关键词: 随机序列, 近因效应, 赌徒谬误, 热手谬误

Abstract: The researchers have studied the recency effect in the random sequences perception. It was thought people had two kinds of opposing expectations: the positive recency (the hot hand fallacy ) and the negative recency (the gambler’s fallacy). The existing studies focused on when the two effects would appear and how they would exchange with each other. Kahneman’s “local representativeness heuristic” (1971) was the first cognitive explanation of the recency effect. They identified the “law of small numbers”, which is the erroneous belief that properties of large samples also apply to very small samples, and the “law of small numbers” was the strategy in the predicting process. Moldoveanu and Leager (2002) tried to explain the effect with the casual model. Roney and Trick (2003) gave the Gestalt explanation. They thought that the random sequence recency involved two stages. The first one was about whether to consider the present and former outcomes as a group; when the outcomes were considered as a Gestalt, the perception entered the second stage, in which the subjects would decide the possible relationship between the present and former outcomes. However, Trick didn’t explain the dividing strategy of the random sequences. Our study aims to examine the Gestalt theory and the hypothesis that the dividing is based on the continuation of the same outcomes in the random sequences. That is, in the coin sequences, when the last outcomes are the same (all heads or all tails), the subjects would incline to consider these outcomes as a cognitive group or unit; while the last outcomes are different, they would be divided into different cognitive units. Moreover, the right/wrong sequences of the expectation make up another random binary series. The dividing of the right/wrong sequences is also based on the continuation. The outcomes of the coin and the right/wrong results are divided with the continuation strategy, and then form the different cognitive units depending on three factors--the continuation of the coin, the right/wrongness of the prediction and the continuation of the result series.
Two experiments were conducted with totally 68 sophomores; all were majored in Chinese or culture and society. All subjects had not taken the probability course. Experiment 1 used the traditional paradigm. The subjects were asked to predict the outcomes of the random binary series in a coin tosses game on computer, and were informed the results of the expectations. After each expectation they were asked to value their confident beliefs of the prediction on a 5-point Linkert scale. Experiment 2 was based on the Experiment 1, in which the outcomes were still random but manipulated by the experimenter such that the participants were told that every five trials were a group.
The results indicated: The subjects demonstrated a two-stage process involved in the recency effect. The first stage involved determining whether the present outcome was to be grouped with previous outcomes or considered as a part of a separate unit. The grouping was based on the continuation of the outcomes. If the present outcome was grouped with past ones, then a second stage occurred, one involving a decision about how the past outcomes were related to the present. When the last two outcomes were not the same, they mostly would predict the outcomes rationally; while the same outcomes continued and the last expectation was correct, the positive recency effect would appear; moreover, after several correct predictions, the fallacy diminished and even disappeared. While same outcomes continued but the last expectation was wrong, the negative recency effect would appear. But the negative recency effect was not affected remarkably by the growing wrong expectations.
Overall, this study supports the Gestalt explanation of the random sequences bias and further elaborates the dividing strategy. People first divide the trials according to the continuation of the trials, and then have different expectations. The possible strategy used in the second procedure supports the casual model and the dual-processing theory

Key words: words the random sequences, the recency effect, Gambler’s Fallacy, the hot hand fallacy