There’s a huge difference between riding on the back of a motorcycle once, and buying a motorcycle to ride every weekend, or between buying a cookie and buying a box of 25 cookies, or between taking a boxing lesson once and sparring regularly.

Unfortunately, our minds don’t necessarily give this difference between doing something one time and doing something T times appropriate weight. In many cases, the risk of the decision actually scales up proportionally to our prediction for T, the number of times we’ll do the thing. The problem is that how “significant” the decision feels to us may NOT scale up proportionally to T. So the “weightiness” of risky decisions can easily be miscalculated. We may be too worried about doing a thing once, and not nearly worried enough about doing it T times.

Consider the basic mathematics of repeated risks. When we do something that has pretty low risk “R” each time we do it (say, a 1 in 1000 chance of being seriously hurt), and the risk each time is independent of the previous times, then if we do it once we have a risk of R, whereas if we do it twice, we have two chances for the bad thing happening, so the risk is about 2*R. Likewise, the total risk we take on when we do it T times (for T not super large) is about T * R. This is the basic risk formula you should keep in your mind.

[A semi-technical side note for the math-interested: when we do the thing twice the risk of the bad thing happening the first time OR the second time if each event is independent is actually R + R – R^2. The R^2 comes about from considering the possibility that the bad thing happens both of the times. For intuition on this point, consider two circles that are slightly overlapping. To find the total area of the circles (i.e., the total probability of the events represented by the circles) you can’t just add up the two areas (i.e., add the probabilities), because you’ll double count the overlapping part (i.e., the part representing the event occurring in both instances), so you’ll have to subtract something away (the R^2 in this case, which has this form due to the assumption that the events are independent). However, if R is small, then R^2 is super small, so we can ignore it by assuming it’s 0; hence the total risk ends up being about 2R = R + R – 0. Therefore, the math mentioned above breaks down if you’re doing a thing with really high risk, or if you do the thing a large number of times relative to the risk level – this makes sense because if you have a 50% chance of dying each time then clearly if you do it four times you don’t have a 450% = 200% chance of dying. Likewise, if you have a 1% chance of dying each time and you do it 200 times, you also don’t end up with 1 %200 = 200% chance of dying. But for small, independent risks that you do a moderate number of times, R * T is a good rule of thumb.*]

So if you’re about to commit yourself to do a thing 30 times, you’re taking on about 30 times the risk compared to if you decide to do it once! Does your brain properly appreciate that huge multiplier? Do you feel on a gut level that doing something 30 times more often is 30 times riskier? Probably not. As the risk R gets bigger, a decision, of course, becomes more significant, but the actual risk is about T * R, so R is not enough to consider. If we mainly just consider R, then we probably end up too risk-averse on one-off decisions, and not nearly risk-averse enough on repeated decisions!

Let’s consider motorcycles. According to the National Highway Traffic Safety Administration, in 2006, you had, on average, about a 1 in 26,000 chance of dying for every 100 miles spent riding a motorcycle. For reference, this is 11x the chance of dying than a 30-year-old male has on a random day or 24x the chance of death that a 30-year-old female has on a random day.

So if you are considering buying a motorcycle, and predict you will ride it 100 miles each week for the next five years, that’s about 52 weeks * 5 years = 260 times that you ride 100 miles, so your risk of dying is amplified by 260:

R * T = (1 / 26000) * 260 = 1 / 100

That means you’ve just taken on a (predicted) 1% chance of death by buying this motorcycle! Of course, injuries are much more common than death (about 20x higher it seems), so the chance of injury you’ve taken on is much higher than that. So this is a very weighty decision. It becomes weightier still if you think you’ll ride it for ten years instead of 5. But even in the five-year case, consider: how much money would you pay NOT to have to roll a 100 sided die where death occurs if you roll a 100, and injury occurs if you roll, say, an 80 or higher? That’s the kind of die roll you’re taking on by choosing to ride a motorcycle 100 miles a week for five years.

[Note: sometimes, the risk PER time that we do something goes down the more we do it because we become more skilled. For instance, when we swim in the ocean as a weak swimmer, we are more likely to drown than if we do it as a strong swimmer. But then again, as a strong swimmer, we may take greater risks by swimming on stormy days, and as a weak swimmer, we may be cautious and stay very close to shore, so the risk per time on average could increase as we do it more. It’s hard to make a general rule about how the risk per time varies as you do something more often.]

