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During S phase, the entire genome must be precisely duplicated, with no sections of DNA left unreplicated. Here, we develop a simple mathematical model to describe the probability of replication failing due to the irreversible stalling of replication forks. We show that the probability of complete genome replication is maximized if replication origins are evenly spaced, the largest inter-origin distances are minimized, and the end-most origins are positioned close to chromosome ends. We show that origin positions in the yeast Saccharomyces cerevisiae genome conform to all three predictions thereby maximizing the probability of complete replication if replication forks stall. Origin positions in four other yeasts—Kluyveromyces lactis, Lachancea kluyveri, Lachancea waltii and Schizosaccharomyces pombe—also conform to these predictions. Equating failure rates at chromosome ends with those in chromosome interiors gives a mean per nucleotide fork stall rate of ~5 × 10-8, which is consistent with experimental estimates. Using this value in our theoretical predictions gives replication failure rates that are consistent with data from replication origin knockout experiments. Our theory also predicts that significantly larger genomes, such as those of mammals, will experience a much greater probability of replication failure genome-wide, and therefore will likely require additional compensatory mechanisms.