Using Stacked Probabilities to Keep Us Safe

Well, we’re in the thick of it now. America has neither returned to normal, nor have we remained in a safe lockdown. Rather, we’re now in this liminal space, filled with cheerleading denial about how we’re “reopening!” and “the economy is coming back!” Meanwhile, in truth, nobody knows what the heck is going on.

However, there is a functional middle ground between complete lockdown and what we have now, which is a devil-may-care complacency about the deaths of 1,000 people a day.

The functional middle ground lays in stacking enough safe behaviors together that the actual risk actually ends up being near zero, and we can get back to normal activities, with precautions in place.

Let’s use sexual behavior in HIV/AIDS prevention as an example:

OPTION #1: ZERO RISK: Abstinence

OPTION #2: LOWER RISK: condoms OR monogamy OR getting HIV status tests

OPTION #3: LOWEST RISK: testing AND condoms AND monogamy

Why is Option #3 better than Option #2? After all, if both partners test negative, you don’t need the other two interventions…right?

It all comes down to probability. Nothing besides abstinence is zero risk. Tests can come back with a false negative. Condoms can break. Partners can cheat.

But if you stack all three risk-reducing behaviors together, your chances of contracting HIV plummet to almost (but not quite) zero. And since life is inherently dangerous, and living without sex forver is unacceptable for most of the population, almost zero is good enough.

Now, I’m going to take a short detour into math to show what almost zero looks like.

Let’s say you flip a coin. What are the chances it turns out heads? 1 in 2, or .50.

Let’s say you throw a die. What are the chances you roll a 6? 1 in 6, or ~.17.

Now draw a card. What are the chances you pick the Ace of Hearts? 1 in 52, or .019.

If your life depended on one of these games of chance, you’d probably sit the game out. One in 52 is improbable, but it’s still highly possible.

But let’s say your life depends on just making sure you don’t get all three simultaneously? That is to say, you’ll be fine unless you get heads AND you roll a 6 AND you pick the Ace of Hearts?

Chance of getting heads:


Chance of getting heads AND rolling a 6:

.50 * .17 = .0085

Chance of getting heads AND rolling a 6 AND picking the Ace of Hearts?:

.50 * .17 * .019 = .0001615

In other words, if you combine the somewhat-low risks of each option, the final risk ends up being .0001616, or roughly one in 6,000.

To put that in perspective, the death rate in 2013 for car crashes was about 1 in 10,000. And we all still decide to get in cars. We’ve decided that the benefits of driving are worth the 1 in 10,000 risk. Not only that, there are risks of not driving, such as being unable to get to jobs, food, healthcare — and they also mean that the benefits are worth more than the risks.

At a certain point, every choice has some risk, so as long as you keep the downside to a manageable number, it’s acceptable.

So let’s look at Covid-19. Right now, we have no silver bullets. We don’t have any drugs like the HIV drug Truvada, which reduces viral load and makes it very hard to pass on the illness. And we don’t even have an effective, available, affordable barrier to contagion that’s as effective as a condom. PPE is in short supply, and even hospital workers who wear it regularly are getting sick.

But what we do have is stacked probabilities. Now, since we don’t have the data yet, I’ll be using “X” and “Y”, but I hope you’ll still be able to see how this works. Remember, the more 0’s after the decimal point, the safer you’ll be:

Chance of contracting Covid in normal interactions: .0X

Chance of contracting Covid when everyone is wearing a mask: .0Y

Chance of contracting Covid when everyone stays 6 feet apart: .0Z

Chance of contracting Covid when avoiding indoor air (outdoors only): .0A


And now let’s look at schools:

Here are some lower-risk changes we can use simultaneously to multiply safety:

  • Fewer kids in classrooms
  • Better ventilation. During temperate weather, keep all windows open, use box fans to circulate air at all times.
  • Better air filtration. Some high-end filters can filter out viruses. It is 100%? No, but one would imagine it’s going to help.
  • Testing as much as possible. If we can test kids / staff on Friday night, we can get results for PCR testing by Monday morning. Even weekly testing would GREATLY reduce risk and spread, so long as it was universal and accurate.
  • Grouping kids into cohorts to keep spread to a smaller potential group.
  • Strategizing about which things really NEED in-person class time. Maybe a teacher can make a video for easy things, and have in-person class for harder things.
  • Allowing kids to learn some subjects remotely, depending on ability. Regular testing to see if they’re keeping up.

I hope we can come up with creative, healthy ways to get schools up and running again. The thing is, all of the best ideas are going to take money. If we teach half the students, we need twice the teachers. If every student is remote half the time, we need money for equipment. If school schedules are constantly changing, then parents can’t work, and they need money to live.

So, we as a community need to push for some of those federal emergency billions to go to the real crisis — education.