Roll The Dice

Question of the Day

I start each class with a question. The Question of the Day. This could be construed as an ice-breaker exercise similar to those held in stuffy corporate settings. To some extent, the purpose is similar. To a greater extent, our setting and purpose is much different. I run a gym. People come to our gym to stay fit and healthy, but also blow off steam from the rest of their day. By being pushed through challenging workouts, our members can both find release from their day-to-day demands and find a bond with everyone in class who shares in the experience of persevering through the physical challenge. I ask the Question of the Day to shake people out of their early morning fog or early evening cloud. To answer the question, you must be present. There is also an ensuing discussion over the commonalities or differences among the various answers.

The Question of the Day can come from anywhere. I describe the Question of the Day to a new gym member with “It can be fitness related, but usually not.” Some of my longtime members will scoff. It’s rarely fitness related. I often spend the last few minutes before a class starts bouncing questions through my head. I’ve resolved to always come up with the questions on my own. 

I have a couple regular questions. At the beginning of a month, I ask: “What are you going to work on this month?” At the end of a month, I ask: “What went well in the last month?” I ask seasonal questions, such as: “When has the season unofficially turned? Not the calendar date of change, but informal signatures such as the first lemonade of summer or pumpkin spice latte of fall.” Some questions reveal quirks of character or interests, such as: “If a song played whenever you entered a room, what would it be?” or “If someone wrote a profile article about you, what publication would you want the article to be in?” Some questions are sheerly for fun: “If you were a professional wrestler, what would your stage name be?” or “What is your go-to karaoke song?” Many questions provide a small window into personal values: “Would you rather always be late or always have to wait for other people?” “Would you rather have people view you as dishonest or incompetent?” I try to not get too controversial or heavy, but some answers lead in that direction.

I recently asked a question that provided a great insight into the way people think about the world. The question included a rational mathematical decision, cognitive bias, and has strong implications for how a person chooses to live their life to the fullest. 

The Question

I sat before the computer screen looking at the roster of members for my 5:30 class. I was again racking my brain for a good Question of the Day. My mind started venturing in the direction of a cash reward for one of two risky endeavors. I was trying to think of two potential challenges that were achievable, but not with 100% certainty. Say, “You can win a $100,000 by performing a perfect parallel parking job or hitting a basketball shot from the free throw line. What do you choose?” That felt unsatisfactory; not everyone plays basketball and we live in a city where not everyone drives. I needed something more uniformly accessible. My mind somehow landed on the rolling of dice. Everyone can roll dice. What I settled on was “You have one roll of a die to win a cash prize. You win the money if you land on the number 3. You can either roll a 6-sided die for the chance to win $100,000 or roll a 64-sided die for the chance to win $1,000,000. What do you choose?”

A little explanation on why I chose those numbers. Both sums of money are large, but neither are enough to retire away on. That said, $1,000,000 is more of a life-changing sum and $100,000 would alter your financial comfort, but not be enough to do something drastic like pay for a house or college education. The 6-sided die was chosen because it’s the standard-issue die and I chose the 64-sided die to make the big win just more than 10 times as risky, since the payout is exactly 10 times as large. I figured if I raised the chances exactly proportional, people would all just play the game for the big money. Since I always play Question of the Day with the class, I knew my answer would be to take the shot with the 64-sided die and go for the big shot. I imagined we’d have some risk takers, but most people would play it safe. After the first round of the question, I would ask some follow ups to see how many people I could get to change their mind by either changing the amounts or changing the odds on the die.

I was a little surprised that in my first class of about 10 people, only 1 person said they would roll for the big prize. My surprise was compounded when I changed the circumstances to a 32-sided die for the $1,000,000. No one budged. I was astounded when I changed the prize of the 6-sided die to $10,000 and kept the 32-sided die at $1,000,000. Only a few people changed their mind. In my morning classes the next day, I didn’t even open with the 64-sided die, I went straight to 32 and no one would take the shot at the $1,000,000. Lowering the payout of the 6-sided die had a similarly small rate of conversion to the risky 32-sided die. 

Number Crunching

There are some relevant mathematical, economic, and psychological elements that provide insight into this question, the response, and my surprise. First off is the Theorem of Expected Value. First arrived at by French mathematicians in the 17th century, Expected Value states that the value of a future gain should be directly proportional to the chance of receiving the gain. In this question, as opposed to some future stock speculation, the chance or probability of the outcome is easily determined because it is fixed by the number of sides of each die, either 1/6, 1/64, or 1/32.

Our Expected Values breakdown is as follows:

1/6  x 100,000 = 16,666.67

1/64 x 1,000,000 = 15, 625

1/32 x 1,000,000 = 31,250 

1/6 x 10,000 = 1,666.67

What we see here is that as I originally construed the question (6-sided for $100,000 and 64-sided for $1,000,000), the expected value is higher with 6-sided die. What I thought, and this was my own reasoning, was that some people would take the risk for the more life-changing amount of $1,000,000. I was wrong. People were risk averse. I was so wrong that even when the EV was clearly higher with the 32-sided die for $1,000,000 (EV=$31,250), people still chose the “safer” route of the 6-sided die for $100,000 (EV=$16,666.67). It wasn’t until I lowered the 6-sided die to $10,000 (EV=$1,666.67) that I got some people to move, though most still chose the 6-sided die. That means that the majority of people I questioned would have chosen to roll the 6-sided dice with an EV for each roll of $1,666.67 instead of $31,250 with the 32-sided die.

