TKI discontinuation possibilities illustrate deterministic versus stochastic modeling differences. Suppose that: (1) CML LSCs have a growth advantage over HSCs in the absence of treatment, but a growth disadvantage under TKI treatment; and (2) treatment is discontinued when the average number of LSCs is just one. What will happen? On a deterministic model, all patients will eventually relapse, as the LSCs repopulate (here schematically indicated as exponential growth). On a more realistic stochastic model, the results are quite different, even if the average number of LSCs at each time equals the deterministic estimate at that time. Here, patients 1 and 2 were “lucky” enough to be fully LSC-free when treatment was discontinued; afterward, they remain disease-free. “Luck” refers to factors not systematically foreseeable with current techniques. Patient 7 was even luckier: both LSC clones died out accidentally, one after the other, despite their growth advantage. On the other hand, patient 8 is substantially worse off than the deterministic model would predict, while patients 5 and 6 have also been rather unlucky. Whether any of the 5 LSC-bearing patients will later suffer a clinical relapse without treatment is in part a matter of luck, but patient 8 has a comparatively large chance of relapse.