Am I Winning or Losing? Probing the Appraisal of Partial Wins via Response Vigor

Attempts to obtain rewards are not always successful. Despite investing much time, effort, or money, sometimes individuals may not obtain any reward. Other times they may obtain some reward, but the obtained reward may be smaller than their initial investment, such as partial wins in gambling. It remains unclear how such ambiguous outcomes are appraised. To address this question, we systematically varied the payoffs for different outcomes in a computerized scratch card task across three experiments. To test outcome appraisal, we used response vigor as a novel proxy. In the scratch card task, participants turned three cards one by one. Depending on the turned cards, they either received an amount that was higher than the wager (win), an amount lower than the wager (partial win), or nothing (loss). Overall, participants responded to partial wins more slowly than losses, but more quickly than wins. Partial wins were therefore appraised to be better than losses, but worse than wins. Importantly, further analyses showed that outcome appraisal was not based on the net win or loss amount. Instead, participants primarily used the configuration of turned cards as a cue for the relative rank of an outcome within a specific game. Outcome appraisals thus utilize simple heuristic rules, rely on salient information (such as outcome-related cues in gambling), and are specific to a local context. Together, these factors may contribute to the misperception of partial wins as real wins in gambling. Future work may examine how outcome appraisal may be modulated by the salience of certain information, and investigate the appraisal process in contexts beyond gambling. Supplementary Information The online version contains supplementary material available at 10.1007/s10899-023-10216-z.


Testing log
Data collection for Experiment 1 took place on 5 Sep 2019.101 participants signed up and finished the experiment. 2 participants initially signed up for the experiment but did no finish the experiment in time (e.g., timed out).Another 9 participants initially signed up but later returned.No data were registered for the latter 11 participants.

Figure S1
Reaction times of all eight responses within an 'episode' in Experiment 1. Error bars stand for 95% within-subjects confidence intervals.

APPRAISAL OF PARTIAL WINS
Figure S1 shows the mean reaction times of all eight responses within one 'episode' of play, as a function of both the amount level and outcome of the current round.

Table S1
Linear regression and pairwise comparisons on start RTs in Experiment 1. Note.lowerCI = lower limit of 95% confidence interval; upperCI = upper limit of 95% confidence interval; BF = Bayes factor; gav = Hedges's average g.P values for the pairwise comparisons were corrected for multiple comparisons with the Holm-Bonferroni method.

Predictor
The analyses on the start RTs (the "Start (next)" phase in Figure S1) showed consistent results as those observed on confirm RTs, although the effect sizes were overall smaller (see Table S1).To control for the effect of proximity, we similarly computed the difference between AAA/ABB and ABC for both the current experiment and Experiment

RTs across all stages
Figure S2 shows the mean reaction times of all eight responses within one 'episode' of play, as a function of both the amount level and outcome of the current round.

Analyses on the start RTs
The results on start RTs were again consistent with those on confirm RTs (Table S2).The difference between AAB/ABB and ABC in start RTs was again larger in For the new comparison between a win and a partial win with the same presented win amount, participants started a new round more slowly after AAA 2-10 (M = 648.5,SD = 258) compared to AAB/ABB 20-10 (M = 620.9,SD = 257.9),diff = 27.6,95% CI = [3.5, 51.9], t(103) = 2.26, p = 0.026, BF = 1.23, gav = 0.107.However, the effect size was smaller than that observed on confirm RTs, and the Bayes factor was inconclusive, which might be due to that the start response was the second response following an outcome.
Overall, the analyses on start RTs thus yielded the same pattern of results.

Table S2
Linear regression and pairwise comparisons on start RTs in Experiment 2. Note.lowerCI = lower limit of 95% confidence interval; upperCI = upper limit of 95% confidence interval; BF = Bayes factor; gav = Hedges's average g.P values for the pairwise comparisons were corrected for multiple comparisons with the Holm-Bonferroni method.

Testing log
Data collection for Experiment 3 took place between 14-16 Dec 2021.264 participants signed up and finished the experiment.3 participants were timed out (no data recorded).20 participants initially signed up but returned (no data recorded).

BFs during sequential sampling
Figure S3 showed the evolution of the Bayes factors during sequential sampling.

Memory of the payoff information
At the end of Experiment 3, participants were presented with the three types of games one by one, and asked to type in the wager and the presented 'win' amount for each outcome.To do the scratch card task, they did not need to remember this payoff

