tend to prevent profitable gamblers from betting (Kaunitz et al., Reference Kaunitz, Zhong and Kreiner2017). Fixed-odds sports betting is established in the UK, is growing in Australia (Queensland Government, 2019) and could grow rapidly in the USA given a recent Supreme Court ruling (Supreme Court of the United States, 2017). In the UK and Australia, sports betting has been associated with a high level of gambling marketing saturation (Newall et al., Reference Newall, Moodie, Reith, Stead, Critchlow, Morgan and Dobbie2019a). Of relevance to statistical risk warnings, fixed-odds sports betting is also associated with large and predictable variations in the house edge.
Current knowledge
Two replicable patterns of variation in the house edge in soccer betting have been found (Hassanniakalager & Newall, Reference Hassanniakalager and Newall2019). The first pattern is that bet types with more potential events are associated with higher house edges. The second pattern is that bets with longer odds in some bet type are associated with larger house edges than bets with shorter odds. Both patterns appear roughly additive (non-interacting), and both patterns mean that bets with longer odds are associated with higher house edges.
A soccer match has three main outcomes: home win, draw and away win. Bets on these outcomes, called ‘home–draw–away’ here, are perhaps the most established type of soccer betting (Kuypers, Reference Kuypers2000). But bookmakers also quote odds on more specific outcomes, such as the home team to win 1–0, 2–0, etc., called the ‘correct score’ bet type here. The odds on any correct score bet must be longer than the odds of that team winning, since winning by a specific score line is a subset of the event of that team winning. If the odds quoted across these two bet types were equivalent, it should be possible to replicate the returns of a ‘home win’ bet using only correct score bets (assuming that, in practice, only a finite number of score lines can realistically occur). But this is not possible, as the odds quoted on correct score bets are less generous than home–draw–away bets, producing a higher house edge on correct score bets, as shown either by odds inconsistencies (Newall, Reference Newall2015, Reference Newall2017) or betting simulations (Dixon et al., Reference Dixon and Pope2004; Hassanniakalager & Newall, Reference Hassanniakalager and Newall2019). This pattern has been observed across a broad range of soccer bet types (Ayton, Reference Ayton1997; Forrest, Reference Forrest, Hausch and Ziemba2008; Newall, Reference Newall2015, Reference Newall2017).
In a home–draw–away bet, one team will usually be predicted to be more likely to win the match (the ‘favourite’), and thus a bet of a fixed size on that team will come with a smaller potential payoff. The team with longer odds is called the ‘longshot’. In fixed-odds soccer betting, longshots are associated with higher house edges than favourites (Cain et al., Reference Cain, Law and Peel2003; Graham & Stott, Reference Graham and Stott2008; Vlastakis et al., Reference Vlastakis, Dotsis and Markellos2009; Deschamps & Gergaud, Reference Deschamps and Gergaud2012; Constantinou & Fenton, Reference Constantinou and Fenton2013; Buhagiar et al., Reference Buhagiar, Cortis and Newall2018; Hassanniakalager & Newall, Reference Hassanniakalager and Newall2019). This pattern has broadly been found in other sports betting markets, perhaps most consistently in horse racing (Snowberg & Wolfers, Reference Snowberg and Wolfers2010), although some exceptions exist (Vaughan Williams, Reference Vaughan Williams1999). This pattern has also been found in the odds quoted by a bookmaker on Twitter in response to actual customer enquiries for custom bets (Newall et al., Reference Newall, Walasek, Vázquez Kiesel, Ludvig and Meyer2019d).
Variation in the house edges across these different soccer bets is large, varying from a low of around 5% for home–draw–away bets (Newall, Reference Newall2015) to highs of over 50% for certain bets at long odds (Hassanniakalager & Newall, Reference Hassanniakalager and Newall2019). This high degree of variation in the house edge exceeds what can be found in any one non-skilled gambling form, providing a strong rationale for the provision of statistical risk warnings in sports betting.
