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## Ergodicity is a Useful Concept to Know

by | Sep 2, 2021

Ergodicity is a concept from thermodynamics. It’s complex but a simplified way to think about it is where group probabilities don’t necessarily apply to individual events. What happens to the population at large isn’t what matters — it’s what happens in your situation that is important to you.

## Examples

The classic example of this is Russian roulette. On average, you’ll survive a single game with a high probability (5/6th). Yet what happens on average isn’t what keeps us from playing — it’s the chance of a single losing spin. Or think about roulette at the casino – on average playing the game results in losing money, but some individuals will walk away winners. It is the unlikely chance of winning that lures gamblers into swimming upstream against the probabilities.

Another good example of this concept is a story from the 1960s when Nobel Prize-winning economist Paul Samuelson asked his lunch partner in the MIT cafeteria if he’d accept a wager in which the colleague would win \$100 on a coin flip if it was heads and lose \$50 if it was tails. This seems like a great bet because it has an expected return of \$25. But Samuelson’s colleague refused the bet, saying he’d only wager if Samuelson would repeat the bet 100 times. The MIT colleague’s response was brilliant. The wager’s expected value might have been \$25, but there was also a 50-50 chance that he’d lose \$50 if he only wagered once. So, if \$50 is more loss than you can stomach, you should decline to play just once even if the expected return is positive. In this case, your chances of making money on the bet improve the more times you play.

## Ergodicity in Action

It’s fascinating to observe how differently we all have acted during the pandemic. Some view the risk of serious illness or death as small (which is true) and thus basically go about their lives. Others have holed up at home and rarely venture out and do so only wearing N95 masks because serious illness or death is a slight possibility. From a group probability standpoint, those who go about their lives are acting rationally, while viewing COVID through an ergodicity lens lends credence to those who take more precautions.

Ergodicity also applies when investing an influx of cash. I wrote about this in an article published on Forbes titled You’ve Received An Influx Of Cash. Is It Best To Invest It As A Lump Sum Or By Dollar-Cost Averaging? On average, it makes sense to invest in a lump sum because the stock market goes up more than it goes down. But “How hypothetical investors fare on average with lump-sum investing is no comfort to the family that invests its hard-earned cash just before the market crashes. For most of the families I’ve worked with, it has been more comfortable for them to invest the money over time and understand that they’ll have a two-thirds chance of not doing as well as if they’d invested it all at once.”

As we move through the world we’re all constantly assessing risk vs. reward of our actions (or inaction). Knowing about the concept of ergodicity can help us understand why we are assessing risk the way we are and can also help us understand why others may make different risk assessments than we do for ourselves.

1. Great post, probability is often ignored when contemplating outcomes.

Two other thoughts: We can weigh the consequence of even a low-probability risk (ie COVID death) but what are the costs of complete avoidance (locking ourselves in a sterile room with no social contact)? Also with respect to mortal threats, we know that certainty of death is 100% for all of us; cause and timing are the only variables. The ultimate question becomes, how will you choose to live your life, regardless of the time remaining?

2. yep — doesnt matter what the group’s odds are — if it happens to you its 100%

3. Love this – I’ve been thinking about this a lot re: the pandemic as well. Another factor that influences how each of us view risk in the world is whether we’ve been the statistically unlucky one with prior life events.

I’ve been in the <1% chance category for at least 2 very different challenging health situations that, according to my doctors, have been pure bad luck (not something I had control over). These experiences have made me forever view things differently any time someone tells me there's a statistically small likelihood of something happening. I now also mentally weigh – "but how bad would things be if I'm the <1 in 100 again?" Since the "how bad" re: COVID can mean death and would also affect my family, it seems important to avoid being the <1% again, especially if I actually have some control over my likelihood of contracting it (vs. sheer bad luck).

Of course, thinking about COVID only from a perspective of "what are the chances I get sick" would be fairly selfish. Wouldn't it be nice if everyone considered that + "what are the chances I could be spreading COVID unknowingly to others?"

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