There are a couple of influential factors to note. An individual’s personal financial situation is certainly relevant. An individual who never has had more than $10,000 in the bank will have a different relationship to $100,000 than an individual who already has $200,000 in savings. Similarly, an individual who could pay off immediate debt or get a jump on homeownership utilizing the $100,000 could view the higher chance of success as more important. The chance of success with the 6-sided die is 16.67% and the 32-side is 3.1%. You are certainly more likely to come away with something rather than nothing with the 6-sided die. The closer your personal financial situation is to nothing you may consider it “rational” to get something, though this still wouldn’t be rational in the classical economic sense of maximizing value. I should also note that a couple investment savvy individuals did the exact calculation for EV and made the choice immediately.

A treatment of this Question of the Day and the response cannot leave out Prospect Theory, a theory of behavioral economics and cognitive bias developed by psychologists Daniel Kahneman and Amos Tversky. Kahneman went on to win the Nobel Prize for his work on the theory. A complete expounding of the theory is beyond the scope of this essay, but the theory deals with the different cognitive biases individuals have in situations of gain and loss. One conclusion of the theory is that in a situation of potential gains, individuals become risk averse. Essentially, just what we saw with the response to the dice question. Even though the potential gains were greater and a rational mathematical analysis would tell you to roll the 32-sided die for the chance at $1,000,000, my limited group of responders overwhelmingly sought the smaller gains due to the lower risk of getting nothing. It’s also worth noting that Prospect Theory also states that in a situation of loss, individuals become risk seeking. So if I were to flip the question to the prospect of losing $100,000 or $1,000,000, I would theoretically get a bunch of risk seeking responders.

The Game of Life      

Oftentimes, I view a Question of the Day that has such a one-sided response as a bit of failure. Not in this case. This was one of my favorite questions and answers. I have often been asked by members of my gym, “Do you record our answers somewhere? Are you going to do anything with them?” This is the only time I’ve felt compelled to do so, and it’s not because of the implications of how people spend or save or invest their money. I’m actually not a person especially concerned with money. I think most people overestimate its value.

And there’s the rub, I am very interested in values. What do you really value? What is important to you? How do you value Joy or Fulfillment? We have a limited time in this life. Are you living your life in a way that maximizes those values?

I can give some concrete examples from my own life. I didn’t always run a gym. I used to be a university administrator. I made a decent salary, had a stable career with an upward trajectory, and worked in a generally respected field. One problem: I hated my day-to-day life. I went to an office full of cubicles and couldn’t wait to get out of it. I experienced no joy in what I did. I value the joy of life. I had a passion for fitness and helping people. Leaving that steady job to work in a different field seemed so risky. Would I make the same money? What would people think of me? I stayed in education administration for years. I chose the safe route. Eventually, though, I started to think about what I valued in life. Was it living a safe life or an enjoyable one? Did I want to dread the space I walked into each day or have reverence for it? I took a leap. I gave up a bunch in salary to start. I worked really odd hours. I had to hustle from one gym to the next. I made it work. When I was a child, gym class was my favorite time of day, I now teach gym class to adults every day. I hang with ex-athletes and talk sports. I teach people who have never been in the gym how to lift weights and see their self-confidence rise. In the fitness industry we have a mantra of making a class the “best hour of their day”. That means that everyday I play a role in the best part of someone’s day multiple times a day. I help facilitate physical development, social bonds, and the joy of play. When making the decision to leave my role in administration, I chose the higher expected value in a joyful life than the financially safe play. I took the risk to live out what was truly valuable to me.

Similarly, I write every day. I am editing the draft of a book. I have ideas for my next two books. I’m finishing up this essay right here. The most likely outcome is that not many people read this. The books I write may never even get published. The safe play would be for me to devote time to personal training and remote programming. I now make a more stable salary than in those initial days in fitness, but the safe thing to do would be to make more money using the skills I have. Why would I waste time writing? People don’t even read anymore. The answer is because I value living a life fully engaged in intellectual and creative pursuits. I value having my voice present in the discussion of ideas. I will take on the risk of writing that book that no one read because I place value in engaging in creative expression. I will take that shot. If I am able to be successful in that endeavor, that is a more radically life altering than getting the income from a few extra clients. I want to live my life to the fullest expression of my values.

Many times, in response to the dice question, people asked, “Can we get multiple rolls of the dice?” I held firm that you could only get one roll. You only get one shot at this life. If you value something, it’s worth taking the risk. To not do so would be irrational.   

2 thoughts on “Roll The Dice

  1. A lot of times folks share such stories with the punchline “And that’s how we can see that people are innumerate.” There is some of that, but I just see more different values – and I appreciate you highlighting that (the smaller amount of money means more to someone who doesn’t earn much). Our internal life – what we feel – is also important. The lottery makes no economic sense as an investment strategy, but buying a lottery ticket allows us to imagine possibilities that dutifully saving pennies doesn’t. So even though the saving pennies “dreams” are more likely to come through, a lot of folks would rather have the chance (based on very small chances) to “dream big.”

    I’m glad you shared this. I miss CCCF, but in assessing risk and looking at alternatives it isn’t the right time to rejoin the fun.

    Like

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