What can we conclude from the way people play the median money game?

If you haven’t played the game yet and haven’t read the results, please take a similar survey here.

A pretend ultra-zillionaire has invited you to participate in the game that will determine the dispersion of his limitless inheritance. Playing is simple — just pick an amount of money, any amount is allowed, and that’s how much of the ultra-rich man’s fortune you receive! However, you only win if most other players picked an amount higher than you did. Half of the group will be winners, half losers, and the line between the groups is the median amount asked for. Do you pick a low number, just to be sure you don’t leave the game a loser? Or do you reach for a bigger number, to maximize your payout? More importantly, what’s a big number in the first place?

This game has been a compelling conversation starter for me for years. The premise is interesting because of the lack of context. There’s no total amount of money to be dispersed, no friend’s guess to go off of, no base number from which to start your train of thought, so participants are basically taking a shot in the dark.

To find a good answer, I posted a survey similar to various social media. Results were very interesting!

Median for all guesses: $40,000

As will all things internet, anonymity is the harbinger of trolls. The majority of people played the game sincerely, but a few picked amounts that were obviously too high to win or too low to be considered participating. A handful of people asked for more money than currently exists in the world. These may have been people who don’t know the difference between mean and median, and wanted to throw off the numbers by losing on purpose to give winners a bigger payout. Above, anyone guessing more than a billion had their answer changed to a billion, so that I could make a reasonable graph.

There are also a few non-players on the low end, asking for less than a dollar. I decided to purge high- and low-guess non-players from the data to produce a data set that better represents what an actual outcome might look like. To pick the upper and lower limits, I invited reddit respondents to PM me if they were curious about whether they won or lost. I considered the highest and lowest of those, and went an order of magnitude higher and lower to get a minimum of 10 and a maximum of 10 million. Results below.

Median: $20,000

So, the magic number is either $40,000 or $20,000, depending on whether or not anyone tries to game the system. My guess is that no one’s picking 4chan users to play their The graph illustrates some interesting trends:

The trend is logarithmic, not linear.

Powers of 10 are popular numbers — the top four most common guesses are $10k, $100k, $1mil, and $1,000, respectively. These times 5 are also popular.

But wait! There’s more! Almost all respondents completed the extra questions portion of the survey. That gives 23 more categories which we can look at more closely to see some more interesting correlations.

Categories are broken down into groups of equal size as much as possible.

It seems the most high-guessing categories are those that have high exposure to money: high income, high debt holders (homeowners), and people older than thirty were the highest guessers, along with people who consider themselves 7 or higher on the greed scale. Speaking of greed, I found it interesting that respondents’ self-reported greed followed a lovely normal distribution curve, with the few expected trolls reporting 10.

Edit June 30 2019:

Wow, this has gotten a lot of attention! People are asking a lot of questions on reddit and elsewhere, so I’ll add some information for clarity.

First of all, the ‘removed’ results were only taken out to get the second log graph, “Curated Guesses.” The categorical bar graph used the complete data, no results purged. A few people were concerned about the use of somewhat arbitrary values to separate those who were acting as if to win money from those who were acting solely to manipulate final results. Results were only purged for the second median ($20,000) if they were an order of magnitude higher or lower than the highest and lowest known serious results, as gathered from over 100 PM’s on Facebook and reddit. I don’t feel bad about doing this since I included the raw number first. Super-outliers had to be truncated in order for any graphic to make sense. 10⁴⁰⁰ makes even the second ranked number indistinguishable from the 1,000th ranked number, even on a log scale.

Actual questions of the survey after introducing the premise:

How much money do you ask for?

How many years old are you (awkward wording, I know)?

What is your gender?

About how much do you make per year?

On a scale of 1 to 10, how greedy would you say you are? 1 is labeled as “I give all my belongings to the poor,” 10 as, “greediest possible human.”

Do you own a home?

Name a color.

Categorical responses in results were divided into bins of equal size as much as possible i.e., the dividing numbers in income and age were decided based on which numbers would split the sample into four bins of roughly equal size. Gender and color categories included only values that had 50 or more responses. There were fewer than 50 responses of a gender other than male or female.

I’m happy to answer any questions about my work here. Feel free to PM me on reddit (u/120Macky) or email me at macky.davies@gmail.com.