Monty Hall’s Three Doors for Dummies

Since its appearance in the literature, Monty Hall’s three doors “anomaly” has attracted the attention of scientists from different fields: economists (Friedman, 1998; Nalebuff, 1987; Page, 1998; Palacios-Huerta, 2003; Slembeck & Tyran, 2004), statisticians (Morgan, Chaganty, Dahiya & Doviak, 1991; Puza, Pitt & O’Neill, 2005), psychologists (Granberg & Brown, 1995; Krauss & Wang, 2003) among others. The reason for such attention may be explained by the fact that this “anomaly” relies on a simple, even if counterintuitive, problem. There are three doors, and only behind one of them there is a big prize. At the beginning of the game, the player is asked to choose just one door. After that, an empty door among the not chosen doors is opened and the player is asked to make a new decision: either to stick with the first chosen door or to change and choose the remaining not-opened door. If people performed the Bayes’ updating correctly, they should realise that switching is the best strategy because it doubles the percentages of winning (as we show in the next section). Nevertheless, the stylised fact from the American TV programme in which this game was firstly performed, and from the controlled experiments that replicated its basic structure (Friedman; Page; Palacios-Huerta; Slembeck & Tyran) is that only a low percentage of people choose to switch.