  The random self-reinforcement mechanism, characterized by the principle of
``the rich get richer'', has demonstrated significant utility across various
domains. One prominent model embodying this mechanism is the random
reinforcement urn model. This paper investigates a multicolored,
multiple-drawing variant of the random reinforced urn model. We establish the
limiting behavior of the normalized urn composition and demonstrate strong
convergence upon scaling the counts of each color. Additionally, we derive
strong convergence estimators for the reinforcement means, i.e., for the
expectations of the replacement matrix's diagonal elements, and prove their
joint asymptotic normality. It is noteworthy that the estimators of the largest
reinforcement mean are asymptotically independent of the estimators of the
other smaller reinforcement means. Additionally, if a reinforcement mean is not
the largest, the estimators of these smaller reinforcement means will also
demonstrate asymptotic independence among themselves. Furthermore, we explore
the parallels between the reinforced mechanisms in random reinforced urn models
and multi-armed bandits, addressing hypothesis testing for expected payoffs in
the latter context.
