These days I have started to think more and more about our actions resulting in a probability distribution over possible futures. There is a probability intrinsically attached to an event and the best you can do is either the estimate is accurately or increase it through action but you can never reach certainty.
If you have noticed on flight booking websites, they ask you to insure your ticket for 200 incase the flight gets cancelled by the airline (you’ll get full refund of ticket). Assuming average flight cost of 5000 is it worth taking the insurance? Calculation tells you that if the chances of cancellation by the airline is less than 4% you shouldn’t take the insurance as it’s better to lose the whole ticket price one time than to spend extra 200 on every flight.
A lot of these decisions we take are not taken like this, they are taken through emotions. It’s difficult to understand which direction the emotions will tilt in a situation of chance (or risk).
Will you take a 1X guaranteed vs 3X with a probability of 50% bet?
If you would take the 3X with 50% then what about 1X guaranteed vs 2.1X with a probability of 50% bet?
It depends on what the bet involves also, in matters of money some people (me) could be conservative and only invest money in FDs, others could be investing in mutual funds, stocks or real estate. In matters of career, someone could be trying out a riskier path and others a more safer route etc.
What bets should be taken then? Should we blindly take bets with the highest expected value? As Lakshmi pointed out, then you would never buy lottery tickets. On thinking more, the following three kinds of bets appear good to take.
Let’s say the range of the bet is the maximum you can win or lose.
Bets with higher expected value when the range is comparable
e.g., 1X (100%) vs. 3X (50%). Take 3X (with 50%).
Bets with lower expected value but where is range is one or two orders or magnitude greater
e.g., 1X (100%) vs. 100X (0.5%). The expected value of the first bet is higher, but in many cases, it would still make sense to play the latter.
The lottery is an obvious example of this case. The winning prize is so life-changing that it makes sense to play it because a reward like that is not accessible through any other means. The other example is insurance. Think medical insurance, for example, the cost of treatment of a chronic disease or a critical surgery can’t be borne by most families. So makes sense to opt for insurance with a much smaller premium (the expected value of treatment must be lesser than the premium because the insurance that’s how insurance companies make money)
Bets with similar expected value but short time interval of success
e.g. 10X (10%) vs. 100X (1%) has the same expected value but makes sense to play the first one because you’ll get the reward early. You might not have enough time or capital to keep playing very high-reward, high-risk bets.