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How Much Should You Bet To Maximize Your Investments, or Your Company's Odds of Success?

If I gave you $1000 to invest, and five investment options how would you decide? What if you were the CEO of a startup, and a VC invested $10m, and each of your five VPs had different project ideas?

This is the question John Kelly, researcher at Bell Labs, sought to answer.

A contemporary of Claude Shannon, Kelly intertwined Shannon’s information theory with probability to develop an idea of his own: the Kelly criterion. His theory would translate into tremendous investing prowess and lead him to one of the best long term track records of all time at Princeton-Newport, a hedge fund he managed to 15% net IRR compared to the S&P at 8%.

Kelly wanted to solve for two key ideas:

  1. avoid total loss: the investment strategy should never result in a 0 or negative balance.
  2. grow the value as quickly as possible.

He developed the Kelly criterion. I won’t dive into the math there, but I will highlight lessons applicable broadly.

First, to calculate the expected value of an investment don’t use the average (also called the arithmetic mean); use the geometric mean. The difference is simple, but powerful.

Imagine you have three investment options, each equally likely. They return 100%, 50% and 0%. The arithmetic mean/average/expected value is 50%: (100+50+0)/3. The geometric mean is 0%: cubic root of (100500). The Kelly criterion says don’t invest. Quite a different result.

Second, size your investment properly. Invest too much and bankruptcy looms. Bet too little, and your returns won’t amount to a pile of beans.

How do you calculate how much to bet? Kelly criterion says to bet more the greater your edge and the likelihood of success.

KC = W - (1-W)/R

KC = kelly criterion (the percentage of your balance sheet to invest) W = probability of winning R = win/loss ratio

Read the intricacies here. and for a longer explanation, Fortune’s Formula.

In practice, many people using Kelly systems bet half or three quarters of the criterion because we tend to overestimate our odds of success. Also, overbetting leads to bankruptcy. Better to be conservative.

There’s a wealth of research on Kelly strategies and many prominent investors use these techniques. Startup CEOs are capital-allocators-in-chief. Their responsibility to decide which bets to make and how large they ought to be.

The Kelly criterion provides both a conceptual and mathematical framework for evaluating those alternatives.