1 The Psychological Record, 2008, 58, Gambling on a Simulated Slot Machine under Conditions of Repeated Play Andrew E. Brandt and Cynthia J. Pietras Western Michigan University A single-subject design was used in 2 experiments about the effects of percentage payback (winnings in proportion to total amount bet) on gambling on a slotmachine simulation in 8 adult humans. In Experiment 1, percentage payback was varied across a wide range of values, and participants were exposed extensively to percentage-payback conditions. Gambling did not vary systematically across levels. In Experiment 2, win probability and win size were manipulated across conditions while percentage payback was held constant. One participant gambled more in the high-win-probability, low-win-size condition than in other conditions; however, gambling by the remaining 2 participants was similar across conditions. Most participants placed fewer bets as each experiment progressed, suggesting that behavior was sensitive to the monetary loss typically produced by gambling. Overall, the results highlight the utility of procedures that provide repeated and extensive experience with gambling contingencies. In laboratory studies designed to investigate gambling and risky choice in humans, risk preferences typically are analyzed by presenting participants with several choices between high- and low-variance options that deliver hypothetical amounts of money (e.g., Kahneman & Tversky, 1982; Rachlin, Castrogiovanni, & Cross, 1987: Silberberg, Murray, Christensen, & Asano, 1988). Studies performed with these procedures have yielded important information about variables that influence decision making under conditions of risk; however, these experimental tasks differ in several respects from games of chance commonly played by gamblers outside the laboratory. For example, most games of chance deliver a variety of possible outcomes, allow the gambler to make repeated plays (as opposed to just a few choices), and allow the gambler to wager real money. Moreover, for the gambler, there is always a cost associated with placing a wager, a characteristic rarely present in gambling investigations. A challenge for gambling researchers, therefore, has been to develop procedures for studying gambling that not only allow a high degree of experimental control but also closely resemble typical games of chance. Andrew E. Brandt is now at Albion College, Albion, Michigan. The authors thank Mark Dixon for providing the computerized slot-machine simulation used to collect data in these experiments. Address all correspondence to Andrew E. Brandt, Department of Psychology, Albion College, 611 E Porter St, Albion, MI
2 406 Brandt and Pietras One experimental procedure that both simulates a typical game of chance and, at the same time, provides the researcher with considerable control over environmental events is a computerized slot-machine simulation developed by MacLin, Dixon, and Hayes (1999). This simulation allows the researcher to control the symbols that appear on the win line, the probability that those symbols will appear as a winning combination, the combinations of symbols considered a win, and the number of credits (i.e., points exchangeable for money) staked to the participant. Slot-machine simulations have been successfully used to investigate the effects on gambling of variables such as the big win (Kassinove & Schare, 2001) and the near miss (Schreiber & Dixon, 2001; Weatherly, Sauter, & King, 2004). In several studies, slot-machine simulations have also been used to investigate the effects of percentage payback on gambling (Schreiber & Dixon, 2001; Weatherly & Brandt, 2004). Percentage payback is calculated by dividing the total amount gained per gambling session by the total amount lost (i.e., amount bet) and then multiplying by 100%. For example, if a person places 100 bets worth 1 credit each and wins 75 credits, the person has experienced a percentage payback of 75%. Because percentage payback is equivalent to net reinforcement, it seems likely that gambling would be sensitive to variations in percentage-payback values. However, studies performed with simulated slot machines have shown that manipulation of percentage payback has no effect on gambling. For example, Schreiber and Dixon (2001) used a betweensubjects group design to investigate the effects of percentage payback (40%, 80%, and 120%) on total bets placed by 12 female participants in a slot-machine simulation. The authors reported no difference between the total bets placed by participants across the three percentage-payback conditions. Weatherly and Brandt (2004) reported a similar result in a between- and within-subjects factorial investigation of the effects of percentage payback and the monetary value of credits on gambling. Three levels of percentage payback (75%, 83%, and 95%) and credit value ($0.00, $0.01, and $0.10) were investigated. Participants were staked with 100 credits and were given the opportunity to play the slot machine for up to 15 min. Participants were instructed that they could bet 1, 2, or 3 credits on any trial and that they could quit at any time. The results of these experiments showed that the total number of credits bet per session varied as a function of credit value but not percentage payback. Weatherly and Brandt (2004) offered several potential reasons for why gambling was similar across percentage-payback conditions. They proposed that (1) gambling was not sensitive to manipulations in percentage payback, (2) gambling might have been sensitive to parameters such as win size or win probability rather than to the net reinforcement (i.e., percentage payback), (3) participants might not have shown sensitivity to percentage payback because they did not receive adequate experience with the programmed contingencies, and (4) insensitivity to percentage payback could have resulted from a discrepancy between the target and experienced percentage payback. Such a discrepancy may have occurred because the trial outcomes were randomized and because participants could quit a session at any time. The authors argued against the possibility that discrepancies between targeted and experienced percentage payback were responsible for the insensitivity to percentage payback manipulations, noting that participants in both experiments had on average more credits remaining at the end of the session
