“Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we're trying to do. It's imperfect but that's what it's all about.”— Warren Buffett
You can train your brain to think like CEOs, professional poker players, investors, and others who make tricky decisions in an uncertain world by weighing probabilities....MUCH MORE
All decisions involve potential tradeoffs and opportunity costs. The question is, how can we make the best possible choices when the factors involved are often so complicated and confusing? How can we determine which statistics and metrics are worth paying attention to? How do we think about averages?
Expected value is one of the simplest tools you can use to think better. While not a natural way of thinking for most people, it instantly turns the world into shades of grey by forcing us to weigh probabilities and outcomes. Once we've mastered it, our decisions become supercharged. We know which risks to take, when to quit projects, when to go all in, and more.
Expected value refers to the long-run average of a random variable.
If you flip a fair coin ten times, the heads-to-tails ratio will probably not be exactly equal. If you flip it one hundred times, the ratio will be closer to 50:50, though again not exactly. But for a very large number of iterations, you can expect heads to come up half the time and tails the other half. The law of large numbers dictates that the values will, in the long term, regress to the mean, even if the first few flips seem unequal.
The more coin flips, the closer you get to the 50:50 ratio. If you bet a sum of money on a coin flip, the potential winnings on a fair coin have to be bigger than your potential loss to make the expected value positive.
We make many expected-value calculations without even realizing it. If we decide to stay up late and have a few drinks on a Tuesday, we regard the expected value of an enjoyable evening as higher than the expected costs the following day. If we decide to always leave early for appointments, we weigh the expected value of being on time against the frequent instances when we arrive early. When we take on work, we view the expected value in terms of income and other career benefits as higher than the cost in terms of time and/or sanity.
Likewise, anyone who reads a lot knows that most books they choose will have minimal impact on them, while a few books will change their lives and be of tremendous value. Looking at the required time and money as an investment, books have a positive expected value (provided we choose them with care and make use of the lessons they teach).
These decisions might seem obvious. But the math behind them would be somewhat complicated if we tried to sit down and calculate it. Who pulls out a calculator before deciding whether to open a bottle of wine (certainly not me) or walk into a bookstore?...
If interested see also:
Paul Tudor Jones On 'Imperfect Information'