The Game of Life
Common in popular culture and many works of dystopian fiction is the trope of risking your life for some gain. From Squid Games to the token contestant on the average game show hoping to cover medical bills for themselves or a loved one, the idea of putting up the ultimate wager is understandably sensationalized. In real life, too, many adults work dangerous jobs in return for higher compensation, or adrenaline junkies view an elevated state of risk as its own reward. But what I’ve always found interesting is the mundane risks we take every day. Going outside, getting into a car with a friend, deciding to drive home after a beer, living in a house with a firearm. Small things that offer some sort of convenience or utility in exchange for an altered chance of that day being our last. These decisions can be modeled with our two player game theory tables, where you are player one deciding whether to do something and fate/chance is the second player deciding whether to punish you for it. Now, of course, there are all sorts of varying outcomes for any decision we make, but for the sake of simplicity we will use the odds in the linked article and view the two outcomes as nothing happening or you dying. I’ve set the payoff of dying at -$1,000,000, and put in perspective how much we must value certain decisions in order for them to be dominant strategies using the mortality statistics linked.
The payoff matrix would thus take the following form. Left column represents deciding to do the activity, and right column choosing to abstain. Top row represents nothing happening, and bottom row represents cruel fate (which doesn’t matter if you didn’t do the activity). Fate’s payoff here is inconsequential as it already has chosen its strategy (a randomized one detailed in the mortality statistics). Since right column’s expected payoff is 0 (nothing ventured, nothing gained!) we find the value such that the top left column multiplied by its probability matches the bottom left column (a negative payoff) multiplied by its probability. Now the results (supplemented by some google searches for how often adults choose to do these activities to give context to the mortality rates):
Owning a firearm: (1/10698) (lifetime chance of dying from accidental discharge) * (1 / 0.22) (percentage of Americans owning a firearm) * (x) – 1000000 > 0, x > $424.88
Crossing the street: (1/41686) (yearlong chance of being killed as a pedestrian) * (1/365) * 5 (estimate of how many times the average American crosses a street in a day) * x – 1000000 > 0, x > $0.33
Not abstaining from drinking, drugs, and opioids throughout one’s life: ((1/49) + (1/51) + (1/67)) * x – 1000000 > 0, x > $54941
Using or occupying a motor vehicle over the course of a day: (1/7782) * (1/365) * (1/0.64) (percentage of Americans who drive every day) * x – 1000000 > 0, x > $0.55
Going swimming at some point over the course of a year: (1/84052) * (1/0.31) (percentage of Americans who swim in a year) * x – 1000000 > 0, x > $3838
And so on and so forth. Nothing super surprising, but it is interesting to see how we value the everyday risks we take.
https://www.iii.org/fact-statistic/facts-statistics-mortality-risk