Game theory can be a powerful tool for generating testable hypotheses concerning biological systems. We present a simple game that has many features analogous to a developing cellular system. The game mimics random turning on of genes in cells. Despite the randomness explicit in the mechanism, the game nonetheless results in deterministic outcomes that are extremely resistant to perturbation. Analysis of the types of mistakes or rule changes that are necessary in order to alter the outcome of the game suggests that there are a very limited number of mechanisms by which the differentiation process can result in tumor formation or carcinogenesis. The most significant causes of altered outcomes are alterations in gene order or number, and alteration of the rule by which the gene sequences are traversed. These alterations correspond to chromosomal defects or rearrangements, changes in chromosomal number, and changes in the "orders" delivered by regulatory genes. Notably, most common mistakes, which correspond to simple forms of mutations, have no effect on the outcome of the game, suggesting that mutation is relevant to tumorigenesis and carcinogenesis only to the extent that it results in altered "rules" for reading other gene sequences.