In most games of chance, the odds are easily figured out. You can calculate the odds in advance for coin flips, dice throws (craps, backgammon), or a spin of the roulette wheel because each has a fixed set of outcomes.

Now take a game like the stock market. Calculating odds gets trickier because it adds complexity and uncertainty. The outcomes are no longer fixed and the number of variables to consider grows exponentially.

Unfortunately, human nature makes this worse. It turns out, we’re terrible at estimating probabilities. Our biases get in the way.

Our troubles begin with availability. A simple rule of thumb tells us to put higher odds on something that happens more often. Unless we have trouble remembering how often that *something* really happens.

The availability bias screws with how we estimate probabilities. When we weigh the probability of an event happening, our estimate is based on how easily we remember a similar event and how often we remember it happening. Unfortunately, how easily we recall something has more to do with recency, vividness, and personal involvement.

For example, if I ask you the odds of making money on your next stock pick, your answer might be carefully thought out after days of research and analysis. Or you’ll rely on your most recent successes (or failures) with picking stocks. The latter has nothing to do with probability and everything to do with recency bias. But we rely on it too often for “gut” decisions.

Sadly, absent personal experience, we’ll turn to the experience of others. Because nothing more accurately represents our potential stock-picking success than our friend’s boastful gains and purposely omitted losses.

Anchoring is next on the list. We often use short cuts to estimate probabilities. In a perfect world, we start with an old estimate, consider any new information, and objectively adjust it from there.

Except, we anchor to the old estimate. In the end, estimates that start too low (too high), end up too low (too high). The solution: always start from scratch.

There’s one issue left. We’re terrible at communicating probabilities. If I were to say, “The stock market is likely to crash sometime in the near term,” two problems stand out.

- How much is “likely”?
- How long is “near term”?

My ambiguity is open to interpretation. The reader and their subjective views determine the odds. Maybe I meant “likely” to be 51%. Someone else read it as 82%. And you might see it differently too.

The book *Psychology of Intelligence Analysis* highlights a study of 23 NATO officers and their assessment of words that denote probability. It showed the wide range of answers for terms like *possibly*, *probably*, *likely*, *almost certainly*, *unlikely*, and so on.

A larger study, which you can still take, was done more recently by Michael Mauboussin and his son. Their survey results show how widely we differ in our interpretation of probability values for different terms.

It’s hard to get a point across if everyone values a word differently. Of course, ambiguous time frames present a similar problem.

Now, a certain class of market forecaster prefers ambiguity because it always gives them an out. For the rest of us, the best way to handle this is to attach a number to it to avoid misunderstanding.

Unfortunately, a few minor biases compound our problems with probabilities too:

- We often treat information in a binary way. Either we accept it completely or reject it entirely. We treat it as accurate or inaccurate. There’s no middle ground or partially accurate. When we treat information as 100% or 0% accurate when it’s really 70% correct, that can lead to under- or overconfidence in our estimates.
- The law of small numbers is the opposite of the law of large numbers. We mistakenly treat a small sample size as though its a large one. And small sample sizes can horribly misrepresent the probabilities seen in a larger sample of data.
- The law of small numbers gets undermined further by another bias. Oftentimes, we put more weight on a single experience — one outlier — over years of data. One terrible meal at a restaurant overwhelmingly outweighs the view of hundreds or thousands of other diners.
- Finally, we overlook the absence of information. It helps to know if important information is missing. When you know what you need to make a good decision, the lack of information — what you don’t know — could be more informative than what you know and lead to a better decision.

Finally, our troubles end with basic math. We’re not great at doing math with probabilities.

What are the odds of flipping a coin and getting heads three times in a row?

Future estimates revolve around an outcome. In most cases, that outcome is due to a sequence of little events — like three coin flips — linked together. Each little event has its own probability. The product of the little events is the probability of the final outcome.

So the odds of flipping three heads in a row is 50% x 50% x 50% or 12.5%. When you add a fourth little event — like another coin flip — the final odds will never get bigger.

And here’s one final tip: the lowest odds of any event in a sequence sets the upper limit for the odds of the entire sequence. No matter how optimistic new information might seem, no matter how dramatically that information might shift the odds of one little event, the odds of the sequence are still limited mathematically.

The trouble is that most people grasp the concept of probability and odds. Putting the numbers to work is the problem. Human nature makes decision making easier in many areas of life. Math and probabilities are not one of them.

### Last Call

- When The Magic Happens – M. Housel
- How Much Conviction Do You Hold in Your Investment Views? – Behavioural Investment
- Risk Is Never as Simple as It Seems – A Wealth of Common Sense
- A Viral Market Update: The Strong (FANGAM) Get Stronger! – Musings on Markets
- Value Investing: An Examination of the 1,000 Largest Firms – Alpha Architect
- Value is Not a ‘Risk Premium’ – Klement on Investing
- Rebalance Timing Luck: The Dumb (Timing) Luck of Smart Beta – Epsilon Theory
- A Conversation about Buffett, Berkshire, Quality Shareholders w/ Lawrence Cunningham – ValIdea
- What a New Marshmallow Test Teaches Us About Cooperation – Behavioral Scientist
- The Beatle’s Breakup and Why Their Music Matters 50 Years Later – RollingStone