Common Sense Math of Investing - Part 2 of Focus Investing Series
If winning yields more than losing costs — you win the game.
Today’s newsletter is about education of an investor.
This is the Part 2 of the focus investing series. You can read Part 1 here.
The aim of this newsletter is to give you the intuition behind the difference between probability and payoffs.
By the end, you’ll see how viewing life events through this lens—and adding this tool to your daily mental habits—can enhance both your investing game and decision-making skills.
Fun Fact: I’ve been aware of this concept for five years, but only grasped the intuition behind it two months ago while walking and thinking about how casinos profit from roulette.
Here what we’ll cover today
The common-sense math behind investing.
Why to think in terms of chances and outcomes ?
How to play for outcomes and become smarter with probabilities?
How to tackle investing challenge using tools - Kelly Criterion and Bayesian analysis?
Problem
The math behind successful investing is actually simple.
But using simple things daily can feel dull—and people naturally avoid boredom.
As Charlie Munger said
“It's very simple algebra. It's not hard to learn. What is hard is to get so you use it routinely almost every day of your life.”
If you can follow Munger’s advice, you’ll avoid many common mistakes and stand among investors who win both in the market and in life.
Instead of searching for complex solutions, reapply the simple tricks that have already worked well for you.
Common Sense Math of Investing
The common sense is to keeping two things in mind:
You need to be right more often than you’re wrong.
When you’re right, you need to win more than you lose when you’re wrong.
That’s it.
That’s the common-sense approach of understanding probability and payoffs.
That’s the only secret you need to keep in your mind.
Get the intuition. Improve your chances of becoming a successful investor.
Probability and Payoffs
Mathematics of investing involves two main components:
Probability – the chance an event will happen.
Payoff – the result or outcome if that event happens.
When we are unsure about a situation but still want to express our opinion, we often preface our remarks with: "The chances are," or "Probably," or "It's not very likely." When we go one step further and attempt to quantify those general expressions, we then are dealing with probabilities.
Robert G. Hagstrom, The Warren Buffett Portfolio Play for payoffs. Become smarter with probabilities.
Let’s deal with payoffs first.
How to play for Payoffs?
Forecasting probabilities can be difficult, but payoffs can be predicted - it follows pattern and we can prepare for them.
We don't know when it rains, but we know when it rains we need umbrella.
Thinking in terms of payoffs gives us an enormous advantage. Now, we can see the world - the money and life games with a new perspective.
❌ Predict the timing
✔️ Predict the outcome
As you see you can't do anything with probability alone.
Example - In roulette, the chance of the ball landing on a chosen number is 1 in 38. That’s probability. But the game becomes meaningful when we add a payoff: a win gives you 35 times your bet. Without payoffs, probability alone isn’t useful.
What matters is what you get, what is the payoff, what is the outcome.
To be precise, here I quote Nassim Taleb
If you make more when you are right than you are hurt when you are wrong, then you will benefit, in the long run, from volatility (and the reverse).
We do not need to understand things when we have some edge.
Here it means if you get the positive asymmetric bet, there is no need for further intelligence.
Positive asymmetric bet is one where when you win you win big, when you lose you lose small.
“Heads, I win. Tails, I don’t lose much.”
—Mohnish Pabrai
How to become smarter with probabilities?
While payoffs are straightforward, probabilities require more brainpower.
Here are two powerful approaches to help you think in terms of probabilities:
1) Bayesian Approach
One tool that will be incredibly helpful for you in markets and life, which you are probably using is - Bayesian Analysis
Bayesian analysis gives us a logical way to consider a set of outcomes of which all are possible but only one will actually occur. It is conceptually a simple procedure. We begin by assigning a probability to each of the outcomes on the basis of whatever evidence is then available. If additional evidence becomes available, the initial probability is revised to reflect the new information.
How does it work?
Let's imagine that you and a friend have spent the afternoon playing your favorite board game, and now, at the end of the game, are chatting about this and that. Something your friend says leads you to make a friendly wager: that with one roll of the die from the board game, you will get a 6. Straight odds are one in six, a 16 percent probability. But then suppose your friend rolls the die, quickly covers it with her hand, and takes a peek. "I can tell you this much," she says; "it's an even number." With this new information, your odds change to one in three, a 33 percent probability. While you consider whether to change your bet, your friend teasingly adds: "And it's not a 4." With this additional bit of information, your odds have changed again, to one in two, a 50 percent probability.
