How Much Could Luck Have To Do With Income Inequality?

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A few months ago, the website DecisionScienceNews.com posted a summary of the results of a game simulation, "Counterintuitive problem: Everyone in a room keeps giving dollars to random others. You'll never guess what happens next." The simulation isn’t just a fun game. It gives some insight into just how much luck can influence wealth distribution. Here are the rules of the game: 45 players each have $45. In each round, each player has to give a dollar to another player on a completely random basis. Each round is independent and random. Players don’t do anything to “earn” the money. Whether or not a player has received money on a previous round doesn’t change the chances they will get a dollar (or more) on the next round. So, in any given round, there are a lot of ways the dollars could get distributed, with most extreme being that each and every player could receive a dollar or one player could get a dollar from each of the other 44 players, leaving all but one other player without a dollar for that round. If a player ends up with no money at the end of a given round, they don’t have to give a dollar on the next round. In other words, no player can end up negative. The simulation was run for 5,000 rounds of the game, and the results are really surprising.

Intuitively, it feels like each player should end up with about $45, since the dollars are distributed randomly. But reality does not remotely live up to this expectation (as you can see by watching the video embedded in the article). Instead, after 5,000 rounds, one player ends up with over $200, and the next two wealthiest players end with $150 apiece. That means that three of the forty-five players end up with 25% of the money.

These results point out important lessons about intuition, randomness, skill, success, and survivor bias (the idea that we concentrate on those that are successful, assuming they have something to teach us, while ignoring those that aren’t).

Because this experiment was a random computer simulation, we know there was no skill difference among the 45 "players." We don't have to debate whether more charming people got more money, or whether moving through the room in a certain pattern improved results, or whether there was some sort of crony collusion that caused the money to end up with certain players. By luck alone, we ended up with something that looks like some serious income inequality, a finding that feels unintuitive. The author of the post said as much: "If on quick reflection you thought 'more or less equally', you are not alone. I asked 5 super-smart PhDs this question, and they all had the same initial intuition."

An outcome like ending up with all the money in a game can raise the question of whether those succeeding had greater skill, but it doesn't provide a definitive answer. The only way to answer whether the most successful player got the money because of skill is to keep playing the same game multiple times and see if the same players end up with all the money. If we reran this simulation, you would end up with three players with 25% of the wealth again, but it would not be the same three players. This game shows that you can win just because you got lucky.

When I shared the results of the simulation with a friend of mine, he had a very insightful and funny comment: "The guy at the right of the distribution (who ended up with all the money by luck) is clearly going to write a book about his amazing strategy for getting rich."

Annie Duke is an author, speaker, decision strategist and a former professional poker player. Her new book, “Thinking in Bets: Making Smarter Decisions When You Don’t Have All the Facts,” will be released on February 6, 2018. Find out more about Annie at www.AnnieDuke.com.