The preponderance of ‘odds advertising’ in gambling advertising, where the odds on specific bets in relation to some upcoming sporting event are highlighted, is another reason to consider statistical risk warnings in sports betting (Newall et al., Reference Newall, Moodie, Reith, Stead, Critchlow, Morgan and Dobbie2019a). Odds advertising around soccer in the UK has been found to be skewed towards bets with long odds and high house edges (Newall, Reference Newall2015), with this tendency becoming more pronounced over time (Newall et al., Reference Newall, Thobhani, Walasek and Meyer2019b).
In fixed-odds sports betting, house edges are variable, depending on market demand and supply. This is unlike most non-skilled gambling forms, where house edges are fixed (e.g., at 2.7% for European roulette). This means that if a significant group of sports bettors can be nudged to be more responsive to price, then all sports bettors might conceivably benefit from greater market incentives to offer bets with more generous odds (and therefore lower house edges). Home–draw–away bets, for example, have become much more fairly priced since the late 1990s, as this market has been transformed by Internet gambling and regulatory changes (Forrest, Reference Forrest, Hausch and Ziemba2008). Current house edges on home–draw–away bets are today roughly half (Buhagiar et al., Reference Buhagiar, Cortis and Newall2018) their average value of 10.5% in the late 1990s (Kuypers, Reference Kuypers2000).
Product-specific issues
In fixed-odds sports betting, the bookmaker posts a number of ‘odds’ before each event corresponding to the risk/reward ratio of betting on various outcomes. Odds can be communicated in different ways, but they always translate into some implied probability of the event happening (Cortis, Reference Cortis2015). For example, the British fractional odds system uses two numbers (e.g., ‘3/1’), where the first number represents the profit from a successful bet of a stake of the second number. In the European decimal odds system, a single number is used to express the total return from a successful bet of stake $1. Decimal odds of 4 and fractional odds of 3/1 are equivalent, since both bets return a profit of $3 if successful (Cortis, Reference Cortis2015). Both of these odds can also be converted into an implied probability of 0.25. The bookmaker's goal to prevent bettors from profiting is to set odds such that the implied probability is greater than the event's actual probability.
Since fixed-odds sports betting involves forecasts of unique events, additional work and often assumptions are required to estimate the information relevant to statistical risk warnings (probabilities can be estimated with more certainty in non-skilled gambling games, such as roulette). The most certain method would be to use historical data from an industry operator, but these data are rarely shared with researchers (Cassidy et al., Reference Cassidy, Loussouarn and Pisac2013). More approximate methods exist, which give largely similar results to each other. The first approximate method is simply to add up the implied probability from the odds for each potential event. The sum of implied probabilities will always exceed 1, which is necessary for a bookmaker that makes imperfect forecasts and wants to set implied probabilities that are greater than actual probabilities for all events (Cortis, Reference Cortis2015). The excess of implied probabilities beyond 1 is called the ‘overround’, which can then be normalized to provide an estimate of the house edge (Kuypers, Reference Kuypers2000). This method has the benefit of being applicable even to single sporting events, but it requires the assumption that bookmakers set odds in a defensive way (Stark & Cortis, Reference Stark and Cortis2017), so that they make a sure profit no matter which outcome occurs, which may not be true in practice (Levitt, Reference Levitt2004). Another approximate method is to simulate the returns from some betting strategy across a larger sample of past sporting events (Hassanniakalager & Newall, Reference Hassanniakalager and Newall2019). This method can simulate the returns under different assumptions of sports bettor behaviour, but it requires more historical data to work with, which may not necessarily provide the best estimate of current returns if the market has recently changed.
One unresolved issue is how best to regulate the disclosure of house edges in sports betting so as to preclude the incentive to game these disclosures. If bookmakers are given a range of potential calculation techniques, they would still have an incentive to use the technique that provides the lowest estimated house edge. For example, if house edges are based on historical data, then bookmakers could choose time windows that do not accurately reflect the current odds on offer or temporarily increase their odds at the end of a reporting period to inflate how attractive their odds seem going forward. If house edges are based on simulated betting returns, then bookmakers could potentially trial many simulations in-house and use the simulation that again provided the lowest estimated house edge.
