  We show that in a variant of the Minority Game problem, the agents can reach
a state of maximum social efficiency, where the fluctuation between the two
choices is minimum, by following a simple stochastic strategy. By imagining a
social scenario where the agents can only guess about the number of excess
people in the majority, we show that as long as the guess value is sufficiently
close to the reality, the system can reach a state of full efficiency or
minimum fluctuation. A continuous transition to less efficient condition is
observed when the guess value becomes worse. Hence, people can optimize their
guess value for excess population to optimize the period of being in the
majority state. We also consider the situation where a finite fraction of
agents always decide completely randomly (random trader) as opposed to the rest
of the population that follow a certain strategy (chartist). For a single
random trader the system becomes fully efficient with majority-minority
crossover occurring every two-days interval on average. For just two random
traders, all the agents have equal gain with arbitrarily small fluctuations.
