The game theory was created on the basis of social as well as gambling games, such as chess,
poker, baccarat, hex, or one-armed bandit. The aforementioned games lay solid foundations
for analogous mathematical models (e.g., hex), artificial intelligence algorithms (hex), theoretical analysis
of computational complexity attributable to various numerical problems (baccarat), as well
as illustration of several economic dilemmas - particularly in the case where the winner takes everything
(e.g., noughts and crosses). A certain gambling games, such as a horse racing, may be successfully
applied to verify a wide spectrum of market mechanism, for example, market effectiveness
or customer behavior in light of incoming information regarding a specific product. One of a lot applications
of the slot machine (one-armed bandit) is asymptotically efficient allocation rule, which was assigned
by T.L. Lai and H. Robbins (1985). In the next years, the rule was developed by another
and was named a multi-armed. The aim of the paper is to discuss these social games along with their
potential mathematical models, which are governed by the rules predominantly applicable to the social
and natural sciences.
 Ananatharam, V., Varaiya, P., Warland, J., 1987.
Asymptotically Efficient Allocation Rules for
the Multiarmed Bandit Problem with Multiple
Plays – Part I: I.I.D. Rewards. IEEE Transaction
of Automatic Control, Vol. Ac–32, No. 11,
 Duda, R., 2010. Lwow School of Mathematics.
Wroclaw: Wroclaw University Publishing
 Ethier, S.N., 2010. The Doctrine of Chances:
Probabilistic Aspects of Gambling. Berlin –
Heidelberg: Springer Verlag.