Genomic instability contributes to tumorigenesis through the amplification and deletion of cancer driver genes. DNA copy number (CN) profiling of ensembles of tumors allows a thermodynamic analysis of the profile for each tumor. The free energy of the distribution of CNs is found to be a monotonically increasing function of the average chromosomal ploidy. The dependence is universal across several cancer types. Surprisal analysis distinguishes two main known subgroups: tumors with cells that have or have not undergone whole-genome duplication (WGD). The analysis uncovers that CN states having a narrower distribution are energetically more favorable toward the WGD transition. Surprisal analysis also determines the deviations from a fully stable-state distribution. These deviations reflect constraints imposed by tumor fitness selection pressures. The results point to CN changes that are more common in high-ploidy tumors and thus support altered selection pressures upon WGD.