# Banking on a Bad Bet: Probability Matching in Risky Choice Is Linked to Expectation Generation

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3 Probability Matching and Expectation Generation 79 choices (7% vs. 44% of participants, respectively), χ 2 (1, N = 127) = 8.4, p =.4. Strict probability matching (predicting the more-likely outcome on 7 of choices), by contrast, was common in the repeated-games condition but not in the unique-games condition (38% vs. 3% of participants, respectively), χ 2 (1, N = 127) = 24.1, p <.1. Experiment 2 In Experiment 1, the various games presented in the uniquegames condition all shared common outcome probabilities of 7% and 3%. This was noted in the instructions given to participants, but how these probabilities were presented varied across the games. In some games, these probabilities were stated directly or given as relative frequencies of occurrence; in other games, the probabilities could be inferred from characteristics of the chance device (e.g., a draw from a bag of tickets, of which 7 were orange and the other 3 were black). Experiment 2 tested whether individuating the outcomes in the sequence would decrease probability matching and increase maximizing even when the games were all based on a common chance device. University of Waterloo undergraduates (N = 129) completed Experiment 2 online in exchange for psychology course credit. They were asked to consider a game involving rolls of a -sided die and to predict the outcome of each roll. Seven sides of the die, they were told, were marked one way, and the remaining 3 sides were marked another way. In the repeatedgames condition, all rolls involved a die with 7 red sides and 3 green sides. In the unique-games condition, each roll was said to involve a different die with unique markings. For instance, in addition to the die marked with red and green sides, another die had 7 sides marked with triangles and 3 sides marked with squares. Other markings included letters and icons, such as flowers and hearts. Data from 1 participant who predicted the unlikely outcome more often than the likely outcome were excluded, as were data from a second participant who did not complete the entire prediction task. For some participants in the repeated-games condition, the sequence was described as a single game consisting of rolls of the die, and for other participants, it was described as games of 1 roll each. This factor had no influence on the results. As Figure 2 shows, participants in the unique-games condition (n = 38) were more likely than those in the repeated-games condition (n = 89) to engage in strict maximization, that is, to predict the more-likely outcome in all choices (76% vs. 56% of participants, respectively), χ 2 (1, N = 127) = 4.6, p =.3. Strict probability matching, by contrast, was more prevalent in the repeated-games condition than in the unique-games condition (18% vs. 3% of participants, respectively), χ 2 (1, N = 127) = 5.4, p =.2. Experiment 3 In Experiments 1 and 2, introducing individuating features to the outcome sequence reduced probability matching and increased rates of maximizing. We suggest that this is because 9 8 Repeated-Games Condition Unique-Games Condition Fig. 2. from Experiment 2: distribution of the number of predictions of the more-likely

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