3 Slot-Machine Gambling, Percentage Payback 407 in the highest percentage-payback condition than in the lower two percentagepayback conditions. The participants average credits remaining per session in the lower two levels of percentage payback, however, were very similar. This discrepancy suggests that the experienced percentage payback may have been similar across some conditions. The goal of Experiments 1 and 2 was to investigate the apparent insensitivity of gambling to percentage payback reported in previous studies. Experiment 1 was designed to investigate the effects of percentage-payback on gambling, whereas Experiment 2 was designed to investigate the effects of win probability and size on gambling as percentage payback was held constant. In both studies a parametric single-subject design was used to expose participants to conditions until responding was stable. In addition, trial outcomes were programmed to limit the variability in programmed percentage payback (Experiment 1) and win probability (Experiment 2) within each condition. Finally, with the exception of 2 participants in Experiment 1 (see below), participants were given experience with the experimental contingencies during brief forced-exposure sessions prior to each experimental session to guarantee exposure to each percentage-payback level. Experiment 1 Experiment 1 was a systematic replication of Weatherly and Brandt (2004). As described above, these authors investigated gambling across three percentage-payback levels (75%, 83%, and 95%). Because the percentage payback range (20%) may have been insufficient to produce differences in gambling, the range used in the current experiment was increased to 60%. Specifically, gambling was investigated across four percentage-payback levels: 50%, 75%, 95%, and 110% (corresponding condition names were PP50, PP75, PP95, and PP110, respectively). Because the first three levels were losing conditions (i.e., gambling would, on average, result in a net loss), a winning condition (110%; i.e., one that would result in a net gain) was also included. The trial outcomes used by Weatherly and Brandt (2004) were randomly generated. Thus, the trial outcomes had a varied distribution that closely resembled real-world gambling conditions, but it also caused programmed percentage-payback levels to differ from target percentage-payback values. In the current study, to increase the probability that the experienced percentage payback would fall within the target range, percentage-payback levels were programmed so as not to vary from the target percentage payback by more than +5%. Therefore, the conditions contained some variation in percentage payback but closely approximated the target percentage-payback levels. This programming also guaranteed no overlap in programmed percentage payback across conditions. Although the trial outcomes were programmed to closely approximate target percentage-payback levels, the percentage payback that a participant actually experienced depended on the total trials played per session. For example, if a participant placed five bets during a session, all of which resulted in a loss, and then quit the session, he or she would have experienced a percentage payback of 0%. Therefore, to guarantee that participants actually experienced the programmed percentage-payback level, participants completed brief forced-exposure sessions prior to each experimental session.
4 408 Brandt and Pietras Method Participants. Western Michigan University s Human Subjects Institutional Review Board approved all aspects of the procedure. Participants were 5 college students (3 female, 2 male) recruited from Western Michigan University via flyers posted on campus. The flyers invited men and women to participate in a gambling study for money. All participants were 21 years of age or older. After informed consent was obtained, all applicants were asked to complete a written version of the South Oaks Gambling Screen (SOGS; Lesieur & Blume, 1987), which is a 20-point questionnaire used to assess pathological gambling. Scores of 5 or greater on the SOGS have been shown to be indicative of pathological gambling. Thus, only applicants who scored 4 or below on the SOGS were recruited for participation. Those applicants who scored 5 or above were given a debriefing script and access to referral information for assistance with potential pathological gambling problems. Over the course of Experiments 1 and 2, 23 people underwent screening with the SOGS. Their SOGS scores ranged from 0 to 10 (mean [M] = 2.5, standard deviation [SD] = 2.7). Of the 23 applicants who were screened, three were excluded due to a SOGS score greater than 4, and 12 dropped out of the study prior to completion for unknown reasons. The SOGS scores for the participants in Experiment 1 were 1, 2, 4, 0, and 2 for Participants 1, 2, 4, 7, and 22, respectively. Participants were paid money contingent on their performance on the gambling task and on attendance. Each participant was staked with money (in the form of credits) to gamble with each session. The number of credits remaining at the end of each session was tallied and paid to the participant at the end of each day. The participants were also paid a completion bonus of $1 per session, which was paid to them only upon completion of their participation. This incentive was used to increase the likelihood that participants would attend each session and finish the experiment. Participants average total earnings were $ (SD = 52.07), and their average per-hour earnings were $8.91 (SD = 2.02). Apparatus. Experimental sessions took place in one of two identical cubicles measuring 1.7 m long by 1.3 m wide by 2.15 m high. Both cubicles were contained in a 2.13 m by 3.51 m room. Each cubicle had a separate entrance covered by a heavy curtain. Inside each cubicle were a desk, a color computer monitor, an optical computer mouse, a camera (in a top corner of the cubicle), and a white-noise generator. For additional noise reduction, participants were required to wear noise-deadening muffs over their ears. A computer in an adjacent room was used to control experimental events. The cameras were connected to the computers in the adjacent room and were used only for real-time monitoring of the participants activity. Slot-machine simulation. The gambling task was a modified version of a computerized slot-machine simulation created by MacLin, Dixon, and Hayes (1999). The main difference between the simulation described by MacLin et al. and the one used in the present study was the manner in which the trial outcomes were generated. Trial outcomes in the MacLin et al. simulation were randomly generated according to input variables set by the researcher, whereas in the modified version, trial outcomes were preprogrammed by the researcher (see below). A payoff table (see Weatherly & Brandt, 2004) that illustrated the winning combinations was attached directly to the computer monitor.