Part of the reason we can underestimate risk is that we convince ourselves that we can stop at any time. For instance, we can buy a motorcycle and then later just decide to stop using it. Sure we can, but the question is, will we? We need to make the decision based on what we predict will happen, not what could theoretically happen.

The point is here that doing a “risky” thing once is far less risky than doing a risky thing many times (about T times more risky!), but your brain won’t necessarily perceive the right relationship. For small independent risks, the total risk of a bad thing happening scales with the number of times T you do the thing. So remember the risk formula: R * T, and teach it to your brain.

So I urge you: be appropriately wary of repeated risks! There are many things that are fine to do once that are a bad idea to do T times, for moderately large T.

Is it worth taking a 1 in 100,000 chance of dying , in order to experience the novel thrill of sky diving? Is a 1 in 500,000 chance of death worth it to go bungee jumping?

It’s hard to know whether these risks are reasonable, because numbers like 100,000 or 500,000 feel so abstract to us. To think more clearly about these numbers, it helps to get our intuitions engaged.

We can start by figuring out the daily risk of dying that we automatically face every day. My “death calculator” tool above will compute yours, as estimated from your gender and age. For instance, in the United States, a 30 year old man has about a 1 in 260,000 chance of dying tomorrow whereas a 30 year old woman has about a 1 in 583,000 chance. A 55 year old man has a 1 in 46,000 chance of dying on any given day and a 55 year old woman a 1 in 79,000 chance. Note that while it’s extremely difficult to estimate a person’s life span (since future technological and societal changes may radically alter how long people live), estimating how likely a person is to die in the next day is much more accurate and straightforward.

Once you’ve used the tool to calculate your own chance of dying tomorrow, you can start thinking about the risk of dangerous activities relative to how much risk you already take each day (merely by going about normal activities). In particular, you can calculate how many total days worth of risk an activity involves. So for instance, if you are a 30 year old male, and ride 100 miles on a motorcycle tomorrow, then you’ll experienced 11.2 days worth of risk of dying tomorrow, rather than a single normal day of risk.

To do the calculation of how many days of risk you’re taking in a day where you do the dangerous activity, simply calculate the following: Start with the probability that you die in a normal day, add to it the probability that you die from doing the risky activity, and then divide the result by the probability that you die in a normal day.

So for instance, if you were to go BASE jumping tomorrow (an activity that appears to have about a 1 in 2,300 chance of death), and if you normally have a 1 in 100,000 chance of dying in a given day (for instance, you’re a 46 year old man) then you’d be taking on ((1/2300)+(1/100000))/(1/100,000) = 44.5 days worth of ordinary daily risk tomorrow, instead of just 1 day of risk.

Would that be worth it? For some people, it might be possible it is worth BASE jumping once in their in life. But suppose you were to go BASE jumping 20 times over the next year, on 20 different days. Then rather than consuming 365 days of typical risk that year (as a 46 year old man), you’d be taking on about 1235 days worth of risk, an additional roughly 2.4 years of risk! It’s hard to imagine that being worth it, even if BASE jumping is incredibly enjoyable. Of course, there is also a high risk of injury, aside from the risk of death.

Below is a table with estimates of the chance of dying from doing various activities.

Taking a 340 mile road trip on occasion with friends seems very reasonable. For instance, a 30 year old male will only be doubling his risk of dying that day, and a 30 year old female will be taking on about 3.3 days of her usual daily risk. But taking a job as a taxi driver in a suburban area or a long distance courier, driving 340 miles most days, would be much more risky. A 30 year old male who took such a job would be doubling his risk of dying every day. Another way to think about it is that despite being a 30 year old male, he would living with the daily risk of a 43 year old male. Similarly, a 30 year old male who decided to go BASE jumping one day, would be living that day with the daily risk of death of an 88 year old man.

So what risks are worth taking? It’s ultimately a subjective question. But thinking in terms of how much you’re increasing your ordinary daily risk, and converting risks into the daily risk of people of different ages, can make these abstract numbers more intuitive. And stronger intuition can help us reason more sanely about our choices.

Disclaimer: these numbers come from the internet, so if you want to be confident about any of them, you should double check them using a reliable source. Note also that actual death rates will depend on a variety of factors, including the amount of experience you have doing that activity and the location where you are doing it. Furthermore, note that for many of these activities there are risks of injury, in addition to risk of death, but I’ve only considered risk of death in this analysis. Be very cautious before deciding to engage in any dangerous activity!