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Gambling games normal results

Postby Tot В» 20.01.2020


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A Nature Research Journal. Online gambling sites offer many different gambling games. In this work we analyse the gambling logs of numerous solely probability-based gambling games and extract the wager and odds distributions. We find that the log-normal distribution describes the wager distribution at the aggregate level.

We discuss possible origins for the observed anomalous diffusion. Today, gambling is a huge industry with a huge social impact. According to a report by the American Gaming Association 1 , commercial casinos in the United States alone made total revenue of over 40 billion US dollars in On the other hand, different studies reported that 0. Researchers have put a lot of attention on studying gambling-related activities.

Economists have proposed many theories about how humans make decisions under different risk conditions. Several of them can also be applied to model gambling behaviors. For example, the prospect theory introduced by Kahneman and Tversky 4 and its variant cumulative prospect theory 5 have been adopted in modeling casino gambling 6. In parallel to the theoretical approach, numerous studies focus on the empirical analysis of gambling behaviors, aiming at explaining the motivations behind problematic gambling behaviors.

However, parametric models that quantitatively describe empirical gambling behaviors are still missing. Our goal is to provide such a parametric model for describing human wagering activities and risk attitude during gambling from empirical gambling logs. However, it is very difficult to obtain gambling logs from traditional casinos, and it is hard to collect large amounts of behavior data in a lab-controlled environment.

Therefore in this paper we will focus on analyzing online gambling logs collected from online casinos. Recent years have seen an increasing trend of online gambling due to its low barriers to entry, high anonymity and instant payout. For researchers of gambling behaviors, online gambling games present two advantages: simple rules and the availability of large amounts of gambling logs. In addition to the usual forms of gambling games that can be found in traditional casinos, many online casinos also offer games that follow very simple rules, which makes analyzing the gambling behavior much easier as there are much fewer degrees of freedom required to be considered.

On the other hand, many online casinos have made gambling logs publicly available on their websites, mainly for verification purposes, which provides researchers with abundant data to work on. Due to the high popularity of online gambling, in a dataset provided by an online casino there are often thousands or even hundreds of thousands of gamblers listed.

Such a large scale of data can hardly be obtained in a lab environment. Prior research has begun to make use of online gambling logs.

It is worth arguing that although our work only focuses on the behaviors of online gamblers, there is no reason to think that our conclusions cannot be extended to traditional gamblers. Naturally, we can treat the changing cumulative net income of a player during their gambling activities as a random walk process 8. Within this paper, we will mainly focus on the analysis at the population level.

Physicists have long been studying diffusion processes in different systems, and recently anomalous diffusive properties have been reported in many human activities, including human spatial movement 9 , 10 , 11 , and information foraging However, this explanation cannot be used in other types of gambling games where there is no interaction among gamblers e.

In this paper, we want to expand the scope of our study to more general gambling games, check the corresponding diffusive properties, and propose some explanations for the observed behaviors. One of our goals is to uncover the commonalities behind the behavior of online gamblers. To implement this, we analyze the data from different online gambling systems. The first one is skin gambling, where the bettors are mostly video game players and where cosmetic skins from online video games are used as virtual currency for wagering 8 , The other system is crypto-currency gambling, where the bettors are mostly crypto-currency users.

Different types of crypto-currencies are used for wagering. As the overlap of these two communities, video game players and crypto-currency users, is relatively small for now, features of gambling patterns common between these two gambling systems are possibly features common among all online gamblers. Not only do we consider different gambling systems, but we also discuss different types of gambling games. In general, there are two frameworks of betting in gambling: fixed-odds betting, where the odds is fixed and known before players wager in one round; and parimutuel betting, where the odds can still change after players place the bets until all players finish wagering.

The four types of games we discuss in this paper will cover both betting frameworks see the Methods section. When a player attends one round in any of those games, there are only two possible outcomes: either win or lose. When losing, the player will lose the wager they placed during that round; whereas when winning, the prize winner receives equals their original wager multiplied by a coefficient. This coefficient is generally larger than 1, and in gambling terminology, it is called odds in decimal format 15 , Here we will simply refer to it as odds.

Note that the definition of odds in gambling is different than the definition of odds in statistics, and in this paper we follow the former one. When a player attends one round, their chance of winning is usually close to, but less than the inverse of the odds. In addition, the website usually charges the winner with a site cut commission fee , which is a fixed percentage of the prize. Although the four types of games are based on different rules, the payoffs all follow the same expression.

From Eq. The house edge represents the proportion the website will benefit on average when players wager. In a fair game or when we ignore the house edge, the expected payoff would be 0.

We then focus on an analysis of risk attitude by studying the distribution of the odds players choose to wager with. We conclude by extending our discussion to the analysis of net incomes of gamblers viewed as random walks. Detailed information about the games and datasets discussed in this paper can be found in the Methods section.

From the viewpoint of the interaction among players, the games discussed in this paper can be grouped into two classes: in Roulette, Crash, and Satoshi Dice games, there is little or no interaction among players, whereas in Jackpot games, players need to gamble against each other. At the same time, from the viewpoint of wager itself, the games can also be grouped into two classes: In games A-G , the wagers can be an arbitrary amount of virtual currencies, such as virtual skin tickets or crypto-currency units, whereas in game H , the wagers are placed in the form of in-game skins, which means the wager distribution further involves the distributions of the market price and availability of the skins.

Furthermore, from the viewpoint of the odds, considering the empirical datasets we have, when analyzing the wager distribution, there are three situations: i For Roulette and Satoshi Dice games, the odds are fixed constants, and wagers placed with the same odds are analyzed to find the distribution.

