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All participants were provided with a description of the study objectives and were asked to read and sign an informed consent prior to participating in the current research. Participants were informed they were free to terminate participation at any time without penalty. Thereafter, participants were asked to complete a short background questionnaire, which included demographic information (gender, age), frequency of gambling, and how knowledgeable they believe themselves to be on the topic of online gambling. A series of open-ended questions were asked of the group as part of a larger project assessing online gambling among young adults. For the present research, two open-ended questions were of importance. The first examined general factors that lead young adults to gamble online, “I’d like to gain a better understanding of the things that lead to online gambling in the first place. Based on what you know, what are the factors, the events, or the influences that result in a young person deciding to bet money on gambling activities online?” The second assessed the social casino game-online gambling link including the potential mechanisms, “You know that social media sites have gambling-type games such as Texas-Hold’em or Sloto-mania. In your opinion, do you think experience with these games leads a person to seek online gambling sites? In other words, do these types of games serve as a form of initiation to gambling online with real money?” A licensed clinical psychologist trained in conducting focus groups led the discussions accompanied by two note-takers. Each group was approximately 60–75 min in duration and discussions were conducted at two Canadian universities. Two recording devices recorded the focus group to ensure no loss of data. Upon the completion of the focus groups, the discussions were subsequently transcribed by a professional coder and coded by two independent reviewers. The initial categories generated by the data were highly consistent between the two raters with regards to general themes and number of categories. The data was reviewed two additional times to arrive at a consensus when disagreements between raters were noted. Categorical names were arrived through consensus after discussion between raters. NVivo 10 qualitative research software for qualitative analyses was used to organize and quantify the data. Results. With respect to frequency of online gambling, 52% of individuals indicated gambling less than once per week, while 48% indicated gambling at least once per week or several times per week. Seventy-six percent of individuals indicated gambling more frequently and/or for longer periods of time than intended (61.9% occasionally; 14.4% often). Participants were asked to indicate on a 7-point Likert scale how knowledgeable they perceived themselves to be on the topic of online gambling. The overall mean score was 4.38. The majority of the sample (85.7%) indicated that they tend to play on one or two online gambling sites, whereas 14.3% stated they like to experiment with different sites. Importantly, more than half (62%) of the participants revealed playing social casino games (e.g., Texas Hold’em ) on Facebook or on other platforms. Of the participants ( n = 3) who spontaneously reported having transitioned from playing for fun to online gambling, they did so in relatively short period of time. One participant reported transitioning after only two weeks, while another stated having moved to real money gambling after a couple of months. General factors leading to online gambling. Several themes emerged in regards to the factors that led the emerging adults to online gambling. For example, some of the emerging adults in the focus groups stated that friends played an important role in their initial participation to online gambling. Specifically, several participants reported having first learned to gamble with friends and thereafter transitioning to online gambling as their friends were not always available. From my personal experience for example, I started gambling online with poker because I started playing poker with friends, and that is how I got to gambling online… with friends they did not always have the time [to play poker]. Gambling online was just easier – with friends they did not always have time. Another theme that was noted in the precipitation of online gambling was the incentives (eg., sign up bonuses) offered by online gambling. The young adult online gamblers noted that the first time they gambled online was when they were offered bonuses and free credits. 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Now, let us focus on the analysis of the diffusive process of the gamblers’ net incomes, starting with the analysis of the change of the mean net income with the number of rounds played (time), \(\langle \Delta w(t)\rangle =\langle w(t)-_\rangle =\langle _^\,_ (i)\rangle \) , where w 0 is the player’s initial wealth, w ( t ) is the player’s wealth after attending t rounds, and \(_ (i)\) is the payoff from the i th round the player attended. \(\langle \cdot \rangle \) represents an ensemble average over a population of players placing bets. In the rest of this paper, \(\langle \cdot \rangle \) will always be used for representing an ensemble average. In Fig. 6 we show the change of \(\langle \Delta w(t)\rangle \) over time. In most of the datasets, players’ mean net income decreases over time, which suggests that in general players will lose more as they gamble more. At the same time, in some datasets such as Ethcrash (D) and Coinroll (F), large fluctuations can be observed. Figure 6. Change of the mean net income with time for the different datasets. Most of the datasets present a decreasing net income as time t increases. Each point is obtained from an average over at least 200 players. An useful tool for studying the diffusive process is the ensemble-averaged mean-squared displacement (MSD), defined as. For a normal diffusive process, \(\langle \Delta ^(t)\rangle \sim t\) , otherwise an anomalous diffusive behavior prevails More specifically, when the MSD growth is faster (respectively, slower) than linear, superdiffusion (respectively, subdiffusion) is observed., सबसे अच्छी स्लॉट मशीन casino india 2023. In Fig. 7, we present the growth of the ensemble-averaged MSD against time for each of the datasets. To reduce the coarseness, MSD curves are smoothed with log-binning technique. The error bars in Fig. 7 represent 95% confidence intervals computed with bootstrapping using 2000 independent re-sampling runs. It is interesting to see that for different datasets we observe different diffusive behaviors. For games csgofast-Crash (C) we observe that the MSD grows faster than a linear function, suggesting superdiffusive behavior. Meanwhile, for games csgofast-Double (A), ethCrash (D), csgospeed (G), and csgofast-Jackpot (H), the MSD first presents a superdiffusive regime, followed by a crossover to a normal diffusive regime. For games csgofast-X50 (B) and Coinroll (F), although the ensemble-averaged MSD roughly presents a linear/sublinear growth, a careful inspection shows that both curves consist of several convex-shaped regimes, indicating a more complex behavior. Convex-shaped regimes can also be observed in csgofast-Crash games (C). Figure 7. The growth of ensemble-averaged mean-squared displacement in different datasets presents different diffusive behaviors. In the figures, the error bars represent 95% confidence intervals, blue dashed lines follow linear functions (slope = 1), and green dotted lines follow quadratic functions (slope = 2). In ref. 8 we argued that the crossover from a superdiffusive regime to a normal diffusive regime in a parimutuel game is due to the limitation of individuals’ wealth and the conservation of total wealth. Similar crossovers are observed in games (G) and (H), two parimutuel betting games, where the same explanation can be applied. On the other hand, this crossover is also found in a Roulette game and in a Crash game, where there is no interaction among gamblers. The limitation of an individual’s wealth can still be a partial explanation, but the conservation of total wealth no longer holds. A different explanation needs to be proposed to model this crossover. In the following we briefly discuss how we can obtain from gambling models the different diffusive processes observed in the data. 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