Human Wagering Behavior Depends on Opponents' Faces
White nodes are hidden variables, and gray nodes correspond to observable information. Arrows between nodes represent conditional relationships between the variables. In this scenario, the probability of winning the bet amount is based on the subject's starting hand (observable variable) and their opponent's hand (hidden variable). Since subjects cannot directly observe their opponent's hand, they can use the fact that the opponent bet (observable variable) to put them on a ‘range’ of possible hands. However, in order to do this accurately, they must have an estimate of their opponent's style of play (hidden variable). More specifically, the probability of a particular hand winning is lower against an opponent who only bets with high-value hands, compared to an opponent who frequently bluffs (i.e, bets with poor hands). Since the opponent's style is also a hidden variable, subjects can use an opponent's face information (observable variable) to estimate their style. This process is called Bayesian ‘explaining away’, as the opponent's face explains-away the possibility of a bluff being the cause of an opponent's bet.