What Archimedes referred to here is leverage. The quote is an illustration of the concept of leverage, which is the idea that a small amount of force applied at the right distance from a fulcrum can move a much larger object. An asymmetric bet is a form of leverage where the potential loss is very limited compared to the potential gain. In rough terms, potential gain is huge while the loss is very limited.
I read this concept in Nassim Taleb’s books and this is a very optimistic strategy when things are in random order. For example when you trade options, it is an asymmetric bet because the potential upside is unlimited, while the potential downside is limited to the premium paid for the option. An option is a contract that gives the holder the right, but not the obligation, to buy or sell an underlying asset at a predetermined price and time.
Let’s use this with our daily life, when you meet good quality people they usually have a great impact on you. If you network with people who have higher integrity and better skills than yourself, you will tend to learn new skills and you have a higher potential to grow with very low chances of doing badly.
Also I have learned from my mentor Mr. Sohi that a 0 to 1 move is always a great strategy. 0 to 1 means that you do something now which pulls you out of randomness and puts you in a position of order. This means that randomness is a place that you don’t wanna be at and order is a place that you desire.If you fail at trying this strategy, it still is a good move because you learn. And if you succeed then 0 to 1 is an infinite multiple move. This is also an asymmetric strategy.
Best poker players are masters at finding asymmetries, and they even fold their loved hand because the loss is way bigger than gain. This is such a simple mathematical move but we humans usually fall into emotions and fail at implementing.
This even works with stock picking. If you notice a huge selloff in a stock and its trading at very low multiples then it creates inefficiencies for buyers. Because most buyers have run away leaving you a higher upside than potential loss. It is always better to buy/sell when there is fear/euphoria. But you have to be a contrarian in your approach. We as humans are wired to follow the tribe for thousands of years. This made sense during the times when our lives depended on tribe’s communication. But in the stock market, sometimes you have to stand alone against the tribe.