Betting vs. Investing: What We Can Learn from Mega Millions

Lotto fever has struck! The jackpot for this Friday’s Mega Millions drawing is a breathtaking $540 million, an all-time record. Undaunted by the incomprehensibly slim odds of 1 in 176 million for picking the winning numbers (about a hundred times worse as the odds of getting struck by lightning), millions of people will be playing, some responsibly and others not so much. If there was no possibility of multiple people buying the same combination of numbers, it would actually be better than a fair game (a dollar spent on a ticket would have an expected payback in excess of a dollar).

One aspect of lottery playing that I find somewhat amusing is the gravitation of ticket buyers to the “lucky retailers” (those stores that have sold an unusually high number of winning tickets in past drawings). A list of these stores may be found on the lottery website. The fallacy that motivates these people to wait in the ridiculously long lines for something they can purchase immediately anywhere else is the notion that randomness implies uniformity. For example, if there are 5,000 stores that sell lottery tickets and over the past few decades, 5,000 winning tickets have been sold, our expectation is that any given store will have sold one winning ticket, assuming that each store sold the same number of tickets overall. While simple intuition would lead us to expect that every store sold one winning ticket, the actual random distribution of winning tickets will be far different. There will be many stores that never sold a winning ticket (about 37% of them) and a few stores that sold six or seven winning tickets, a nice multiple of the one winning ticket that would be expected from chance alone. The simple fact that often eludes us is that in any random distribution, there are always clusters that trick us into thinking that there is something non-random occurring. Thus, some of us rush out to patronize the “lucky retailers,” wasting precious time and gasoline.

The application of this idea to investing is straightforward. As we have shown in Step 5 on ifa.com, there is a very large element of luck in the returns obtained by active managers. The fact that there are so many active managers (about 7,000 for mutual funds alone) means that we should expect to see quite a few with “winning streaks” of 5 years or longer. The problem is that we don’t see more peer-beating or benchmark-beating managers than we would expect from chance alone. This concept is discussed at greater length in “Will the Manager You Picked Deliver Alpha or Have you Been Fooled by Randomness?”