Probability Matching and Nature

This is an esoteric topic this week, but it’s also one that I find really interesting. Probabilities can sometimes predict the future with surprising precision, just like physics models can predict how a car will drive or how electrical current will flow through a system. We know that flipping a coin will always yield 50% heads and 50% tails, maybe not on 10 tries, but on 100 or 1000 tries, the probability will always converge to 50/50 with 100% certainty. That certainty makes probability useful both in explaining the world and predicting the future.

Probability matching is an area of probability study that I was less familiar with until recently. It helps explain why some people seem to make obvious suboptimal decisions. Nature’s goal is to maximize survival and overall growth over time under all circumstances. Over time is a critical variable here. Consider the classic Murphy’s law: Anything that can happen will happen. It’s true, and nature somehow tends to take that into account.

It turns out that people and animals naturally organize themselves according to underlying probabilities, which we can observe even if we don’t yet know the probabilities of the outcome, just like you can observe flipping a coin. You would think that every participant would only make the optimal choice because it’s obvious, but they don’t. This phenomenon has been studied both in practice and in theory. Fish fed 70% on one side of the tank, and 30% on the other will group themselves on both sides proportionately instead of sticking to the 70% side only. WW2 army pilots were given a choice to wear flack jackets to protect against bullets or parachutes to protect against rockets. At the time, they knew bullets were the more common risk. The army assumed the flack jackets would be everyone’s choice because it’s optimal at the individual level, but it turns out roughly 30% of the pilots chose parachutes, and that roughly ended up matching the underlying probability. When the army tried to mandate flack jackets, there was a revolt, and the army went back to allowing for random choice, which again ended up around 30% parachutes once again.

Bitcoin comes to mind here. Before you roll your eyes, I’m not part of any fundamental group pro or against Bitcoin. I mention it because the probabilities and distributions of outcomes for Bitcoin at this time are pretty straightforward because they are extreme. Probability matching tells us how to approach investing in Bitcoin based on how people have “randomly” organized. If 10% of the population and 1% of the capital are aligned with Bitcoin, that tells us what we need to know. That translates roughly to a 10% chance that people end up using Bitcoin for anything useful in the future and a 1% chance that it will become a global currency standard. This also means that it’s logical to put roughly 1% of your wealth into Bitcoin to maximize your probability of success at this time under all scenarios. I’m not pitching Bitcoin; I’m using it as an example because it represents optimally diversifying using the current distribution of how people have made their choices.

Florida and climate change also come to mind. A certain portion of the population refuses to live in Florida due to extreme climate risk, while another portion enjoys the daily sunshine, low taxes and beautiful beaches. If you’re optimizing for daily enjoyment, Florida is fantastic. If you’re optimizing long-term to avoid ocean climate disasters, you’re not picking Florida. The probability in this scenario is not 0% or 100% on either side. People sort themselves into both locations to maximize collective long-term opportunity and enjoyment while ensuring survival.

If we’re speaking purely economically, the group that makes only concentrated optimal choices will tend to dominate. The problem with that “optimal” strategy is that it is explicitly exposed to disaster scenarios. Nature is more concerned with overall survival, so people will group accordingly. Some will fall into that short-term optimal bucket of thriving and then not surviving, and others will make suboptimal choices that end up working out for them in the end.

When you apply probability matching to investment strategy, you have the same goal as nature: to maximize long-term opportunity while ensuring survival. This means that optimal investment strategies will always have a portion that is questionably or curiously allocated suboptimally, like holding extra cash as Warren Buffett tends to do, owning anything other than the best-performing asset in a bull market or owning weird, controversial assets like crypto. Probability matching suggests we can uncover underlying probabilities in a system by observing how people ‘randomly’ distribute themselves. As the world changes and people adapt, their choices reveal how probabilities shift over time.