Aneuploidy is prevalent in most solid tumors and can significantly alter cellular phenotype and fitness. Despite its critical role in tumor evolution, a detailed quantitative understanding of the evolutionary dynamics of aneuploidy remains elusive. To bridge this gap, we developed a novel method to infer the fitness landscape of chromosome-level karyotypes. This method utilizes longitudinal single-cell karyotype data from evolving cell populations to estimate the fitness of thousands of karyotypes proximal to the observed data in karyotype space, enabling the emergence of karyotypes not-yet seen in the input data to be predicted. We validated the predictive capability of our approach using both synthetic data from an agent-based model and empirical data from in vitro and in vivo passaged cell lines. Our analysis of the fitted landscapes suggests several key insights: (1) Whole genome doubling promotes aneuploidy by increasing the spectrum of potentially beneficial copy number alterations; (2) Cisplatin treatment alters the fitness impact of these alterations; (3) The fitness consequences of a copy number alteration (CNA) vary depending on the parental karyotype; (4) The rate of chromosome missegregation can dictate the predominant karyotypes in an evolving population.