Many different equity principles may need to be traded off against efficiency when prioritizing health care. This paper explores one of them: the concept of a 'fair innings'. It reflects the feeling that everyone is entitled to some 'normal' span of health (usually expressed in life years, e.g. 'three score years and ten') and anyone failing to achieve this has been cheated, whilst anyone getting more than this is 'living on borrowed time'. Four important characteristics of the 'fair innings' notion are worth noting: firstly, it is outcome based, not process-based or resource-based; secondly, it is about a person's whole life-time experience, not about their state at any particular point in time; thirdly, it reflects an aversion to inequality; and fourthly, it is quantifiable. Even in common parlance it is usually expressed in numerical terms: death at 25 is viewed very differently from death at 85. But age at death should be no more than a first approximation, because the quality of a person's life is important as well as its length. The analysis suggests that this notion of intergenerational equity requires greater discrimination against the elderly than would be dictated simply by efficiency objectives.