This chapter is about distinguishing what is constant and predictable about handedness from what is superficial and changeable. What are the facts about which we can be certain? Chapters 2 and 3 tackled the principal source of uncertainty, the different incidences between studies. It was argued that incidences reflect thresholds, or cut-off points, along an underlying asymmetry continuum. The RS solution to the problem of relationships between asymmetries of hand and brain depends on the assumption that people who do and do not carry an agent promoting left hemisphere advantage differ for handedness only in the locations of R–L distributions along the continuum. Handedness distributions in families and in pairs of twins are predictable on the assumption that the RS factor is a single gene “for” left hemisphere advantage. Handedness itself depends on chance, accidents of congenital development. This might seem to imply that handedness will be unpredictable and therefore not accessible to scientific study. On the contrary, the laws of chance are highly predictable, provided the groups studied are of reasonable size and drawn without selection biases. Small samples may differ through accidents of sampling, a problem for the interpretation of findings in the laterality literature. In order to understand the influence of the RS + gene, we need to discover what systematic influences reliably affect the chance distribution of asymmetry.