Suppose you regard tldroptions.io's probability distributions and outcomes as correct, and the only thing you care about is maximizing the long-term rate of goal of your capital. Then the Kelly Criterion (https://en.wikipedia.org/wiki/Kelly_criterion , a.k.a. Fortune's Formula) says that you should try to maximize the geometric mean of your capital, which amounts to maximizing the expected logarithm of your capital.
To make this concrete, suppose you are choosing between two options:
- (Startup): Working at series C+ start-up for three years, where you receive 1% equity and $100k/yr salary, and have a 20% chance of getting ~$60 million in 3 years (according to tldroptions.io)
- (AmaGooFaceSoft): Working at AmaGooFaceSoft for three years, where you receive $300k/yr total comp (according to patio11)
For simplicity, I will ignore taxes and the time value of money. All monetary amounts below are in millions of dollars. If you have no money in the bank to start with, the geometric means of your alternatives after 3 years are:
- (Startup): exp(.2 log[60+0.3 ] + .8 log[0.3]) = $0.86 million
- (AmaGooFaceSoft) = $0.9 million
In this case, AmaGooFaceSoft is slightly better.
On the other hand, suppose you already have $1 million. After 3 years you will still have the $1 million, plus your salary and whatever money you get from your equity. Here the geometric means are:
- (Startup) exp(0.2 log[6+1+0.3] + .8 log[1 + 0.3]) = $2.8 million
- (AmaGooFaceSoft): 1+0.9 = $1.9 million
In this case, it's better to join the start-up.
The base salary matters a lot. If you have no money in the bank, but you get $150k year at the startup instead of $100k, then the geometric mean of the Startup option after 3 years is better than that of AmaGooFaceSoft:
- (Startup): exp(.2 log[60+0.45 ] + .8 log[0.45]) = $1.2 million