Behavioral analysis of habit formation in modern slot machine gambling

Figures & data

Figure 1. The ‘Cleo’s Gold’ slot machine simulation task. Top: a screen capture from the game’s main graphical display that depicts one segment of a multiline win animation involving the ‘wild’ pyramid symbol. The artwork was from a commercial graphics set (Envato Pty Ltd., Melbourne, VIC), used under license. Touch input was disabled on the display. Bottom: an illustration of the button panel configuration with which participants gambled. Participants configured the number of lines (top button row) and/or the bet amount per line (bottom button row), or used the repeat bet button, for each spin.

Table 1. Descriptive statistics of gambling sessions.

	Gambling session
	1 (n = 10,715)	2 (n = 10,872)	3 (n = 10,525)
Categorical variable counts and percentages
Losses	7567 (70.62%)	7641 (70.28%)	7405 (70.36%)
Losses disguised as wins	1484 (13.85%)	1524 (14.02%)	1467 (13.94%)
Wins	1664 (15.53%)	1707 (15.70%)	1653 (15.71%)
Bet switches	4762 (44.44%)	3846 (35.38%)	3470 (32.97%)
Credits exceeded $15 bonus	1813 (16.92%)	2739 (25.19%)	2143 (20.36%)
Numeric variable means and standard deviations
Spin initiation latency (s)	2.52 (3.55)	1.69 (1.94)	1.38 (1.31)
Bet denomination (credits)	2.60 (1.49)	2.51 (1.52)	2.44 (1.56)
Lines played	21.17 (15.51)	21.72 (15.42)	21.73 (15.81)
Total bet size (credits)	61.34 (63.13)	61.00 (61.62)	60.44 (64.20)
Loss streak length	4.55 (5.98)	4.81 (7.26)	5.61 (9.83)
Win magnitude (credits)	206.01 (423.06)	206.06 (394.33)	202.50 (385.62)
Credit balance	4335.86 (1387.18)	4518.62 (1571.43)	4296.33 (1472.03)
Final credit balance	4130.34 (1768.61)	4316.57 (1663.55)	4088.69 (1775.84)
Session length (min)	24.35 (4.74)	21.89 (3.66)	20.53 (3.59)

Note: N indicates the total number of observations (i.e. spins) with which the descriptive statistics were calculated. Statistics for Final Credit Balance and Session Length use single data points collected at the end of each session. Frequency counts and the proportion of occurrence among all spins (parentheses) are reported for the categorical variables. Mean and standard deviations (parentheses) are reported for continuous variables. All values were calculated before removal of spin latency outliers and following the removal of trials occurring during bonus rounds and at the beginning and end of gambling sessions. Values for Loss Streak Length and Win Magnitude were calculated only on losing and winnings trials, respectively. All values are for the untransformed variables.

Figure 2. Plots depicting predicted probabilities for models integrating winning and losing trials. Models for log transformed Spin Initiation Latency (ms) and Bet Switching log odds are depicted in the top and bottom rows, respectively. Predicted probabilities for both outcome variables are plotted as a function of Trial Type (Losses, Losses Disguised as Wins, and Wins; displayed across the horizontal facets), Trial Number, and Session. The models controlled for Credit Balance (centered at the grand mean) and Sequence version (averaging across Sequences A to C). Probabilities for Spin Initiation Latency additionally controlled for Bet Switching (centered on trials that were repeat bets).

Table 2. Regression results for models separating wins and losses.

	Spin initiation latency after a win			Bet switching after a win			Spin initiation latency after a loss			Bet switching after a loss
Predictors	Estimate	95% CI	p	Odds ratio	95% CI	p	Estimate	95% CI	p	Odds ratio	95% CI	p
Trial number	−0.0017	−0.0019, −0.0016	<.001	0.99694	0.99603, 0.99785	<.001	−0.0024	−0.0026, −0.0023	<.001	0.99378	0.99316, 0.99439	<.001
Session	−0.20	−0.21, −0.18	<.001	0.81170	0.76081, 0.86600	<.001	−0.24	−0.25, −0.23	<.001	0.69649	0.66754, 0.72669	<.001
Bet change	0.37	0.35, 0.40	<.001				0.42	0.40, 0.44	<.001
Credit balance (log)	0.000016	0.0000084, 0.000023	<.001	0.99995	0.99991, 0.99999	0.017	0.000023	0.000017, 0.000029	<.001	0.99990	0.99987, 0.99993	<.001
Sequence B Sequence A	−0.0077	−0.033, 0.017	0.543	0.73410	0.64396, 0.83685	<.001	−0.030	−0.049, −0.010	0.003	0.77325	0.70873, 0.84364	<.001
Sequence C Sequence A	−0.10	−0.13, −0.077	<.001	0.69350	0.60833, 0.79060	<.001	−0.077	−0.095, −0.059	<.001	0.73658	0.67781, 0.80044	<.001
Trial number × Session	0.0014	0.0011, 0.0016	<.001	1.00196	1.00085, 1.00307	<.001	0.0015	0.0013, 0.0016	<.001	1.00309	1.00234, 1.00385	<.001
Win magnitude (log)	0.078	0.070, 0.085	<.001	1.06292	1.02318, 1.10421	0.002
Trial number × Win magnitude (log)	0.000001	−0.00012, 0.00012	0.987	1.00025	0.99963, 1.00087	0.426
Session × Win magnitude (log)	0.011	0.0026, 0.019	0.011	1.02312	0.97883, 1.06941	0.311
Trial number x Session × Win magnitude (log)	−0.000060	−0.00021, 0.000086	0.422	1.00046	0.99970, 1.00123	0.233
Loss streak (log)							−0.049	−0.058, −0.039	<.001	0.96598	0.92636, 1.00729	0.105
Trial number × Loss streak (log)							0.000037	−0.00012, 0.00019	0.636	0.99868	0.99794, 0.99942	<.001
Session × Loss streak (log)							−0.011	−0.022, −0.00071	0.037	0.92911	0.88463, 0.97584	0.003
Trial number × Session × Loss streak (log)							−0.00015	−0.00033, 0.000037	0.118	0.99829	0.99738, 0.99920	<.001
Observations	9351			9499			22,384			22,613

Note: CI = Confidence Interval. Trial Number was centered at trial 100 and Session was centered to session 2. All continuous predictors were grand mean centered. Estimates for Sequences B and C consider Sequence A as the reference category. Bet Switching was binary coded according to whether the participant switched their bet (1) or repeated it (0) and was included as a predictor only for Spin Initiation Latency models. All models used robust estimation. Estimates for Spin Initiation Latency are reported to two significant figures.

Table 3. Slope estimates for trial number for gambling sessions 1 and 3.

	Trial number
Model	Session	Estimate	95% CI	p
Spin initiation latency after a win	1	−0.0031	−0.0034, −0.028	<0.001
	3	−0.00037	−0.0063, −0.00010	0.007
Spin initiation latency after a loss	1	−0.0039	−0.0041, −0.0037	<0.001
	3	−0.00098	−0.0012, −0.00077	<0.001
Bet switching after a win	1	0.99500	0.99359, 0.99640	<0.001
	3	0.99890	0.99744, 1.00036	0.138
Bet switching after a loss	1	0.99071	0.98978, 0.99165	<0.001
	3	0.99685	0.99585, 0.99786	<0.001

Note: Estimates for bet switching models represent odds ratios. Estimates for spin initiation latency are reported to two significant figures.

Data availability statement

The data and analysis scripts that support the findings of this study are openly available in the UBC Dataverse Collection at https://doi.org/10.5683/SP3/KWJTFU.