 In particular, if the car is hidden by means of some randomization device – like tossing symmetric or asymmetric three-sided die – the dominance implies that a strategy maximizing the probability of winning the car will be among three always-switching strategies, namely it will be the strategy that initially picks the least likely door then switches no matter which door to switch is offered by the host.Strategic dominance links the Monty Hall problem to the game theory.In the zero-sum game setting of Gill, 2011, discarding the non-switching strategies reduces the game to the following simple variant