WE INTRODUCE A ONE-DIMENSIONAL RANDOM WALK, WHICH AT EACH STEP PERFORMS A REINFORCED DYNAMICS WITH PROBABILITY ? AND WITH PROBABILITY 1??, THE RANDOM WALK PERFORMS A STEP INDEPENDENT OF THE PAST. WE ANALYSE ITS ASYMPTOTIC BEHAVIOUR, SHOWING A LAW OF LARGE NUMBERS AND CHARACTERIZING THE DIFFUSIVE AND SUPERDIFFUSIVE REGIONS. WE PROVE CENTRAL LIMIT THEOREMS AND LAW OF ITERATED LOGARITHM BASED ON THE MARTINGALE APPROACH.