We provide a quantitative explanation of the patterns commonly observed during the collision of two floating ice sheets (ice floes): simple rafting, finger rafting, or the formation of a pressure ridge. In particular, we analyze the equilibrium configurations of the ice in each of the two types of rafting and show that these are only possible if the ice thickness is below a threshold value that we determine in terms of the strength and elastic modulus of the ice. We construct a regime diagram to characterize the regions of thickness-strength parameter space for which each type of deformation can occur. Using typical values for the strength of sea ice, we find that finger rafting can only occur in ice with thickness ≲8 cm, and simple rafting can typically only occur in ice with thickness ≲21 cm. These estimates are quantitatively consistent with most field observations reported in the literature. Finally, by quantifying two common complications that occur in reality, we are also able to account for some of the discrepancies between theory and observation that remain. We show that the presence of rubble may allow ice with a thickness of up to 1 m to perform simple rafting, but multiple rafting of thin sheets does not increase the maximum rafting thickness.