# On Probability

## What most people don’t understand about the world around us

“In a strategy that entails ruin, benefits never offset risks of ruin“ — Nassim Nicholas Taleb

There are two types of probabilities that are of utmost importance when acting in our (uncertain) world. Ensemble probability and time probability. Let’s consider a thought experiment to illustrate the difference (taken from *Skin In The Game *by Nassim Nicholas Taleb).

**First case**: 100 people go to a casino to gamble for a day. In the evening, when all participants leave the casino, 1 out of the 100 people lost all their money. Based on this, you can calculate that around 1% of gamblers go bust on average.

**Second case**: One person goes to a casino to gamble 100 days in a row. On day 28 he loses all his money. Consequently, there is no day 29 as all his money is lost. The probability of going bust is 100%.

The difference between the two is that in the first case, one gambler was not affected by the other (they were independent). However, in the second case, one day affected the next day as it was a sequence of trials. The probability of the first case is called **ensemble probability (**as the average taken from a group is considered). The second case demonstrates **time probability** (as one person is exposed to the same event over time).

What matters in this context is to understand **tail risks**. If you consider a normal distribution for events that could take happen, many of which are on the tails of the distribution (i.e. extremely unlikely to happen). Based on the first case, going bust has an extremely low probability of happening. However, when thinking in financial terms, fat tail risks are the cases where the value of a security can move significantly (more than 3 standard deviations) resulting in the destruction of value. Those “black swan” events, despite being unlikely judging from an ensemble probability standpoint, are likely to happen from a time probability standpoint. Hence, when ruin is at stake, this risk needs to be accounted for.

What we can learn from this is that *sequence matters*. “In a strategy that entails ruin, benefits never offset risks of ruin“ — Nassim Nicholas Taleb. So we must think wisely about the risks we are taking in our (personal) lives.