Calculation of location scores is one of the most computationally intensive tasks in modern genetics. Since these scores are crucial in placing disease loci on marker maps, there is ample incentive to pursue such calculations with large numbers of markers. However, in contrast to the simple, standardized pedigrees used in making marker maps, disease pedigrees are often graphically complex and sparsely phenotyped. These complications can present insuperable barriers to exact likelihood calculations with more than a few markers simultaneously. To overcome these barriers we introduce in the present paper a random walk method for computing approximate location scores with large numbers of biallelic markers. Sufficient mathematical theory is developed to explain the method. Feasibility is checked by small-scale simulations for two applications permitting exact calculation of location scores.