With this very simple sequence, you have performed a Bayesian analysis. Each new piece of information affected the original probability, and that is a Bayesian inference.
Source → From book The Warren Buffett Portfolio by Robert G. Hagstrom
This is what means when people say think in probabilities.
In practice: Think of all possible outcomes. Assign probabilities to them. Revise them when new information arises.
This is a core skill in making investment decisions.
2) Subjective Interpretation of Probability
For a die, the outcomes are certain - we can't get a number other than 1 to 6. But in real life, there are infinitely many outcomes.
So how can we deal with it?
When enough repetition of certain events are possible, we can estimate probability based on the frequency of it's occurring.
For example, if we toss a coin 100,000 times, the number of events that are expected to be heads is 50,000. Note that I did not say it would be equal to 50,000. The law of large numbers says the relative frequency and the probability need be equal only for an infinite number of repetitions.
If an uncertain event is repeated often enough, the frequency of the outcomes should reflect the probability of the different possible outcomes.
But what will be the probability when enough repetition of certain events are not possible?
Then, we have to rely on our own sense. We will interpret probabilities based on 'our degree of belief'.
This is what focus investors use - the subjective probabilities.
In subjective probability, the burden is on you to analyze your assumptions.
Stop and think through your situation.
Our degree of belief doesn't mean we will believe anything we think, but it will be based on Bayesian analysis
by collecting historical information and
gathering most recent data.
Look for Prime Bets
Now that you know the importance of payoffs and probabilities, aim for Prime Bets
Prime bets are reserved for serious plays when two conditions occur:
confidence in the stock’s ability to outperform is high, and
payoff odds are greater than they should be.
Prime bets call for serious money.
Investing Challenge
Another challenge, with focus investing (where you choose only a few stocks), is deciding how much to invest in each. Since some companies will perform better than others, the goal is to allocate more to the high-potential stocks—solving this allocation problem is key.
Why it matters?
Imagine you have $10,000 in capital and a portfolio of 10 stocks you plan to hold for 5 years.
Case 1: You invest $1,000 in each stock, evenly distributed. After 5 years, the portfolio is worth $20,000.
Case 2: You allocate more to stocks with higher potential returns. At the end of 5 years, your portfolio is worth $30,000.
The difference is clear—learning to weigh investments by their expected returns can be transformative.
Tools - Kelly criterion
For smart allocation, we have a tool named Kelly criterion.
The Kelly Criterion is a way to help you decide how much money to invest each time to make your investments grow the most, without losing much if things don’t go your way.
When odds are strongly in your favor, it suggests a larger bet; with modest odds, a smaller bet; and when odds aren’t in your favor, no bet at all.
It’s a way to balance being careful and being brave, so you can grow your investment the smartest way possible over time.
“The Kelly system is for people who simply want to compound their capital and see it grow to very large numbers over time. If you have a lot of time and a lot of patience, then it's the right function for you.”
-Ed Thorp
Learn more about Kelly criterion here.
Today’s edition will help you put big bets on high-probability events - the core of focus investing covered in our last newsletter.
If you’re finding these insights valuable, don’t miss out on the next update—subscribe now to stay ahead!
Key Takeaways
1. Understand the difference between chances and outcomes.
2. Prepare for payoffs. Play for payoffs. Become smarter with probabilities.
3. Seek prime bets
1. Higher chance of winning than losing.
2. Winning yields more than losing costs.
4. Learn Smart Allocation using tools like Kelly Criterion.
5. Note: With positive asymmetric bets, you don't need extra knowledge or intelligence — volatility and uncertainty of life will work in your favor.
Content Diet This Week
🎥 How To Manage Your Time & Get More Done
🔉 Daniel Pink | The Power Of Regret | Talks at Google
📝 A Project of One’s Own by Paul Graham (rereading). Check my notes here.
📖 Stolen Focus by Johann Hari (Currently Reading)
P.S.
Thanks for reading Part 2 of the Focus Investing series!
In the next edition, we’ll explore the psychology of human misjudgment in investing, including common biases and strategies to recognize and overcome them.
See you guys next week!
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