Twenty-five traditional land-races, gynogenetic lines and two-line hybrids of common carp, Cyprinus carpio, have been collected in Hungary. Nearly 600 hybrids could be produced from these. Performance tests for such a high number of hybrid would be impractical. Distributions of the body weights of fish in simple crosses (lxl) and in a group created by using sperm and eggs of all available parents (kxx) were compaired to predict the efficiency of a large scale hybridization program. According to our model, the distribution in the (Ext) grorp can be computed as the sum of the distributions in the (lxl) groups. We estimated the probabilities of finding hybrids, that perform 5, 10, 20, 30, ...etc. % better than the average, when randomly choosing 1, 2, ....20 crossings. The probability for genetic improvment of carp through hybridization is high.