Cancer is a disease in which cells accumulate genetic aberrations that are believed to confer a clonal advantage over cells in the surrounding tissue. However, the quantitative benefit of frequently occurring mutations during tumor development remains unknown. We quantified the competitive advantage of Apc loss, Kras activation, and P53 mutations in the mouse intestine. Our findings indicate that the fate conferred by these mutations is not deterministic, and many mutated stem cells are replaced by wild-type stem cells after biased, but still stochastic events. Furthermore, P53 mutations display a condition-dependent advantage, and especially in colitis-affected intestines, clones harboring mutations in this gene are favored. Our work confirms the previously theoretical notion that the tissue architecture of the intestine suppresses the accumulation of mutated lineages.