Distributive judgments under uncertainty: Paccioli's game revisited.

Many decision biases arise from the inability to ignore past events. The coherence of decisions is also compromised by the inability to fully use information related to the future. In Paccioli's game, a stake of money goes to the first player to score a certain number of wins. When the game is prematurely interrupted, they may divide the stake according to the proportions of wins relative to rounds played. Alternatively, they may assess the probability that a player would reach the criterion number of wins first if the game were continued. The first decision rule (ratio), which is past-oriented, leads to contradictions across games. The second rule (probability), which is future-oriented, does not. In seven studies, use of the ratio rule emerges across testing methods, in games of chance and games of skill, and independently of extraneous factors (such as random responding, lack of awareness, or proneness to other past-oriented biases).