Best linear unbiased prediction (BLUP), which uses pedigree to estimate breeding values, can result in increased genetic gains for low heritability traits in autotetraploid potato. Conventional potato breeding strategies, based on outcrossing followed by phenotypic recurrent selection over a number of generations, can result in slow but steady improvements of traits with moderate to high heritability. However, faster gains, particularly for low heritability traits, could be made by selection on estimated breeding values (EBVs) calculated using more complete pedigree information in best linear unbiased prediction (BLUP) analysis. One complication in applying BLUP predictions of breeding value to potato breeding programs is the autotetraploid inheritance pattern of this species. Here we have used a large pedigree, dating back to 1908, to estimate heritability for nine key traits for potato breeding, modelling autotetraploid inheritance. We estimate the proportion of double reduction in potatoes from our data, and across traits, to be in the order of 10 %. Estimates of heritability ranged from 0.21 for breeder's visual preference, 0.58 for tuber yield, to 0.83 for plant maturity. Using the accuracies of the EBVs determined by cross generational validation, we model the genetic gain that could be achieved by selection of genotypes for breeding on BLUP EBVs and demonstrate that gains can be greater than in conventional schemes.