After I finished my treatments, months passed and my cancer did not return. According to my doctors, the longer I went without a recurrence, the less likely I was to have one. That meant my odds of survival were not a static 9 percent, as I’d thought, but actually increased over time. By November 2015, I had gone 19 months with no evidence of the disease, and based on the calculations of a physicist friend of mine, my odds of survival were 70 percent. The chances were high — very high — that I would beat my cancer for good.

Around Christmas of that year, however, I began to have trouble eating. One night, shortly after a small meal, I started to feel the sensation of being repeatedly stabbed in the belly with a knife. I had to go to the emergency room, for the first of several hospital stays. Soon, I was no longer able to eat solid foods, only protein shakes, and after a while I couldn’t even drink those anymore. I was living on 700 calories a day, and at 5 feet 10, I saw my weight drop to 105 pounds. Walking took enormous effort, and my starvation coincided with a seemingly never-ending battery of CT scans, ultrasounds, X-rays, procedures and biopsies, until my cancer’s return was confirmed.

It had not returned when my chance of recurrence was high but when it finally became low. So the fact that my outlook had become rosy meant nothing in the end. My surgeon had been right to say that the numbers weren’t predictive — neither when they were against me nor, unfortunately, when they were in my favor.

In retrospect, I’d used survival rates not as a piece of information, but as a coping mechanism. I’d used them to measure the amount of hope I could give rope to. They’d allowed for my otherwise unjustifiable optimism to feel rooted in reality. Deep down, every cancer patient wants to believe he is going to make it, and the survival rate is the blunt, messy tool we use to convince ourselves.

However, cancer does not respect the rational nature of numbers. It operates within its own cruel logic. Nowhere is this truer than in the way cancer is treated today. Stage 4 cancer used to be pretty much a death sentence to all patients; the rise of immunotherapy has turned the battle against the disease into a wheel of fortune in which some people continue to die while others live longer and a few achieve seemingly miraculous long-term remission.

In one trial, patients with advanced melanoma who received immunotherapy had a response rate of about 50 percent to 60 percent. But that’s not true for most patients with solid tumors. In a recent clinic trial for the drug Opdivo, for instance, only 14 percent of stomach cancer participants benefited.

My 10-year-old niece recently saw one of the $2 bills that I carry in my wallet. She’d never seen one before, and asked me if she could have it. I hesitated, wondering if I was going to have to either dispense with some good luck, or saddle her with the opposite. But the hesitation passed, and I handed her the note.