Abstract: The invention relates to a finely divided, starch-containing aqueous polymer dispersion which is obtainable by free radical emulsion polymerization of ethylenically unsaturated monomers in the presence of at least one redox initiator and starch, wherein the ethylenically unsaturated monomers comprise (a) from 30 to 65% by weight of acrylonitrile and/or methacrylonitrile, (b) from 35 to 60% by weight of at least one C1-C12-alkyl acrylate and/or at least one C1-C12-alkyl methacrylate, (c) from 0 to 35% by weight of at least one other ethylenically unsaturated copolymerisable monomer, in which the sum of (a), (b) and (c) totals 100%, and in which the aqueous polymer dispersion comprises, (d) from 10 to 55% by weight of an ionic tapioca starch, in which the weight of (d) is based on the total solids of components (a), (b), (c) and (d) of the aqueous polymer dispersion.