5 Slot-Machine Gambling, Percentage Payback 409 Procedure. Participants completed six sessions per day, 3 5 days per week. Sessions lasted a maximum of 20 min, and participants were given a 5-min break between sessions. Prior to their first session, participants were told how many credits they would be staked per session and were instructed that each credit was worth $0.05. Participants were instructed that the amount of credits remaining after each session would depend upon their performance on the gambling task, and that any remaining credits were exchangeable for money after the last daily session. Upon arriving at the laboratory for the first experimental session, participants were asked to sit in the waiting area. While participants were in the waiting area, the researcher gave them a copy of the following instructions: For the next 30 minutes, you will be given the opportunity to play a computer-simulated slot machine. At the beginning of each session, you must place 40 bets. Once you have placed the 40 bets, you will be removed from the cubicle for a few seconds. When you reenter, you will have the opportunity to play the slot machine as long as you like up to 20 minutes. Three symbols will appear on the slot machine as you are playing: Bells, Cherries, and Blanks. The winning combinations of these symbols, as well as the payoffs for those combinations, appear on the Payoff Table. To win, a winning combination must appear on the middle row. Each session, you will be staked with 70 credits, 20 for the first 40 bets and 50 to bet as you choose. Each credit is worth $0.05. Thus, you are being staked $3.50 for each session. You will be paid in cash at the end of each day for the total credits you accumulate. You may quit at any time by clicking the exit button at the bottom of the screen. The session will end when a) you click exit, b) you reach 0 credits, or c) 20 minutes has elapsed. Do you have any questions? [underline in original] The researcher allowed the participant to read the instructions and answered any remaining questions by referring back to the relevant portion of the instructions. Prior to each experimental session, participants completed a brief forced-exposure session. Participants started each forced-exposure session with 20 credits and were required to place 40 bets. After the 40th bet, the session ended automatically and participants exited the experimental chamber. Approximately 1 min later, participants were escorted back to the chamber to start the experimental session and were given the following verbal instruction: You may play the slot machine as long as you want, up to 20 min. Participants were staked with 50 credits during each experimental session. Because participants could gamble with only the money staked to them, it was impossible for them to lose any of their own money. It was possible, however, for a participant to finish a session with fewer credits, more credits, or the same number of credits as originally staked. Participants were not under any overt obligation to play the simulation and could therefore press the exit button without placing a bet and receive the money they were staked. If participants quit the session before 20 min had elapsed, they were asked
6 410 Brandt and Pietras to remain in the waiting area until the next scheduled session time (25 min from the start of the previous session). Thus, participants could not leave the laboratory early by quitting before the end of a session. Participants were exposed to four levels of percentage payback in a counterbalanced order, and each was replicated once. Upon completion of the study, participants were asked to complete a postexperimental questionnaire, used primarily to gain information about potential strategies that participants employed to earn money during the experiment. For each percentage-payback level, 20 unique experimental sessions of 240 outcomes were programmed (pilot work demonstrated that 240 outcomes exceeded the number of plays that could occur in a 20-min period). To control variability in the programmed percentage payback within each session, several blocks of 40 outcomes were first randomly generated at each percentage-payback level. Then six 40-outcome blocks that had a percentage payback of +5% of the target percentage payback were selected to create a 240-outcome session. No block was used twice, and therefore all sessions within each level of percentage payback were unique. Procedural deviations. For the 2 participants who were recruited first (Participants 1 and 2) the procedures deviated somewhat from those described above. First, Participants 1 and 2 did not undergo forcedexposure sessions. Second, the credits were worth $0.10 instead of $0.05. Third, they did not complete a postexperimental questionnaire. Lastly, these participants experienced the PP110 condition only once, near the end of the experiment. Data analysis. Visual analysis of graphical data was used to assess stability within each phase. A minimum of three stable sessions per condition were required for a condition change. Conditions were considered stable if session-to-session variability of total trials played was low and there was no trend in the direction of expected behavior change (e.g., an increasing trend in a PP75 condition would be considered stable if it was to be followed by a PP50 condition). Conditions were also changed if stability was not achieved after 10 sessions (which occurred only twice during the experiment). Results Figure 1 shows for Participants 1 and 2 and Figure 2 shows for Participants 4, 7, and 22 the number of credits remaining at the end of each session and the total number of trials (bets) per session across conditions. Participant 4 was the only one whose responding varied as a function of percentage payback, and this variance occurred only during the first exposure to each condition. In the first condition, PP75, Participant 4 bet approximately 50 trials per session. When the condition changed to PP110, total trials decreased to 36 but then increased quickly over the next three sessions to 103 total trials. When the percentage payback was reduced to PP50, total trials decreased sharply and continued to decrease across the condition. When the percentage payback was raised to PP95, total trials again increased. In Session 15, total trials decreased to 45 and remained near that level for most of the experiment.