Figure S3
Bayes factors from the four planned comparisons during sequential testing in Experiment 3.
information, as the different 'win' amounts for the different outcomes were always presented on the top of the screen.We nevertheless explored the answers provided by participants, and examined whether these answers influenced the main comparisons of interest in a set of exploratory analyses.
Participants answered 12 questions in total (4 questions for each game).The memory data from one participant was missing, thus the sample contained 249 participants.The overall memory accuracy was high, M = 83.2%,SD = 19.8%.1.74% of the answers were numbers that had never occurred in the task (e.g., one participant indicated winning 70 pence in a Type 1 game, while there was no 70-pence chip) and were therefore excluded.For the remaining answers, the proportion of each answer occurring for each question was computed and plotted (Figure S4).
Descriptively, the memory accuracy for the 'win' amount for AAB/ABB and AAA outcomes in Type 3 games was lower than those in Type 1 and Type 2 games.Note that AAB/ABB in Type 1 and 2 games were worth 20 pence, but 0 pence in Type 3 games.
AAA in Type 1 and 2 games were worth 60 pence, but 20 pence in Type 3 games.The mismatch between Type 3 games, on the one hand, and Type 1 and Type 2 games, on the other hand, may explain why memory for AAB/ABB and AAA amount was reduced in Type 3 games.Note that for the loss amount, memory was highly accurate for all three types of games, as a loss (i.e., ABC) was always associated with 0 pence.
Next we examined whether memory would influence the four primary comparisons reported in the main text.First, we selected participants who answered all 12 questions correctly.One hundred and seven participants met this criterion.Using this subset of participants, we repeated the four comparisons (Table S3).The results were descriptively all in line with the ones reported in the main text.While Comparison (3) between AAB/ABB 10-20 and AAA 10-20 was still statistically significant, the BF was no longer conclusive.For Comparison (4) between AAB/ABB 30-20 and AAB/ABB 10-0 , the BF now provided moderate support for the alternative hypothesis, in the predicted direction.

Table S3
Pairwise comparisons on confirm RTs in Experiment 3 (N = 107 participants who answered all 12 questions correctly).Only including participants who answered all 12 questions correctly seemed to be a rather stringent requirement.Indeed, fewer than half of the 250 participants met this inclusion criterion.We thus repeated the analyses above, but this time using a more lenient criterion.That is, for each comparison, we included data from participants who correctly remembered the wagers and 'win' amounts for the current comparison (regardless of whether they remembered the payoff for other outcomes correctly or not).The sample sizes involved in each comparison thus differed.Again, the results were descriptively in line with the ones reported in the main text, and only Comparisons (3) and (4) were statistically reliable (Table S4).

Table S4
Pairwise comparisons on confirm RTs in Experiment 3 (participants who remembered the payoffs correctly for each comparison).

Wager amount in appraisals
Table S5 Exploratory pairwise comparisons on the effect of wager amount on confirm RTs and start RTs in Experiment 3.
To further explore whether participants incorporated the wager amount into their appraisals of different outcomes, we selected pairs where both the card configuration and  S5 for the corresponding results).
the presented 'win' amount was matched, with only the wager amount differed.Three new pairs were compared (see Figure S5 and Table S5).For Comparison (1), participants responded to AAA 30-60 more quickly than AAA 10-60 , for both confirm RTs and start RTs.
However, the p values were close to .05, and the BFs were inconclusive.There was thus some evidence that participants incorporated the wager amount when appraising wins.
Response vigor after losses showed a different pattern.When confirming losses, wager amount had no effect.However, when starting a new trial, wager amount had reliable effects (Comparisons (2) and ( 3)).Participants started a new trial more quickly after ABC 30-0 than ABC 10-0 .This result is in line with that observed for AAB/ABB in the manuscript (Comparison (3), between AAB/ABB 30-20 and AAB/ABB 10-20 ).When the wager was made salient as in Experiment 3, participants thus could incorporate the wager amount into their appraisals of outcomes, but this might take some time (at least for AAB/ABB and ABC outcomes).

Presented 'win' amount in appraisals
In another set of exploratory analyses, we evaluated the effect of presented 'win' amount on response vigor, with both the wager amount and the card configurations matched.We identified and compared two pairs (see Figure S6).S6 for the corresponding results).Note.lowerCI = lower limit of 95% confidence interval; upperCI = upper limit of 95% confidence interval; BF = Bayes factor; gav = Hedges's average g.P values were not corrected for multiple comparisons.
The results on confirm RTs were broadly in line with those observed in Experiments 1 and 2. While confirm RTs after AAA were modulated by the win amount, confirm RTs after AAB/ABB were not.For start RTs, the results showed a different pattern.Start RTs after both AAA and AAB/ABB were modulated by the presented 'win' amount.In line with the exploratory analyses presented in the previous section, for the best outcome (i.e., AAA), participants incorporated the presented 'win' amount into the appraisal, while for other outcomes (i.e., AAB/ABB) it might take some time.
Figure S2Reaction times of all eight responses within an 'episode' in Experiment 2. Error bars stand for 95% within-subjects confidence intervals.

Figure S4 Proportion
Figure S4 Proportion of answers provided by participants in the memory test in Experiment 3. The green bar stands for the correct answer for each question.Loss = ABC, Partial Win = AAB/ABB, Win = AAA.

Figure S5 Confirm
Figure S5 Confirm RT (left) and Start RT (right) as a function of outcome and game type in Experiment 3. Error bars stand for 95% within-subjects confidence intervals.The numbers in red, green and blue stand for the wager and the presented win amount in each game (wager-win).The numbers 1-3 in black show the two cells involved in each of the three comparisons (see TableS5for the corresponding results).

Figure S6 Confirm
Figure S6 Confirm RT (left) and Start RT (right) as a function of outcome and game type in Experiment 3. Error bars stand for 95% within-subjects confidence intervals.The numbers in red, green and blue stand for the wager and the presented win amount in each game (wager-win).The numbers 1-2 in black show the two cells involved in each of the three comparisons (see TableS6for the corresponding results).

Table S6
Exploratory pairwise comparisons on the effect of presented 'win' amount on confirm RTsand start RTs in Experiment 3.