Abstract: In risky decision making, the subtle interplay between single-play and multiple-play is well illustrated by the literature that has followed an early paper by Paul Samuelson (1963). The article summarized the difference between responses for single-play and multiple-play and questioned traditional theoretical explanations. Most risky decision-making theories are based on the same assumption: a rational decision maker behaves as if he or she were attempting to maximize some kind of expectation. However, based on a combination of research evidence, maybe we could infer that the multiple-play and single-play gambles were in fact so utterly different that the short run one was perhaps not based on the expectation rule. From multiple-play to single-play, it is likely to represent a strategy shift from expectation rule to non-compensatory rule (qualitative change) rather than pure change on the number of gamble times (quantitative change). The status and perspectives on the applied researches of multiple-play were introduced and the research prospect was put forward as well.

Key words: multiple-play, single-play, risky decision making, expectation rule