7 Slot-Machine Gambling, Percentage Payback 411 Figure 1. Total trials (filled circles) and credits remaining (open triangles) per session for Participants 1 (P1) and 2 (P2). Phase labels 50, 75, 95, and 110 indicate percentagepayback conditions 50%, 75%, 95%, and 110%, respectively. Gambling by Participants 1, 7, and 22 did not vary systematically with manipulations in percentage payback; however, each showed a similar pattern of responding. That is, each tended to gamble at high or moderate levels during early conditions of the experiment but gambled much less during subsequent conditions. The decrease in gambling was often marked by an abrupt shift in responding. For example, Participant 1 responded variably during the first three conditions (4 135 total trials per session), but after Session 23, in which the participant placed 74 bets and earned only 10 credits, gambling decreased to a low level (2 36 total trials per session) for the remaining sessions. Similarly, Participant 7 responded variably during the first two conditions (6 55 total trials per session), but after Session 14, in which the participant
8 412 Brandt and Pietras Figure 2. Total trials (filled circles) and credits remaining (open triangles) per session for Participants 4 (P4), 7 (P7), and 22 (P22). Phase labels 50, 75, 95, and 110 indicate percentage payback conditions 50%, 75%, 95%, and 110%, respectively.
9 Slot-Machine Gambling, Percentage Payback 413 placed 102 bets and earned only 10 credits, the number of bets placed per session decreased to approximately for the remaining sessions. Participant 22 also responded variably (6 119 total trials per session) until Session 23, during which the participant placed 52 bets and earned only 20 credits. The number of bets placed decreased in the next session and were low (0 10 total trials per session) for the remainder of the experiment. Unlike the other participants, Participant 2 responded at a high level (120 total trials) in the first session but then responded at a low level in nearly all subsequent sessions (typically around total trials per session), although responding was slightly elevated in the second PP95 condition. Participant 2 placed 50 or more bets in only 4 of 43 sessions. Figure 3 shows the median experienced percentage payback for all sessions within each condition. The first and second bars for each condition show the experienced percentage payback for the first and second (replication) exposures, respectively. For most participants, the experienced percentage payback tended to vary systematically across conditions, with lower percentage payback typically experienced in lower percentage-payback conditions. Experienced percentage payback, however, did sometimes differ from the target percentage payback, especially when gambling was very low (see Participant 22). There were also discrepancies between the experienced percentage payback in the initial exposures and replications that probably were due to the decrease in gambling across the experiment. Figure 4 shows for all participants the mean number of credits remaining across conditions. Average session earnings increased systematically as percentage payback increased. Therefore, despite variability in experienced percentage payback, there were clear differences in the net earnings across percentage-payback conditions. Figure 5 shows for all participants the correlation between total trials completed and credits remaining at each level of percentage payback (Pearson s r coefficients and associated p values are shown on each plot). As expected, under PP50, PP75, and PP95 conditions, remaining credits decreased as total trials increased. This relationship was most pronounced in lower-percentage-payback conditions in which the participants were more likely to experience large losses after high rates of gambling. Alternatively, under PP110 conditions, there was no such relationship between total trials completed and credits remaining. As described above, Participants 4, 7, and 22 were asked to complete a questionnaire at the end of their participation. The primary data of interest from the postexperimental questionnaire were the participants responses to the following two items: Please describe any strategies that you may have used to earn money. Did any of your strategies change across the experiment? and Did the money influence any of your decisions or strategies during the experiment? If so, how? Participants responses to these questions were collected to provide some potential insight into variables that may have influenced gambling. (A transcript of the participants verbal report is available upon request from the first author.) The verbal reports suggested that participants tried to keep the total number of credits at the end of each session above a target level. For Participants 4, 7, and 22 the reported targets
10 414 Brandt and Pietras Figure 3. Median experienced percentage payback for all sessions of each condition for participants in Experiment 1. The interquartile range is indicated by the upper and lower limits of the error bars. The first bar for each condition shows the values for the first exposure to a condition, and the second bar shows the values for the replications. For Participant 22 (P22), the median and 75th quartile values for the second bar in the PP110 condition appear next to the bar.
