The necessity to repair genome damage has been considered to be an immediate factor responsible for the origin of sex. Indeed, attack by a cellular restriction enzyme of invading DNA from several bacteriophages initiates recombinational repair by gene conversion if there is homologous DNA. In this work, we modeled the interaction between a bacteriophage and a bacterium carrying a restriction enzyme as antagonistic coevolution. We assume a locus on the bacteriophage genome has either a restriction-sensitive or a restriction-resistant allele, and another locus determines whether it is recombination/repair proficient or defective. A restriction break can be repaired by a co-infecting phage genome if one of them is recombination/repair proficient. We define the fitness of phage (resistant/sensitive and repair-positive/-negative) genotypes and bacterial (restriction-positive/-negative) genotypes by assuming random encounter of the genotypes, with given probabilities of single and double infections, and the costs of resistance, repair, and restriction. Our results show the evolution of the repair allele depends on b(1)/b(0), the ratio of the burst size b(1) under damage to host cell physiology induced by an unrepaired double-strand break to the default burst size b(0). It was not until this effect was taken into account that the evolutionary advantage of DNA repair became apparent.