Luck Egalitarianism has frequently been discussed in the recent literature because of the potential impact of this theory on health financing. Luck Egalitarianism puts forth a theory of distributive justice which says that the fundamental aim of equality is to compensate people for undeserved bad luck such as being born with poor native endowments, having difficult family circumstances or suffering from accidents and illness. On the other hand, if individuals face ill health because of faults of their own, then society has no duty to supply health services to them. Many arguments for and against this theory have been raised since it was first introduced. The proponents of Luck Egalitarianism focus on the concepts that free choice and respecting the autonomy of the individual determine whether health services are deserved. The criticisms against the concept of Luck Egalitarianism are that it is harsh to the needy and abandons the wretched, discriminates against the disabled, is against basic humanitarian principles, is incompatible with human dignity, and is in dissonance with real life. We agree with the basic proposition of Luck Egalitarian theory, which states that "inequalities deriving from unchosen features of people's circumstances are unjust and therefore should be compensated for". Our agreement leads us to an opposite conclusion. We propose that the "unchosen features of people's circumstances" include more than personal disadvantages. The social features to be included in the context of inequalities deriving from unchosen features of peoples circumstances are, socioeconomic status (SES), access to social determinants of health, and the ethnic, cultural and religious identity of individuals. Our other propositions are the mutable character of choices which makes individual responsibility of preferences implausible; the problematic causal relationship between responsibility and ill-health; the disregard of the motives behind decisions; problems with implementation in real health service circumstances; and the contradictory nature of Luck Egalitarianism for principles of medical ethics. These arguments draw attention to possible ethical and practical consequences of implementation of health policies arising from Luck Egalitarian view for patients and for health care providers. In this paper, we will first define Luck Egalitarianism. Then, we will discuss arguments for and against the theory in the literature. Our final task is to suggest additional criticisms of the theory and justify them.