On the Monty Hall Dilemma and Some Related Variations - Dragan, Valeriu (Communications in Mathematics and Applications, 2016)
The current paper refers to the probabilistic problem posed by Monty Hall dilemma. The classical variation was considered along with two proposed variations on this two round chance game. Random number generators were used to obtain samples for individual games in order to assess the outcome, depending on the strategy employed by the player. An assumption was made and confirmed numerically, that if the decision in the second round is made randomly, the odds become \(1/2\) both ways whereas if the player uses an "always switch” approach, they increase their winning chances - confirming vos Savant's hypothesis. Hence the main conclusions are that there is no mandatory chronological order for the two decision stages and that "stick-or-switch” choice refers to the choice to play the original or the converse game. The dilemma has a wide range of applications from social psychology to other fields of science such as quantum mechanics.