The limit doesn't matter so much as striking it in the first place. Realistically, all of the mentioned investments are within the realm of reasonable thought. The presumption of a black swan is that it is completely outside the ability for one to rationally assess a system then predict it with decent success. 5/40 would be a phenomenally high success rate.

Lottery is totally not black swan, which is exactly what I was trying to say. Despite having prior knowledge of the company's situation (unlike a completely random lottery), it seems to me that these investments are closer to the lottery than black swan.

You don't place bets on a specific black swan, but you could place a different, outside bet on a disrupting event (kind of the idea of antifragile, benefiting from disorder). I think under Taleb's comments in Antifragile, living life as an artist as opposed to someone who is inherently reliant on the stability of say, an office job, is placing that bet every day.

The point is that is that you can precisely calculate the (negative) expectation value of investing in lottery tickets. Or even the expectation value of lottery tickets.

But you can't calculate the expectation value of startup investments. One outlier skews the whole sample, and there is no limit on how high.

Taleb explicitly placed startup investments as those that are antifragile.

I also misunderstood this

    It's more like when a small group of people split a large powerball jackpot

as

    [A Black Swan is] more like when a small group of people split a large powerball jackpot

Why is it even unusual for multiple people to split a large powerball? By definition: a large powerball means there's more tickets and thus more possible matches for the random draw.

Another minor point: there's gotta be dozens of people playing the Lost numbers, the Miami heat starting lineup, etc... every time, so there are natural clusters of group splitting jackpots for lotto winners .

I just said group because presumably he wasn't the only investor in those companies, so a group of people stand to profit. If he was the only investor I would have said individual. It's also meant to highlight the fact that multiple people are in on this, whereas an actual black swan event is something that tends to be much more difficult to predict or be a part of.

I would be amazed if someone could go 5/40 in predicting black swan events under their original definition.

I think the "group" here splitting the Powerball implied a group of people collectively owning/splitting a single winning ticket (such as an office, team, or family pooling money to buy a block of tickets) rather than more than one winning ticket splitting the jackpot.

Much like a group of investors investing in early stage companies.

Ahh, I see the confusion now, sorry. Thanks, edited for clarity.

> I think there's a difference from a Powerball jackpot. There, the upper limit is defined. Whereas there's no upper limits on Sam's investments.

Statistically, you can still define a finite expectation value for an unbounded probability distribution, just as you can compute a finite value for an infinite sum.

How does that work?

In the general case, you'd take whatever formulas you have for return rate and corresponding probability (e.g. exponentially lower chances of exponentially higher returns), and feed that into a definite integral from -infinity to infinity (0 to infinity in the case of a model like investment return rate where you theoretically can't lose more than you put in). Consider, for instance, that the area under a standard normal curve (like any probability distribution) is 1, yet that curve extends infinitely in both directions, and there's a non-zero chance of it producing an arbitrarily large value.

If you have a continuous analytic model, you can integrate that analytically (or for the various standard models, just look up the answer based on the parameterization). If you have a discrete analytic model (a step function), you can construct an infinite series. If you have a model based on discrete statistical samples and extrapolations thereof, you can use a combination of numeric integration/summing and model-based bounds.

So, even though the total possible return on a business venture is potentially unbounded, you can still establish a finite expectation value for it.

> Whereas there's no upper limits on Sam's investments.

There's no public company with a valuation above $1 trillion, so there's an implied upper limit in practical terms.