Predicting Outcomes in a Sequence of Binary Events: Belief Updating and Gambler's Fallacy Reasoning (original) (raw)

Do Causal Beliefs Influence the Hot-Hand and the Gambler's Fallacy?

An open problem in the study of randomness perception is why, given the same sequence of independent and equiprobable events, sometimes people exhibit a positive recency effect (hot hand fallacy) and sometimes a negative recency effect (gambler's fallacy). In this paper we provide evidence of the role of causal belief about the source generating the sequence in predicting the next outcome. People that faced a streak with a nonrandom generating source tended to commit the hot hand fallacy, while people that faced a streak with a random source tended to commit the gambler's fallacy. No differences between the generating source were found in sequences that looked random.

Extending the two faces of subjective randomness: From the gambler's and hot-hand fallacies toward a hierarchy of binary sequence perception

Memory & cognition, 2015

In this study, we examined perceptions of binary sequences under uncertainty in an attempt to depict a holistic and unifying framework. The first experiment applied a projection method that motivated participants to observe binary series and provide descriptions of their possible underlying mechanisms or processes. This procedure revealed four distinct perceptual categories: two previously studied categories of chance mechanisms and human performance, associated with the gambler's and hot-hand fallacies, and two newly identified categories-periods and processes and traits and preferences. The next three experiments tested the associations between the four categories and the alternation rates of the observed sequences under three categorical decisions structures: screening, discrimination, and classification. The results reveal the relativity of binary sequence perception. They show that the categories of chance mechanisms and periods and processes reflected rather stable percept...

Losses and External Outcomes Interact to Produce the Gambler's Fallacy

When making serial predictions in a binary decision task, there is a clear tendency to assume that after a series of the same external outcome (e.g., heads in a coin flip), the next outcome will be the opposing one (e.g., tails), even when the outcomes are independent of one another. This so-called " gambler's fallacy " has been replicated robustly. However, what drives gambler's fallacy behavior is unclear. Here we demonstrate that a run of the same external outcome by itself does not lead to gambler's fallacy behavior. However, when a run of external outcomes is accompanied by a concurrent run of failed guesses, gambler's fallacy behavior is predominant. These results do not depend on how participants' attention is directed. Thus, it appears that gambler's fallacy behavior is driven by a combination of an external series of events and a concurrent series of failure experiences.

What's next? Judging sequences of binary events

Psychological Bulletin, 2009

The authors review research on judgments of random and nonrandom sequences involving binary events with a focus on studies documenting gambler's fallacy and hot hand beliefs. The domains of judgment include random devices, births, lotteries, sports performances, stock prices, and others. After discussing existing theories of sequence judgments, the authors conclude that in many everyday settings people have naive complex models of the mechanisms they believe generate observed events, and they rely on these models for explanations, predictions, and other inferences about event sequences. The authors next introduce an explanation-based, mental models framework for describing people's beliefs about binary sequences, based on 4 perceived characteristics of the sequence generator: randomness, intentionality, control, and goal complexity. Furthermore, they propose a Markov process framework as a useful theoretical notation for the description of mental models and for the analysis of actual event sequences.

Perception of randomness and predicting uncertain events

Thinking & Reasoning, 2008

Four types of relatively consistent strategies of predicting uncertain binary events have been identified: (1) a strategy insensitive to short-run sequential dependencies involving the prediction of the long-run majority category -thereafter the long-horizon momentum strategy;

The Gambler's and Hot-Hand Fallacies: Theory and Applications

Review of Economic Studies, 2010

The Gambler's and Hot-Hand Fallacies: Theory and Applications* We develop a model of the gambler's fallacy -the mistaken belief that random sequences should exhibit systematic reversals. We show that an individual who holds this belief and observes a sequence of signals can exaggerate the magnitude of changes in an underlying state but underestimate their duration. When the state is constant, and so signals are i.i.d, the individual can predict that long streaks of similar signals will continue -a hot-hand fallacy. When signals are serially correlated, the individual typically under-reacts to short streaks, over-reacts to longer ones, and under-reacts to very long ones. We explore several applications, showing, for example, that investors may move assets too much in and out of mutual funds, and exaggerate the value of financial information and expertise.

The perception of probability

Psychological Review, 2014

We present a computational model to explain the results from experiments in which subjects estimate the hidden probability parameter of a stepwise nonstationary Bernoulli process outcome by outcome. The model captures the following results qualitatively and quantitatively, with only 2 free parameters: (a) Subjects do not update their estimate after each outcome; they step from one estimate to another at irregular intervals. (b) The joint distribution of step widths and heights cannot be explained on the assumption that a threshold amount of change must be exceeded in order for them to indicate a change in their perception. (c) The mapping of observed probability to the median perceived probability is the identity function over the full range of probabilities. (d) Precision (how close estimates are to the best possible estimate) is good and constant over the full range. (e) Subjects quickly detect substantial changes in the hidden probability parameter. (f) The perceived probability sometimes changes dramatically from one observation to the next. (g) Subjects sometimes have second thoughts about a previous change perception, after observing further outcomes. (h) The frequency with which they perceive changes moves in the direction of the true frequency over sessions. (Explaining this finding requires 2 additional parametric assumptions.) The model treats the perception of the current probability as a by-product of the construction of a compact encoding of the experienced sequence in terms of its change points. It illustrates the why and the how of intermittent Bayesian belief updating and retrospective revision in simple perception. It suggests a reinterpretation of findings in the recent literature on the neurobiology of decision making.