11 Slot-Machine Gambling, Percentage Payback 415 Figure 4. Mean number of credits remaining across conditions of percentage payback. Data from all participants in Experiment 1 are collapsed across each condition of percentage payback. Error bars indicate ±1 standard deviation. were 30, 35, and 50 credits, respectively. For example, Participant 4 stated, I made sure that I did not go under 30 credits. As seen in Figure 1, gambling in Participants 4 and 7 was generally consistent with the reported strategy. For these participants, gambling was consistent with the reported target in 83% and 88% of sessions, respectively. For Participant 22, gambling was consistent with the reported target in only 43% of sessions. Discussion When 5 participants were exposed to four levels of percentage payback, gambling in only 1 participant (Participant 4) varied across percentagepayback conditions and the pattern was not maintained during replications. There were no systematic differences in gambling across percentage-payback conditions in the other participants. The results are therefore generally consistent with those reported by Schreiber and Dixon (2001) and Weatherly and Brandt (2004). It is uncertain why only Participant 4 showed sensitivity to percentagepayback conditions. One possibility is that Participant 4, who scored a 4 on the SOGS, may have had a different gambling history than other participants (who all scored between 0 and 2). A SOGS score of 4 is the highest score that is indicative of nonpathological gambling, but it may indicate a higher level of gambling experience than individuals with a lower score. Weatherly and Brandt (2004) suggested that persons with more experience gambling might show greater sensitivity to percentage-payback manipulations than those with less experience. The performance of Participant 4 supports this possibility. Future studies might investigate this relationship more directly, such as by
12 416 Brandt and Pietras Figure 5. Bivariate plots showing the relationship between total trials (i.e., bets) and credits remaining at each level of percentage payback. Data from all participants in Experiment 1 are shown. Pearson s r correlation coefficients and associated p values are shown for each condition. investigating gambling in pathological and nonpathological gamblers across a wide range of percentage payback values. Such research might help identify how gambling differs between these two groups. One aim of the present study was to investigate gambling across a wider range of percentage-payback values than used in the Weatherly and Brandt (2004) studies. Despite the wider range of percentage-payback values, most participants did not respond differentially across percentage payback conditions. It is possible however, that if percentage payback had been manipulated over an even wider range (e.g., 0% to 200%) different response patterns may have been observed. Weatherly and Brandt (2004) suggested that participants might not have responded differentially across percentage-payback conditions because participants did not receive sufficient exposure to conditions. In the Weatherly and Brandt study, participants experienced only 1 session in Experiment 1 or 9 sessions in Experiment 2. Thus, another aim of the present study was to investigate gambling when participants were given more exposure to percentage payback conditions. Participants in the present investigation experienced an average of 41.6 (SD = 3.4) total sessions and an average of 5.5 (SD = 0.7) sessions per condition. The increased exposure, however, did not result in greater sensitivity to the changes in percentage payback across conditions. Although gambling did not vary across percentage-payback conditions, gambling did appear sensitive to net earnings. As described above, in every percentage-payback condition (except for PP110), repeated gambling would be expected to produce a net loss of credits. In fact, as
13 Slot-Machine Gambling, Percentage Payback 417 Figure 5 shows, in all conditions except for PP110, as the number of trials played per session increased, session earnings tended to decrease. Across the experiment, gambling in most participants eventually decreased to a low level. The decrease in gambling indicates that behavior was sensitive to the net loss produced by repeated gambling in most conditions (i.e., percentage payback < 100%). With the exception of Participant 4, gambling was also low in the PP110 condition. In the PP110 condition, gambling would produce a net gain in earnings and high levels of gambling would be expected. It is unclear why gambling was low in this condition, but one likely explanation is condition sequence. In most cases the PP110 condition was experienced only after participants had experienced lower percentage-payback conditions. Thus, the prior exposure to low percentage-payback conditions may have affected responding. Three participants in Experiment 1 (Participants 4, 7, and 22) completed a postexperimental questionnaire that asked them to describe any strategies they may have used during the experiment. All 3 participants reported a strategy that included what may be described as an earnings target, that is, a specified acceptable level of credits remaining at the end of a session. Gambling was frequently consistent with the reported target in 2 of 3 participants (Participants 4 and 7). Although the exact nature of the relationship between participants verbal report obtained at the end of the experiment and their gambling during the experiment is unknown, the consistency between the reports and gambling suggest that self-generated rules may have influenced gambling patterns (see the General Discussion for a more detailed consideration of this issue). Experiment 2 Experiment 1 showed that inadequate exposure to percentagepayback conditions could not alone account for the insensitivity to changes in percentage payback shown in previous research (Weatherly & Brandt, 2004). As described above, Weatherly and Brandt offered several other possibilities for why gambling might not have varied across percentage-payback manipulations. For instance, gambling might have been sensitive to local reinforcement parameters (e.g., win size or win probability) rather than to net reinforcement. In support of this possibility, Kendall (1987) showed that when net reinforcement was held constant, pigeons tended to prefer choice options consisting of high win probabilities and low win sizes. Kendall trained two pigeons to key peck one of two illuminated response keys. A response to the no-risk alternative resulted in access to a (fixed-ratio) FR 30 schedule of food delivery. A response to the risky alternative, the gamble, resulted in a 1-min time-out or an opportunity to respond on a FR 10 schedule of reinforcement. The probability of the FR 10 availability and the number FR 10 presentations (i.e., the number of reinforcers that could be collected) was manipulated across conditions. Thus, choosing the risky option could produce either a high-probability, low-valued outcome or a low-probability, high-valued outcome. Kendall showed that subjects tended to prefer the gambling option most when the low-value, highprobability reinforcer was available.
