“Without risk, there is no reward.”
But what does that actually mean?
A player starts with resources $X. She is offered a seat at the table for a certain game. Based on what she knows of the game, she makes a risk/reward calculation. “If the game goes well, what are my different positive outcomes? If it doesn’t go well, what are my negative outcomes? Am I okay with the worst possible outcome? Does my willingness to risk the worst possible outcome depend on my calculation of the best possible one? What is my projected probability distribution of these different outcomes?”
Generally, downside means ending worst than when you began (end the day with less than your starting $X). Thus you must ‘risk’ some starting resources in order to play. Downside can be expressed as a distribution of these negative values (e.g. 5% of losing $1, 2% of losing $10, etc.). Upside is the same for positive values (e.g. 2% of winning $2, %20 of winning $100, etc.).
Just because a game has a positive expected value (all scenarios, multiplied by the probability of that scenario, add up to more than zero), doesn’t mean it’s always worth playing. That’s because the downside is not always balanced out by the upside: individual risk preference determines whether downside is acceptable or not.
Different games have different possible distributions:
Note the axes in these is critical to understanding what these represent: the x-axis represents the value of the outcome (for example, bigger is better), and the y-axis is how probable an outcome is.
Importantly, each of these distributions is not uniquely tied to a game: the distribution is one person’s model, and multiple people can have multiple models for the same game. In fact, it is these differing models that allow for positive-sum economic transactions, since two people can make a trade for a piece or all of a game in such a way that moves their expected outcome up and to the right.
A distribution can be carved into multiple pieces, which can be progressively characterized. In this example, the negative outcome is so bad that it outweighs whatever winnings one might gain in the positive scenarios. Additionally, the negative outcome might be so bad that the player can play no future games, known as ‘blow-up’ risk, which is effectively Game Over.
It is worth noting that distributions can be aggregated, which is sometimes a way to create value. For example, car insurance works because one person cannot run the risk of being bankrupted by an accident, no matter how low the probability. That person is willing to pay an amount greater than the EV of accident scenario (say, 1/10000 chance of $100,000 of damage for -$10). An insurer is willing to charge $20 for this, because by aggregating thousands of car insurance plans, they can guarantee they will never go bankrupt given some average number of accidents. In essence, their aggregated risk-reward distribution is different than an individual’s, allowing them to provide a service that is worth more to an individual than what they pay for it (creating a market).
With this framing, we can start to evaluate all sorts of projects through the lens of risk and the buying and selling of liability (responsibility for negative outcomes). A construction project, for example, entails a series of such transactions.
Consider the game: a developer decides to buy a piece of property, build a home on it, and sell the home. The game is only worth it if the home sells for more than the property was purchased for. However, there are hundreds of things that could go wrong, up to and beyond an unfinished or unlivable home.
There is a small chance that the developer pays for the property, but is actually defrauded by someone falsely claiming to own the property. The outcome in that scenario would be pretty negative, because the developer would have lost the money in the purchase (only regained after criminal investigation and court) and completely unable to ever recoup that money by selling a house on that property. This is solved by title insurance, a service that verifies that the seller is in fact in a position to sell the property. Title insurance companies use an insurance business model - when they certify ownership, they in fact sell an insurance policy, so that if it turns out the certification was faulty and the developer is defrauded, the title insurance company will be on the line for the whole purchase amount.
There is also a small chance that the map that is used to design the building, and which is the foundation for all construction plans, is flawed. In this case, the developer might learn halfway through a project that their site plans are inaccurate and therefore illegal or unworkable, etc. A surveyor certifies the map and takes on liability in case such a flaw is found, so that the developer no longer has as much downside in that scenario.
As a third example, the architects and engineers drawing up and working on the building plans could design a flawed building, that is so bad that it is marked as unlivable and therefore unsellable. Again, the developer would be left with a half-finished house, completely unable to recoup any money without tearing down the house and starting again. And so the architects and the engineers certify their respective plans, taking on liability in the case of any terrible errors.
Therefore, a product like title insurance is able to completely transform the distribution of outcomes for the developer.