At the same time, for each dataset we perform a distribution analysis of wagers at the aggregate level. Within the same dataset wagers placed under different maximum allowed bet values are discussed separately. We plot the complementary cumulative distribution function CCDF of the empirical data and the fitted distribution to check the goodness-of-fit, see Fig.

In games A — G , where players are allowed to choose arbitrary bet values, the wager distribution can be best fitted by log-normal distributions 3. The fitting lines represent the log-normal fittings. Wagers placed under the different maximum allowed bet values are discussed separately, e. On the other hand, in game H where wagers can only be in-game skins, the wager distribution is best described by a pairwise power law with an exponential transition, see Eq.

The red dotted line represents the log-normal fitting and the blue solid line represents the fitting of a pairwise power law with an exponential transition. Meanwhile in game D , the fitted log-normal distribution is truncated at an upper boundary x max , which might result from the maximum allowed small bet value and the huge variation of the market price of crypto-currencies.

During model selection, we notice that when we select different x min , occasionally a power-law distribution with exponential cutoff is reported to be a better fit, but often it does not provide a decent absolute fit on the tail, and overall the log-normal distribution provides smaller Kolmogorov-Smirnov distances, see the Methods section.

On the other hand, as we have pointed out in the previous study 8 , when players are restricted to use in-game skins as wagers for gambling, the wager distribution can be best fitted by a shifted power law with exponential cutoff. Now, with a similar situation in game H , where wagers can only be in-game skins, we find that the early part of the curve can be again fitted by a power law with exponential cutoff, as shown in Fig.

However, this time it does not maintain the exponential decay of its tail; instead, it changes back to a power-law decay. The overall distribution contains six parameters, given by the expression. We believe that when players are restricted to use in-game skins as wagers, the decision to include one particular skin in their wager is further influenced by the price and availability of that skin.

These factors make the wager distribution deviate from the log-normal distribution, which is observed in games A-G. This is very clear when comparing the wager distributions of games G and H as both games are jackpot games of skin gambling, and the only difference is whether players are directly using skins as wagers or are using virtual skin tickets obtained from depositing skins.

This commonality of log-normal distribution no longer holds when this arbitrariness of wager value is violated, e. Log-normal distribution has been reported in a wide range of economic, biological, and sociological systems 17 , including income, species abundance, family size, etc.

Economists have proposed different kinds of generative mechanisms for log-normal distributions and power-law distributions as well. One particular interest for us is the multiplicative process 18 , The results reveal that the values of consecutive bets exhibit a strong positive correlation, with all the correlation coefficients larger than 0.

At the same time, the bet values are following gradual changes, rather than rapid changes. These conclusions can be confirmed by the small mean values and small variances of log-ratios between consecutive bets. The high probability of staying on the same wager indicates that betting with fixed wager is one of the common strategies adopted by gamblers. The distribution of the logarithmic of the ratio log-ratio between consecutive bet values.

For games A — C , the log-ratio can be described by a Laplace distribution. For games D , F — H , the log-ratio presents bell-shaped distribution. In general, the distributions are symmetric with respect to the y-axis, except in games D , F. The multiplication process can be explained by the wide adoption of multiplicative betting systems. Although betting systems will not provide a long-term benefit, as the expected payoff will always be 0 in a fair game, still they are widely adopted among gamblers.

A well-known multiplicative betting system is the Martingale sometimes called geometric progression In Martingale betting, starting with an initial wager, the gambler will double their wager each time they lose one round, and return to the initial wager once they win. Apart from multiplicative betting, there are many other types of betting systems, such as additive betting and linear betting The reasons why multiplicative betting systems are dominant in our datasets are: 1 Martingale is a well-known betting system among gamblers; 2 Many online gambling websites provide a service for changing the bet value in a multiplicative way.

For example, for the Crash games csgofast-Crash C and ethCrash D , both websites provide a simple program for automatically wagering in a multiplicative way. For the Roulette games and Coinroll F , the websites provide an interface with which the gambler can quickly double or half their wager.

However, for Satoshi Dice E and csgospeed-Jackpot G , no such function is provided, yet we still observe similar results, indicating that gamblers will follow a multiplicative betting themselves. We can see that although there is a high probability for sticking to the same bet values, the most likely outcome after losing a round is that the gambler increases their wager.

Betting big on video game gambling, time: 7:13
Posts: 946
Joined: 20.01.2020

Re: gambling games normal results

Postby Mezimuro В» 20.01.2020

In our analysis, we can examine such behaviors based on the gambling logs from Crash and Satoshi Dice games. Players who played less than rounds are filtered out in each dataset. Skip to main content. Correlations in the motion of atoms in liquid argon. Similar crossovers are observed in games G and Htwo parimutuel betting games, where the same explanation can be applied.

Posts: 128
Joined: 20.01.2020

Re: gambling games normal results

Postby Tolabar В» 20.01.2020

As the overlap of these two communities, video game players and crypto-currency users, is relatively small now, features of source patterns common nor,al these two gambling systems are possibly features common among all online gamblers. Online gambling addiction: the relationship between internet gambling and disordered gambling. A well-known multiplicative betting system is the Martingale sometimes called geometric progression Category Commons Wiktionary WikiProject.

Posts: 745
Joined: 20.01.2020

Re: gambling games normal results

Postby Akinogami В» 20.01.2020

To remove the effects of this inequality, we randomly sample in each dataset the same number of bets from heavy gamblers. Gambling, Crime and Society. In the previous examples of gambling experiments we saw some of the events that experiments generate. Skip to main content. Casinos attract a substantial number of overseas visitors.

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