14 418 Brandt and Pietras More recently, Dixon, MacLin, and Daugherty (2006) investigated gambling preference between two concurrently available slot machines that differed in win rate and probability but had an equal net payout (i.e., percentage payback). Participants were initially staked with an equal number of credits on each slot-machine alternative. During the session, participants could bet one or two credits on one slot machine at a time but could freely switch between alternatives. One slot-machine alternative delivered 10 credits per 10 bets, and the other paid out 50 credits per 50 bets (payouts based on a one-credit bet). Thus, the programmed percentage payback was equal across the two alternatives (100%), and only the size and probability of wins differed. Dixon et al. (2006) showed that participants preferred the option that delivered frequent small wins to the option that paid out infrequent large wins, a finding similar to that of Kendall (1987). A preference for high-probability, low-valued outcomes over lowprobability, high-valued outcomes may have influenced responding in Experiment 1. In Experiment 1, win probability and win size covaried with percentage payback. That is, the mean experienced win probability decreased from 0.30 (SD = 0.02) to 0.28 (SD = 0.02), 0.21 (SD = 0.02), and 0.17 (SD = 0.05) across percentage payback levels of 50%, 75%, 95%, and 110%, respectively. In addition, the mean experienced win size increased from 1.59 (SD = 0.04) to 2.58 (SD = 0.37), 4.05 (SD = 0.27), and 6.54 (SD = 1.76) credits across percentage payback levels of 50%, 75%, 95%, and 110%, respectively. Therefore, it is possible that gambling in Experiment 1 was similar across conditions because changes in percentage payback were confounded with win probability and size. That is, gambling may have been maintained under low-percentage-payback conditions because the wins, although small, had a high probability of occurrence. Similarly, gambling under high-percentage-payback conditions may have been low because the wins, although large, had a low probability of occurrence. The purpose of Experiment 2 was to investigate the effects of win probability a nd size on gambli ng. To determ i ne whether the probabi lit y and size of the wins would affect gambling in the absence of any changes in percentage payback, three levels of win probability and size were investigated while percentage payback was held constant. Method Participants. Participants were 3 college students (1 female, 2 male) recruited from Western Michigan University. The recruitment process and SOGS criteria were the same as in Experiment 1. The SOGS scores of the participants in Experiment 1 were 1, 1, and 2 for Participants 16, 25, and 26 respectively. The average total earnings were $ (SD = 4.72), which averaged $7.58 (SD = 0.24) per hour. Apparatus and slot-machine simulation. The apparatus and slotmachine simulation was the same as in Experiment 1. Procedures. Experiment 1 showed that there was no reliable difference in gambling across percentage payback values raging from 50% to 110%. Thus, a midrange percentage payback (75%) was selected
15 Slot-Machine Gambling, Percentage Payback 419 for use in Experiment 2. The percentage payback was held constant at 75% across all conditions. To keep percentage payback constant, it was necessary to manipulate both win probability and win size simultaneously across conditions. Participants were exposed to three levels of win probability and size (WPS). Conditions were designated by win probability (WP; 0.05,.015, and 0.25) and win size (S; S for small, M for medium, and L for large). In the WPS 0.05L condition, 8- and 16-credit wins were possible and winning trials occurred with a probability of In the WPS 0.15M condition, 2-, 4-, and 8-credit wins were possible and winning trials occurred with a probability of In the WPS 0.25S condition, 1-, 2-, and 4-credit wins were possible and winning trials occurred with a probability of Therefore, these conditions roughly consisted of many small wins, several mediumsized wins, or a few large wins. Outcomes were generated the same way as Experiment 1 at the PP75 level; however, the outcome selection process was also based on win probability and win size. For each condition, a series of random outcomes containing only the appropriate win sizes was generated. Then, six blocks of 40 outcomes that were +2% of the programmed win probability and within +5% of 75% payback were used to create a 240-outcome session. No block was used twice, and therefore all sessions within each level of win probability and size were unique. Winning outcomes were the same as in Experiment 1. Each level of win probability and size was replicated once. All other aspects of the procedure, including the forced-exposure sessions, were the same as in Experiment 1. Results Figure 6 shows the number of credits remaining at the end of each session and the total trials per session for all participants. Total trials for Participant 25 tended to be higher in the WPS 0.25S condition than in the other two conditions, suggesting that gambling was sensitive to the win probability and size manipulation. Responding during the first exposure to WPS 0.05L condition was initially high and variable but then quickly dropped to a low level. Responding during the replication of this condition was also low. A similar low level of responding was also observed in the first exposure and replication of the WPS 0.15M condition. Participants 16 and 26 showed no sensitivity to changes in win probability and size. Participant 16 responded consistently through the first 15 sessions, placing approximately 35 bets per session, although a slight decreasing trend across the condition was observed. In Session 16, Participant 16 placed 133 bets and ended the session with 8 credits. After Session 16, responding decreased to approximately 10 total trials per session (M = 10.29) and remained at this level for all subsequent sessions. Participant 26 responded at a low level (M = 30 total trials per session) throughout most of the experiment. For this participant, the number of credits remaining at the end of a session was very consistent. Throughout the experiment, Participant 26 ended a session with fewer than 40 credits only twice in 39 sessions.
