Preference for playing order in games with and without replacement: Motivational biases and probability misestimations

This research explores the preference for playing order in games in which each of several players draws a random event (e.g., a ball from an urn), with and without replacement after each draw. Three studies show that people tend to prefer to draw early regardless of whether the game is with or without replacement, although the expected probability of winning is the same irrespective of the draw order. The reasons for preferring earlier draws differ depending on the game type. For games without replacement, the biased preference for earlier draws is related to multiple motivational factors such as aversion to uncertainty, ambiguity, and uncontrollability. Game valence also affects draw order preference through the misestimation of winning probabilities: people tend to prefer earlier draws in a gain-dominant game (i.e., a higher probability of winning) but prefer later draws in a loss-dominant game (i.e., a higher probability of losing). For games with replacement, preference for earlier draws is mainly explained by uncertainty aversion, with little bias in probability estimations.