We believe that historical loss rates given over some recent time period would be the most relevant to sports bettors. A standardized formula, which does not give operators any leeway to pick favourable subsets of data, seems the best approach. A fixed formula based on the last $x amount of money bet on a market (and corresponding $y amount lost, where y/x = the house edge) appears robust to gaming, while providing incentives for bookmakers to maintain favourable odds.
House edge information could be applied for each separate bet type, since, for example, the house edge is higher on correct score than home–draw–away bets in soccer. House edge statements could also be applied to subsets of a given bet type in order to reflect the fact that bets at longer odds tend to have higher house edges. An overall figure could be given for correct score bets, for example, with an additional figure given for correct score bets at odds of 19/1 or longer. Such a statistical risk warning system would capture both predictable patterns of variations in the house edge in soccer betting.
Recommendations for future research
We know of no previous studies that have explored the effect of statistical risk warnings on skilled gambling behaviour. Given the high and currently obscured variation in house edges in fixed-odds sports betting, it is possible that risk warnings might be effective here. It may, however, prove difficult to change skilled gambling game behaviour, as non-skilled gambling game behaviour has thus far proven to be (Harrigan et al., Reference Harrigan, Brown and Barton2017). It is also unknown whether in-play sports betting, which can be considered a high-frequency repeated gambling form, produces similar illusions regarding the total amount of money bet as electronic gambling machines do (Harrigan et al., Reference Harrigan, Brown and Barton2017). The potential for interactive displays should also be considered for skilled gambling. If a sports bettor chooses to make a potential bet size on a given bet, then a popup display could notify the bettor of the corresponding theoretical loss, rather than requiring the bettor to estimate this value based on their bet size and displayed house edge.
The provision of historical house edges would also benefit sports betting researchers, who generally do not have access to industry data (Cassidy et al., Reference Cassidy, Loussouarn and Pisac2013). At present, research in this area involves a number of steps and approximating assumptions that would not be necessary with the mandatory disclosure of detailed historical house edge information. This would help researchers’ attempts to replicate findings across different sports betting markets. Better access to data would also speed up the process of understanding the determinants of gamblers’ losses in other skill-based gambling games.
Discussion
Many researchers recommend treating gambling as a public health issue (Browne et al., Reference Browne, Langham, Rawat, Greer, Li, Rose and Best2016; Bowden-Jones et al., Reference Bowden-Jones, Dickson, Dunand and Simon2019; Orford, Reference Orford2019; van Schalkwyk et al., Reference van Schalkwyk, Cassidy, McKee and Petticrew2019; Wardle et al., Reference Wardle, Reith, Langham and Rogers2019). Statistical risk warnings emphasizing theoretical loss are, like standard drink or calorie labelling, only one potential element to a public health approach to gambling. But as in alcohol and food, they could play a useful and minimally invasive role in conjunction with other health promotion initiatives (Nuffield Council on Bioethics, 2007). Improving current statistical risk warnings and introducing novel and comparable statistical risk warnings for additional gambling products could help gamblers to make better-informed product choices. Information about either the theoretical loss or the house edge can provide gamblers with a clear view of how much they can expect to lose over the long term. The provision of transparent pricing information could foster price competition between operators with potential longer-term benefits to gamblers.
Just like a public health approach to alcohol or other risky products, we recommend that any implementation of statistical risk warnings should be considered alongside other potential interventions, such as more restrictive changes to the gambling product experience (Palmer du Preez et al., Reference Palmer du Preez, Landon, Bellringer, Garrett and Abbott2016; Byrne & Russell, Reference Byrne and Russell2019; Stevens & Livingstone, Reference Stevens and Livingstone2019), attempts to improve gamblers’ decision-making skills more broadly (Williams & Connolly, Reference Williams and Connolly2006; Broussard & Wulfert, Reference Broussard and Wulfert2019), personalized interventions for those who have suffered high losses (Jonsson et al., Reference Jonsson, Hodgins, Munck and Carlbring2019) and product-specific warnings for uniquely harmful products (Ginley et al., Reference Ginley, Whelan, Pfund, Peter and Meyers2017).
