The occurrence of linear cholesterol-recognition motifs in alpha-helical transmembrane domains has long been debated. Here, we demonstrate the ability of a genetic algorithm guided by coarse-grained molecular dynamics simulations---a method coined evolutionary molecular dynamics (evo-MD)---to directly resolve the sequence which maximally attracts/sorts cholesterol within a single-pass alpha-helical transmembrane domain (TMDs). We illustrate that the evolutionary landscape of cholesterol attraction in membrane proteins is characterized by a sharp, well-defined global optimum. Surprisingly, this optimal solution features an unusual short hydrophobic block, consisting of typically only eight short chain hydrophobic amino acids, surrounded by three successive lysines. Owing to the membrane thickening effect of cholesterol, cholesterol-enriched ordered phases favor TMDs characterized by a long rather than a short hydrophobic length. However, this short hydrophobic pattern evidently offers a pronounced net advantage for the binding of free cholesterol in both coarse-grained and atomistic simulations. Attraction is mediated by the unique ability of cholesterol to snorkel within the hydrophobic core of the membrane and thereby shield deeply located lysines from the unfavorable hydrophobic surrounding. Since this mechanism of attraction is of a thermodynamic nature and is not based on molecular shape specificity, a large diversity of sub-optimal cholesterol attracting sequences can exist. The puzzling sequence variability of proposed linear cholesterol-recognition motifs is thus consistent with sub-optimal, unspecific binding of cholesterol. Importantly, since evo-MD uniquely enables the targeted design of recognition motifs for distinct fluid lipid membranes, we foresee wide applications for evo-MD in the biological and biomedical fields.