Deep-tech, Venture Capital, and Saint Petersbug's Paradox

Venture capital funds are well-known to pursue the following strategy: pick a large number of potential heavy-hitters to fund, and and hope that a few of them will turn out to be wildly successful, so those that do work more than make up for the investments which don’t.

This approach can make a lot of sense for VC portfolio managers that have the benefit of diversification — but what about the entrepreneurs that get funded as one of many bets in the portfolio of the venture capital firm?

VC funding can be both a blessing and a curse. As the upside is well-known, the downside resides in the dynamics in which VC-funded companies are usually put into: a high-growth rate is either achieved soon, or the project will be determined to have failed. Combine that with the “fail fast” mentality, and we have a hit-or-miss bet with a low probablility of success.

The situation reminded me of Saint Petersburg’s paradox, a theoretical lottery game whose expected payoff approaches infinity, but nevertheless, the lottety ticket is worth only a very small amount to the participants.

Saint Petersburg’s lottery game

The game is about tossing a coin, where the ammount of the price is doubled every time a tail appears, and is collected when a head does. Mathematically, the expected return is inifite, in view of the following sum:

$$E = \frac{1}{2} 2 + \frac{1}{4} 4 + \frac{1}{8} 8 + \cdots = 1 + 1 + 1 + \cdots = \infty$$

however, the question is how much would a ticket to pay this game be worth, realistically?

Considering nothing but the expected value of the game, you should pay any ammount of money in order to be able to participate. However, most reasonable people wouldn’t bet more than $20 at this infinite expected-value lottery, given that the actual probability of collecting a sum larger than any given ammount decreases exponentially fast.

One of the ways of resolving Saint Petersbug’s paradox, Daniel Bernoulli’s, introduces a logarithmic expected utility function, which values any possible outcome by the logarithm of the ammount it changes the gambler’s total wealth $w$. If $c$ is the cost of the ticket, Bernoulli’s fair value calculation yields:

$$\Delta E(U) = \sum_k \frac{1}{2^k} \log(w - c + 2^k) < \infty$$

According to this formula, the wealthier a person is, the ammount this person should be willing to bet on this game should also increase. On the other hand, poor people shouln’t want to place high bets on this game.

Bootrapped vs venture-funded startup

But what does this tells us about bootsrapping vs venture-funding, and deep-tech or sci-preneurship?

What sort of entrepreneur should be willing to take the bet offered by venture capital firms — of a small probability of obtaining a huge payoff, rather than that of a good probability of obtaining a good level of success?

I believe that creating a startup is more of a career decision than a financial decision. So who should switch careers into vc-backed startup entrepreneurship?

Going back to the lottery game, the later you decide to switch careers, the higher is the price ($c$) you are probably paying. Dropping out of college to create a venture-backed compnany? That is some price to pay for sure, specially if it was a good and prestigious school you were attending. Dropping off from a career in big tech? Well, that’s an even higher ticket price.

But what about deep-tech, from the point of view of so called science-preneurs — that is, indivuals how seek to transform scientific discoveries into real-world applications, in some cases, discoveries done by themselves or people around them. Should they go straight after VC funding when they think they have something of value?

For early-stage academics, joining a vc-backed company probably means leaving behind a highly-competitive career, which, regarless of the pay or the work-life balance it brings, was hard enough to get into already. And for recent PhDs, I believe that the probabilities of landing a great industry job are reasonably high, specially considering that PhDs can realatively easily switch fields into areas like finance, consulting, or software engineering.

In a few words, I believe most science-preneurs (PhDs or academics) are indeed placing a big bet ($c$) if they ever decide to go venture-backed. So, unless they are already wealthy (high $w$), the rational thing to do, I believe is to strive for more reasonable odds of success than those typically offered by classical VC funds.

Funding EpsilonForge: an R&D studio and scientific software factory

For quite some time, I thought that the only way of launching a startup, specially a deep-tech startup, had to start with 30-second elevator pitches to potential investors. I also knew that this just woulnd’t be possible for me.

The reason is that I tend to try to chase good ideas, not necesarily big ones.

It was not until I found about bootstrapping or indie hacking, that I got excited with the idea of launching a startup. And in that spirit, is that I set my goals and expectations with this project.

While developing products aligned with my R&D background is my top priority, the risk of commercial failure is still quite high. So, in order to balance the risk, I came to the conclusion that some diversification can be built into the business model by including services like software development for third-parties, or consulting, which are sure not going to make any VC excited about this business.

So, at EpsilonForge we will try to produce propietary producs based on our R&D, but also to provide a wide variety of services that align with the technical strengths that we defined as our core. And that’s the reason I’m calling EpsilonForge an “R&D studio and scientific software factory”.

This is very early on this journey, so stay in touch if you want to follow along or connect in any way.