The specific format and presentation of warning messages can profoundly affect consumer responses (Bar-Gill, Reference Bar-Gill2019). Therefore, policymakers should be sure to implement current best practices in format and presentation. Potential industry responses to warning message requirements are another reason for policymakers to enforce best practices. It has been argued that many firms might do the minimum to comply with the letter rather than the spirit of regulations intended to help inform consumers (Page, Reference Page2019). Evidence from warning labels in UK online casinos is consistent with this view (Newall et al., Reference Newall, Walasek, Ludvig and Rockloff2020d). Statistical risk warnings in sports betting could similarly be undermined if operators are allowed freedom around the presentation or selection of statistical information.
Although we have argued for theoretical loss as the key statistical issue regarding gambling products, economists also highlight how the volatility of returns can also impact consumer welfare. That is, even if losses to operators were removed, highly volatile games will tend to result in very few players making large wins, but the large majority of players losing their total stake. Even in the case of zero net group losses, diminishing marginal welfare benefits derived from wins means that net harm can accrue to gamblers. It has been noted that gamblers tend to bet smaller amounts on high-variance bets, perhaps as a natural reaction to this aspect of product risk (Feess et al., Reference Feess, Müller and Schumacher2014). Although relevant to consumer welfare, the volatility issue is unlikely to counteract product labelling regarding theoretical loss/house edge, given that higher-variance products also tend to have higher house edges (Turner, Reference Turner2011). However, the volatility of gambling products is a unique issue that requires further research (Newall et al., Reference Newall, Walasek and Ludvig2020c).
Any enhanced consumer disclosure does run the risk of either unintended consequences (Bar-Gill, Reference Bar-Gill2019) or ‘backfire’ effects (Stibe & Cugelman, Reference Stibe, Cugelman, Meschtscherjakov, De Ruyter, Fuchsberger, Murer and Tscheligi2016). Standard drink alcohol labels may, for example, be used by teenagers to consume as much alcohol as possible given their budget (Wells et al., Reference Wells, Graham and Purcell2009). In statistical risk warnings for gambling products, there is, according to one argument, a potential indirect route for backfiring. All else being equal, gambling products with lower house edges allow gamblers to go on longer winnings runs. Since problem gamblers tend to remember big wins, it has been argued that lower house edge gambling products might therefore be the most harmful to gamblers (Harrigan & Dixon, Reference Harrigan and Dixon2010). In the present context, this consideration suggests that improved statistical risk warnings might shift gamblers and operators towards lower house edge products, which may then cause more harm due to an increased rate of winning streaks. Although the relationship between the house edge and winning streaks is true, this argument does neglect other relevant considerations. Loss chasing is another aspect of problem gambling (Ferris & Wynne, Reference Ferris and Wynne2001; Zhang & Clark, Reference Zhang and Clark2020), and lower house edge products should also induce a lesser need to chase losses, which should also reduce harm. Backfire effects could plausibly happen through a number of channels, however, so due caution should always be exercised.
Further research should continue to explore the various product-specific issues surrounding statistical risk warnings. Continuous gambling products such as electronic gambling machines allow for money to be bet repeatedly, which can cause confusion regarding the total amount of money staked (Harrigan et al., Reference Harrigan, Brown and Barton2017). This confusion could potentially be corrected in a number of ways. Preventing the automatic reinvestment of winnings is one potential method (Byrne & Russell, Reference Byrne and Russell2019). Another method could be to create an interactive display forecasting a gambler's theoretical loss and corresponding 95% confidence interval of potential returns based on their current machine settings (stake level, betting frequency, etc.). For sports betting, a more pressing issue might be studies exploring the extent to which sports bettors’ choices are modified when house edge information is given for different bet types.
Conclusion and recommendation
Although more research is always beneficial, we will make the following recommendations based on the evidence so far. Jurisdictions that currently disclose the return-to-player percentage on non-skilled gambling games should benefit from switching to the house edge and by making this information more prominent. House edge information should also be beneficial in sports betting and should be provided both at point of use and in sports betting marketing. Statistical risk warnings can be a useful input to a multifaceted public health approach to gambling.
Financial support
The authors received no funding for this research.
