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Tumors frequently display high chromosomal instability and contain multiple copies of genomic regions. Here, we describe Gain Route Identification and Timing In Cancer (GRITIC), a generic method for timing genomic gains leading to complex copy number states, using single-sample bulk whole-genome sequencing data. By applying GRITIC to 6,091 tumors, we found that non-parsimonious evolution is frequent in the formation of complex copy number states in genome-doubled tumors. We measured chromosomal instability before and after genome duplication in human tumors and found that late genome doubling was followed by an increase in the rate of copy number gain. Copy number gains often accumulate as punctuated bursts, commonly after genome doubling. We infer that genome duplications typically affect the landscape of copy number losses, while only minimally impacting copy number gains. In summary, GRITIC is a novel copy number gain timing framework that permits the analysis of copy number evolution in chromosomally unstable tumors. Significance: Complex genomic gains are associated with whole-genome duplications, which are frequent across tumors, span a large fraction of their genomes, and are linked to poorer outcomes. GRITIC infers when these gains occur during tumor development, which will help to identify the genetic events that drive tumor evolution. See related commentary by Taylor, p. 1766.