The idea of developing a network of mental models is based on the concept that everyone should approach problem-solving from many difference perspectives. The traditional teaching method used in the typical American classroom revolves around the idea that topics should be learned in isolation from other topics. This inhibits students from learning that ideas from multiple disciplines can be used with great success when trying to solve problems. Focus investors should develop their own systems of mental models to help them make better investment decisions.

In the following section of this article the various individual areas of knowledge that Mr. Munger has discussed in several of his speeches will be covered on an individual basis. This information should help everyone develop and enhance his or her own system of mental models.

### Mental Models: Mathematics

It is critical that investors have at least an understanding of high school level mathematics. Compound interest, the time value of money, and the basic ideas of probability theory, for example, are vital concepts that all investors should have a firm grasp on; they must be a part of their basic repertoire of skills. If investors fail to add these skills to their repertoire they will be at a severe disadvantage to others in the investing field who are equipped with these skills.

Let’s examine more mathematical concepts that should be part of your investment toolkit. In this section we will cover probability theory, decision trees, and the law of large numbers. Compound interest and the time value of money were covered in Part 1 of the Focus Investing Series and as such will not be covered here.

### Mental Models: Probability Theory

“Fear of harm ought to be proportional not merely to the gravity of the harm, but also to the probability of the event [occurring]” – Blaise Pascal

“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 In 1654, Blaise Pascal, a prominent French scientist, mathematician, and philosopher, and Pierre de Fermat, a government official and mathematician, exchanged a series of letters that discussed the odds involved in games of chance. They formed in those letters the basis of what today is known as probability theory.

Probability theory is the branch of mathematics that develops models to help explain random phenomena. Traditional questions that involve randomness include, `will it rain today?’ or `will I be dealt a royal flush today?’ These two questions have one common feature: the outcome (it rains today; being dealt a royal flush) cannot be accurately predicted on a consistent basis in advance, but we know that if enough days are observed, it will rain, and someone will eventually be dealt a royal flush.

The practical aspects of the theory were soon realized. For instance, the study of human mortality by life insurance companies resulted from applying this theory. Probability theory is now a major branch of mathematics with widespread applications in science and engineering.

Probability theory also helps us manage risk. In his excellent book, Against the Gods, Peter Bernstein states that the “essence of risk management lies in maximizing the areas where we have some control over the outcome while minimizing the areas where we have absolutely no control over the outcome and the linkage between effect and cause is hidden from us.” This can certainly be applied to investing and is why investing only within your circle of competence is so critical to the success of the focus investor.

#### See full article on The Focus Investing Series Part 3: The Munger Network of Mental Models in PDF format here.

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