16 420 Brandt and Pietras Figure 6. Total trials (filled circles) and credits remaining (open triangles) per session for Participants 16 (P16), 25 (P25), and 26 (P26). Phase labels 0.05, 0.15, and 0.25 indicate win probability and size conditions WPS 0.05L, WPS 0.15M, and WPS0.25S, respectively.
17 Slot-Machine Gambling, Percentage Payback 421 Figure 7 shows the median experienced win probability for all sessions within each condition. The first and second bars for each condition show the experienced win probability for the first and second (replication) exposures, respectively. Experienced win probability sometimes differed from the programmed levels because participants could quit a session at any time. For example, participants in the WPS 0.05L typically experienced a win probability closer to 0.10 than to However, Figure 7 shows that, overall, a lower experienced win probability was typically observed in lower win-probability and win-size conditions. Figure 7. Median experienced win probability for all sessions of each condition for participants in Experiment 2. The interquartile range is indicated by the upper and low limits of the error bars. The first bar for each condition shows the values for the first exposure to a condition, and the second bar shows the values for the replications.
18 422 Brandt and Pietras As in Experiment 1, verbal reports were collected to informally assess participants gambling strategies. Reports by 2 participants (Participants 16 and 26) suggested that they tried to keep the total number of credits at the end of each session above a target level (48 and 40, respectively). Participant 16 s gambling performance was generally inconsistent with this strategy during the first half of the experiment (only 25% of sessions were ended with 48 or more credits remaining) but was quite consistent with this strategy during the latter half of the experiment (75% of sessions were ended with 48 or more credits remaining). Participant 26 s gambling was consistent with the reported target level in 95% of sessions. Participant 25 reported, The strategy I came to use toward the end of the study was to win more than the starting amount and get out. While this participant did have more than 50 credits remaining in several sessions during the second exposure to the WPS 0.05L condition, overall, there was little consistency between this strategy and the participant s performance. Discussion Three participants were exposed to three levels of win probability and size as percentage payback was held constant. Gambling in only 1 participant (Participant 25) varied across win probability and size conditions. Participant 25 tended to place more bets in the WPS 0.25S (high win probability, low win size) condition than in the other two conditions. The performance of Participant 25 was therefore consistent with previous research showing that options delivering high-probability, low-value outcomes are generally preferred to options delivering low-probability, high-value outcomes (Dixon et al., 2006; Kendall, 1987). Because gambling in only 1 participant varied across win probability and size manipulations, it seems unlikely that the influence of win probability and size on gambling can fully explain the insensitivity of behavior to changes in percentage payback shown in Experiment 1. It is uncertain why gambling in the other 2 participants (Participants 16 and 26) was insensitive to the win probability and size manipulations, but one possible reason is that in these participants gambling occurred at low levels. Such low levels of gambling may have obscured any effects that win probability and size may have had on responding. It is likely that gambling occurred at low levels in these participants because the percentage-payback was below 100%. In Experiment 1, there were no systematic effects on gambling of manipulating the percentage-payback value, so in Experiment 2 a midrange percentagepayback value (75%) was used. At this level of percentage payback, however, repeated gambling produces a net loss in earnings. As with participants in Experiment 1, gambling by Participants 16 and 26 either gradually decreased across conditions or was relatively low across all conditions, indicating that behavior was sensitive to the loss in earnings produced by gambling. It is possible that responding would have been more sensitive to changes in win probability and size if higher percentage-payback values were used. Because gambling by 2 of the 3 participants did not vary across win probability and size manipulations, their performance differs from that shown in the gambling study by Dixon et al. (2006), which also used simulated slot machines. Procedural differences may account for this discrepancy. As described above, Dixon et al. investigated the effects of win probability and size on gambling using a choice procedure rather than a single-option
19 Slot-Machine Gambling, Percentage Payback 423 procedure. Moreover, gambling in each participant was studied for only a brief period (50 min) under a percentage payback of 100%. As in Experiment 1, participants completed a postexperimental questionnaire that asked them to describe any strategies they may have used during the experiment to earn money. Although the validity of such self-report data is suspect, as noted above, the purpose was to gather information about variables that might have influenced gambling and contributed to individual differences in responding. The verbal reports were similar to those collected in Experiment 1 in that participants reports suggested that they tried to keep session earnings above specific target values. Furthermore, verbal reports in 2 of the 3 participants were often consistent with their gambling patterns. General Discussion The present experiments were investigations of the effects of percentage payback (Experiment 1) and win probability and size (Experiment 2) on gambling in human adults on a slot-machine simulation. The results showed that at least across the range of percentage payback and win probability and size values studied here, gambling in most participants