How much would someone have to pay you to play Russian roulette? It’s a game where a revolver is loaded with one bullet, the cylinder is spun, the gun is pointed at your head and the trigger is pulled. In essence, gambling with your own life. Is there any amount of money I can offer you to play this game? Almost everyone I’ve asked answers no. But what if God or a genie came down and could offer you things besides money, and you could have anything your heart desired; then would you play? Of course, you could always ask to guarantee a spot in heaven (or whatever you believe in), but let’s assume your wishes were restricted to the “real world”. I love this question, and I ask it a lot but I’ve never really figured out if there was any kind of fair value that could be computed for playing the game. I’d assume fair value goes beyond money as most people can’t really put a price on their own lives, but I’ve decided to try.

First and foremost, what are the factors that should influence the pricing of gambling with your own life?

• Current Wealth: The more money you have, the higher the price you would demand to play the game
• Current Happiness: I’d have to assume that if you already have a decent life you aren’t really willing to risk it for any amount. If your life pretty much sucks and you were contemplating committing suicide anyways, well then you’re probably more inclined to play.
• Number of chambers: What if the number of chambers (holes where the bullets reside) was increased from 6 to 12? Or to ten thousand?
• Life expectancy: If doctors told you that you were going to die within the next week anyways you might as well try to have one hell of a week

Hmmm… OK, now where do I go? The factors I’ve listed here sound reasonable and I’ve been thinking about this for weeks but I can’t figure out how to make use of them. There are too many non-quantifiable parameters here. Current happiness? How in the world do you figure that out and more importantly how does it fit into an equation? Life expectancy? For most normal people an estimate of how long they have to live is all but a wild guess. I don’t think this is going to work.

There is another way to look at things. It is a somewhat grim, dark way of looking at life but this game of Russian roulette is already something that we  play every day. No one goes to the extreme by living in a bubble and using every thought to figure out how to stay alive and escape death. What we do do is go ahead and eat heart clogging cheeseburgers, not put on our seat belts because the destination is only 5 miles away, figure that a condom is enough protection, amongst a long list of other minuscule, almost insignificant risks we incessantly take daily. And I say almost insignificant because when one of those microscopic, higgs boson sized risks do pull through, you’re dead, which is by no means insignificant… The only difference is that in this daily game of Russian roulette there are more chambers; instead of an 1-out-6 chance there is a 1 out of a million chance of death. So, an easier way to look at this problem is to figure out the prices people already play this game for and see what that implies they’ll play the original version of the game with only six chambers for. I got the data for the table below from the NSC (www.nsc.org) . It shows the number of deaths in 1999 due to various causes and the odds that the average person will die of those causes. Noteworthy are the risks that people take which could be avoided but are chosen to be taken because the rewards outweigh the risks for that particular individual. Things like alcohol, operations of war, automobile accidents and contact with machinery.

If you would like to play along, find an item on this list that definitely fits your own profile. Or, better yet, think of an activity you do that has even the slightest chances of death. Do a little Google searching and find out what the number of deaths for that activity within a given year are. Next, download the following spreadsheet.

OddsOfDeath.xls

I’m going to use two examples to walk you through the spreadsheet. A really good example is an activity like sky diving. It is a total unnecessary risk for someone to take, but it brings satisfaction that is well worth the risk of admission. According to howstuffworks.com (http://adventure.howstuffworks.com/skydiving8.htm) there are 30 deaths per year from skydiving and around 3 million jumps per year.

Inputs into spreadsheet for skydiving example:

Total deaths per year – Input the total death statistic here. As mentioned earlier, for skydiving, this would be a grand total of 30

Estimate the number of times this was done in total per year – Estimate or find a statistic for the number of times this particular activity in was done in a given year. Thankfully, for skydiving, the howstuffworks.com links states that it was around 3 million

Estimated monetary equivalent benefit for doing this – Estimate how much benefit you specifically receive from participating in such an activity. For skydiving I would have to assume that the sheer thrill, the adrenaline rush, the natural high must be so amazing that it could command quite a high price. The rush must feel better than the craziest drugs on the planet but with no side effects (well, except if something goes awry and you die, but other than that…). Is it better than sex? For some people, maybe? I don’t know, I’m going to set the price equivalent to sex with a high class hooker which probably sets one back a cool $5000.  Sex with a high class hooker versus skydiving, they seem roughly equivalent.

Power growth factor for additional risk – There are two models I’ve come up with. The first simply linearly compensates you taking on additional risk which is completely unrealistic. For example, if you are willing to play a 1 in 10 shot of death game for $100, then with this simple model you would be willing to play a 1 in 5 shot of death game for twice as much, $200. Since a person is literally risking it all here, as the probability of death in the game approaches 100% the player will demand more and more as they are having to risk so much. So, the second model corrects this by taking things to a power as we step closer to that 100% certainty of death factor. The input here defines that power and it completely depends on the person. This number is what takes input from some of the factors I first described earlier, current wealth, happiness and life expectancy. The higher the number here indicates the better off you currently are. I’ve set it to 3 which means that we are rewarded by a power of 3 for each additional unit of probability of death we take on.

The results are to follow soon. I’m going to discuss the inputs for another example, namely driving. From the same howstuffworks.com skydiving article, they mention a few key statistics about driving. They state that 40,000 people die each year from driving and estimate that if you drive 10,000 miles per year your odds of death are 1 in 6000.

Inputs into spreadsheet for driving example:

Total deaths per year - 40,000

Estimate the number of times this was done in total per year – According to the Department of Transportation there are just under 200 million drivers in the US. Estimating that they all drive an average of twice per day (mostly to and from work) for 360 days a year, I’m estimating that the activity of driving is done around 144 billion times per year.

Estimated monetary equivalent benefit for doing this – Not much really. Most of the time we’re driving to and from work, to grab groceries, run errands, visit friends or go to the movies. We get some convenience out of it since we don’t have to walk or take public transportation to the destination. I’d say it’s worth $50, but could be more or less depending on the destination. Less if it’s just to get to work, more if it’s to go pick up that hooker from the last example…

Power growth factor for additional risk - I’ve left it at 3 to stay consistent with the previous example.

Results

Well, there you go folks. We all drive and therefore the price someone should pay you to play Russian roulette is just under 11 quintillion dollars. Quintillion being 10^18. And if you are a crazy skydiver then you should be willing to accept only 23 quadrillion dollars. Quadrillion being 10^15.