In this paper we consider some elementary and fair zero-sum games of chance to study the impact of random effects on the wealth distribution of N interacting players. Even if an exhaustive analytical study of such games between many players may be tricky, numerical experiments highlight interesting asymptotic properties, in particular, we underscore that randomness plays a key role in concentrating the wealth to the extreme with a single player. From a mathematical perspective, we interestingly recover for small and high-frequency transactions some diffusion limits extensively used in population genetics. Finally, the impact of small tax rates on the preceding dynamics is discussed for several regulation mechanisms. We show that taxation of income is not sufficient to overcome the externe concentration process contrary to a uniform taxation of capital that stabilizes the economy preventing agents to be ruined.