A Remark on the Guessing Game

The Guessing Game on numbers between zero and N and with a non negative parameter is considered in a 1-shot setting with k levels of thinking. The model proposed is based on two assumptions: 1.) Players consider intervals rather than numbers, parametrized by a non negative parameter called the confidence parameter; 2.) Each player readjusts her guess successively during the sequence of iterations according to her recent belief. Under mild conditions, in this model the expected Winning Number is found to be different form zero and the "classical" result 17 is obtained for a quite wide interval of confidence, after 4 levels of thinking only. Further, if the confidence parameter has a skew distribution on [0,1], then we also obtain a skew distribution for the guessed number. This matched to the real data on the Guessing Game.