Why playing the lottery can be seen as an asymmetrical investment

Lottery Asymmetrical Investment

For millions of people playing the lottery is one of the highlights of their week. The possibility that you can walk away with millions if not billions creates a glimmer of excitement and hope that would otherwise not have been there.

For the opponents of gambling (or anything that looks like gambling), this is madness. They will quickly tell you that your chances of being hit by lightning are much higher than winning the lotto.

Could they be wrong? Can the lotto in fact be seen as an asymmetrical investment? Before we discuss that possibility, let’s first make sure we are on the same page as to what asymmetrical and symmetrical investments are.

Asymmetrical and symmetrical investments

Asymmetrical investments

This term refers to a type of investment where the potential profit is greater than the amount risked. An example is an investment where the upside is technically speaking unlimited, while the downside is not only clearly defined, but also limited.

Symmetrical investment

A symmetrical investment, on the other hand, refers to a situation where the risk/reward ratio is balanced, i.e. the expected profit is the same as the potential loss.

Can the lottery be viewed as a form of investment?

By now quite a few Warren Buffett fans have probably already fainted. How can anyone view a situation where someone parts with any amount of money in return for a 1 in nearly 300 million chance to win the jackpot be regarded as an investment? After all, if you hand your money to Buffett’s Berkshire Hathaway fund, you have a much higher chance than 1 in 300 million to walk away with a profit.

To expose the fallacy behind this way of viewing things one has to adopt a purely logical approach and use mathematics to substantiate your claims. The best way to do this is to start by looking at the total amount risked over a certain period of time and then comparing it to the potential profit. In the process, you also have to take into account the probability that you will be able to realize that profit.

Amount risked

As most of our readers probably already know, the amount you risk on a single lottery ticket is $2. For that amount, you stand a chance to win any prize, including the jackpot. By paying an additional $1 fee you can boost the payout for non-jackpot prizes by multiples of 2,3,4,5, or even 10, provided that the estimated jackpot is not higher than $150 million.

Amount you stand to gain

The amount that your $2 or $3 (add Powerplay) investment could realize depends on how many numbers you get correct. It starts with a meager $4 for 1 number, but if you have 5 numbers correct, you stand to win a very useful $2 million.

These relatively small prizes are, however, not why most people play the lotto. They hope to win the jackpot. To do this you’ve got to have 5 numbers right, plus the Powerball.

This is where things get interesting and where all comparisons with Berkshire Hathaway fly out of the window. While the average jackpot payouts are somewhere between $100 million and $200 million, it’s the unusually high payouts that make lotto investors coming back week after week. Look at these figures:

– In March 2019 a 24-year-old guy from Wisconsin bought a single lotto ticket and became the sole winner of $477 million, the third-highest win in the history of the U.S. lottery.

– In August 2017 a 53-year-old mother of 2 walked away with $750 million after buying a Powerball ticket in Massachusetts.

– Compared to this one, however, these two were still small fry: In January 2016, the total amount of the jackpot was a whopping $1.586 billion. The three ticket holders each received $528.8 million.

How does playing the lotto compare to investing in an investment fund?

When comparing a $2 or $3 investment with a potential reward of more than a billion dollars, there is no doubt that one can consider the lotto as an asymmetrical investment. The risk is limited and the potential reward is much higher, theoretically unlimited.

How does this differ from Berkshire Hathaway investors handing over their money to Warren Buffet and his team in the hope of making a profit? In both cases, the risk is known and limited. In both cases, the potential reward is higher than the risk.

The biggest difference is that the Berkshire Hathaway investor risks a much larger amount of money than the lotto player. On the other hand, there is a relatively low probability that he or she will lose that money. In return for this, he or she gains a fairly high chance of gaining a relatively small return on their investment.

The lotto player, on the other hand, accepts a relatively high risk of losing a very small amount in return for a fairly low chance of gaining a much higher return on that money than any Berkshire Hathaway investor has ever dreamt of.

Risk versus reward

By now it should be clear that the only difference between playing the lotto and investing in a more conventional type of investment is the different risks, rewards, and probabilities.

Playing the lotto

Winning the jackpot if you just keep on trying

Since buying a single ticket and winning (or not winning) the jackpot is not how most people approach the lotto, we will get a much clearer idea of the bigger picture if we accept that many dedicated lotto fans dutifully fork out $2, $10 or $15 a week for many years in the hope of eventually striking gold.

Let’s look at the hypothetical example of an investor called John Doe who spends $2 on a Powerball ticket twice a week for 40 years. Over this period he would spend $2 x 2 x 52 x 40 = $8,320.

His maximum possible loss would be limited to $8,320, which would represent 100 percent of his initial investment.

His potential reward could vary anywhere from $0 to $1.586 billion (if we limit ourselves to the maximum historical payout).

The probability of him actually winning the jackpot during this period would be the odds of winning with a single ticket multiplied by the number of tickets he bought over the 40 years.

Winning other prizes

Opponents of the lotto system are quick to note that, even over a long period of time, your chances of winning the jackpot are relatively small. What they often overlook is the fact that there are many other prizes to be won, and over a long period winning one or more of these could quickly add up to a significant return on your initial investment. You could also improve your odds of winning by buying more tickets.

For example: Even if you have 0 numbers correct but you get the Powerball, you still have a 1 in 38 chance of winning $4. That is a meager win – but it nevertheless represents a 100 percent return on your initial investment of $2. Are the chances of a Berkshire Hathaway investor making a 100% return on his investment in one week really much bigger? Let’s have a closer look.

The case for traditional investing

If we want to compare this to traditional investing, we have to understand the similarities as well as the differences.

When a conventional investor hands over his $100 million investment to a fund such as Berkshire Hathaway, he is in the same boat as the guy who plays the lotto in two important respects.

The possibility of loss

In the first place, he or she stands to lose their money. While most investors choose to never think of this possibility, it is nevertheless a real one. Investment funds do go bankrupt, their owners abscond with the money, or investors find out too late that the whole thing was a pyramid scheme. Granted, the probability of this happening is smaller than for the lotto player losing his ticket money, but the amount the latter risks is typically much lower.

The hope to make an unknown amount of profit

In the second place, just like the lotto player, the traditional investor hopes to make a profit on his investment. Unlike the lotto player, however, he or she does not even dream of turning $2 into $1.6 billion. Not in a week and very seldom in 40 years.

Bringing it all together

At this stage, we would like to argue that both conventional investments (Warren Buffett style) and playing the lotto are asymmetrical forms of investing.

The reason we believe this is the case is that in both instances there is risk and in both cases, the potential reward is not the same as the risk (as would be the case with symmetrical investing) but much higher, i.e. it is asymmetrical.

Of course, the probabilities are not the same. Conventional investing represents a low-risk, low-reward type of investment while playing the lotto over a long period of time represents a high-risk, high-reward type of investment.

That, however, is not unlike the difference between investing in Treasury bills and investing in a hedge fund. The former comes with relatively low risk, but the potential return on your money is also relatively low. The latter undoubtedly comes with higher risk, but also offers a significantly higher return if things go according to plan.

Wrap up

In our view playing the lotto falls into the same high-risk, high-return investment category. Since the actual amount one risks can be kept very low, however, we believe that for ordinary working-class people it is still a safer form of investment than, for example, handing your life’s savings to a cryptocurrency fund and hoping for the best. As is the case with any form of investing, it is important to use your common sense when playing the lotto by not risking money you and your family can not afford to lose.

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