"The 1-shot alpha-beauty contest is a non-equilibrium strategic game under bounded rationality conditions, while equilibrium is approached if the game is played iteratively sufficientlynmany times. Experimental data of the 1-shot setting of the 0-equilibrium game show a common pattern: The spectrum of announced numbers is a superposition of a skew backgroundndistribution and a regime of extra ordinarily often chosen numbers. Our model is capable ofnquantitatively reproducing this observation in non-equilibrium as well as the convergence to-nwards equilibrium in the iterative setting. The approach is based on two basic assumptions:n1.) Players iteratively update their recent guesses in the sense of eductive reasoning and 2.)nPlayers estimate intervals rather than exact numbers to cope with incomplete knowledge innnon-equilibrium. The width of the interval is regarded as a measure for the confidence ofnthe players' respective guess. It is shown analytically that the sequence of guessed numbers approaches a (finite) limit within only very few iterations. Moreover, if all playersnhave infinite confidence in their respective guesses, the asymptotic Winning Number equalsnthe rational Nash equilibrium 0, while if players have only finite confidence in their recentnguess, the Winning Number in the 1-shot setting is strictly larger than 0. Our model is alsoncapable of quantitatively describing the ""path into equilibrium"". Convergence is shown tonbe polynomial in the number of rounds played. The predictions of our model are in goodnquantitative agreement with real data for various alpha-beauty contest games.n "