was insensitive to percentage payback and win probability and size. The primary goal of Experiment 1 was to explore the possibility that the insensitivity of gambling to percentage-payback reported in prior studies (Schreiber & Dixon, 2001; Weatherly & Brandt, 2004) was due to an insufficient exposure to percentagepayback conditions. Experiment 1 systematically replicated the Weatherly and Brandt study using a parametric single-subject design that provided participants with a greater exposure to the percentage-payback conditions. Despite the greater exposure, gambling in 4 of 5 participants in Experiment 1 did not vary as a function of percentage-payback value. In Experiment 2, whether gambling would vary as a function of win probability and size was investigated and only 1 of 3 participants (Participant 25) showed sensitivity to this manipulation. Experiment 2 therefore provided only limited support for the view that the variations in win probability and size were responsible for the lack of effect of percentage payback on gambling in Experiment 1. Although gambling was generally insensitive to across-condition changes in percentage payback and win probability and size, gambling in most participants appeared to be sensitive to net earnings. As described above, whenever the percentage payback was below 100%, participants could maximize their earnings by not gambling (i.e., quitting without placing any bets). In Experiments 1 and 2, by the end of the study, gambling by 6 of 8 participants (Participants 1, 2, 7, 16, 22, and 26) had decreased to a low level. The low levels of gambling indicate sensitivity to the gambling contingency and are generally consistent with previous risky-choice research showing that behavior in adult humans is typically risk-averse (Hershey & Schoemaker, 1980; Pietras & Hackenberg, 2003; Schneider, 1992; Schneider & Lopes, 1986). The low levels of gambling in both experiments were observed only after participants had experienced several experimental sessions, suggesting that the repeated experience with the gambling contingency produced the decrease in responding. In several instances, gambling abruptly decreased after a session in which a large loss of credits was experienced, indicating that the lower session earnings may have had a suppressive (punishing) effect on gambling.
20 424 Brandt and Pietras One benefit of investigating gambling repeatedly across many sessions was that gambling could be evaluated under steady-state conditions. During the first few sessions of the experiment, gambling in most participants occurred at a high level but varied substantially from session to session. By the end of the experiment, most participants gambling had decreased to a low level (see Figures 1, 2, and 6). Thus, gambling levels in the first few sessions of the experiment were often not representative of gambling in later sessions, and gambling levels in the first exposure to a condition often did not resemble gambling levels in subsequent replications. The present findings therefore suggest that gambling procedures that give participants an extended exposure to a gambling task might produce different levels or patterns of gambling than procedures that give participants only a brief exposure to conditions. Most previous investigations of gambling on slotmachine simulations have exposed participants to conditions only briefly, such as for a single session. Such brief exposures do not allow performance to repeatedly contact the outcomes of gambling, and therefore gambling levels may not represent stable responding. Given that gambling in most participants eventually decreased to a low level, it is perhaps not surprising that gambling in most participants did not vary across conditions of percentage payback or win probability and size. It is possible that under other procedures greater sensitivity to these variables would be observed. For example, if the effects of win probability and size were investigated across a higher level of percentage payback, then gambling may differ more substantially across conditions. In addition, if gambling was studied using concurrent-operant procedures rather than a single-operant preparation, it is likely that there may be greater sensitivity to percentage payback. As described above, Dixon, MacLin, and Daugherty (2006) investigated the effects of win probability and size on gambling using a concurrent preparation and found that slot machines that delivered frequent, small wins were preferred to those that delivered infrequent, large wins. If participants are given repeated choices between two slot machines that differ in percentage payback, then gambling may also be sensitive to differences in percentage-payback values. With percentage-payback values below 100%, however, the effects of percentage payback on gambling may be transitory given that gambling may eventually decrease. Self-reported strategies were collected for 6 participants across Experiments 1 and 2. Four participants reported a strategy that specified an earnings target or a statement about the minimum level of earnings that was acceptable during a session. Interestingly, gambling was often consistent with their reported strategies. The finding that participants reported specific earning targets for the number of credits remaining per session is consistent with previous risky-choice research that has shown that participants often report a target outcome (sometimes called an aspiration level) for their choices (e.g., Lopes, 1984; Lopes & Oden, 1999). Furthermore, these data raise the possibility that differences in target values may contribute to individual differences in the level or patterns of gambling. Although participants gambling patterns were often consistent with their reported strategies, it is uncertain whether these strategies or target functioned as self-generated rules. The present study was not explicitly designed to evaluate self-generated rules, and verbal reports were not collected in a manner that permitted a more precise analysis of their potential effects.
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