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Investing vs. Lottery: what are your odds?

March 24, 2018

 

Feeling lucky? You'd better be if you play the lottery. Depending on which one you play, you have some pretty long odds. For example, the odds of winning a recent Powerball drawing in Tennessee was 1 in 292.2 million. To put this in perspective, you have a one in 2,320,000 chance of being killed by lightning, a one in 3,441,325 chance of dying after coming into contact with a venomous animal or plant, and a one in 10 million chance of being struck by falling airplane parts. Most people would agree the risk of any of these events actually happening to them is pretty slim. 

Let's look at it another way. Assume you went to the largest stadium in the world (which happens to be in North Korea). The stadium was filled to capacity. As part of the price of your ticket, you were entered into a lottery where you could win a new car. In that case, your odds of winning are 1 in 150,000.

Would you be sitting on the edge of your seat in that stadium as they're reading the ticket number or would you believe that, realistically, you're not going to win? To equal the odds of winning the lottery, you would have to fill that same stadium to capacity 833 more times and put all of those people together and have the same drawing for the one car. Would anybody believe they could actually win in a crowd of people that large?

Still not convinced? If they were giving away a new home to just one person and everybody in the six most populated states in the United States entered, that would equal your chances of winning the lottery.

 

 

Of course, someone has to win the lottery, and the only way to win it is to be in it, as the ads say. But what's the best way to be in it? The rules of probability dictate you do not increase your odds of winning the lottery by playing frequently; each time you play the lottery there is independent probability—much like a coin toss where each and every toss, regardless of the number of tosses, has a one in two probability of landing on heads. The odds stay the same, in the lottery and the coin toss, regardless of the frequency of playing.

You can, however, increase your odds by purchasing more tickets for the same lottery drawing. Keep in mind, though, that two tickets might increase your odds from one in 14 million to two in 14 million, which is not a significant improvement, statistically speaking. Someone would have to buy a lot of tickets to appreciably increase their odds of winning. Even if a person could afford to, however, he or she could not buy enough lottery tickets to guarantee a win unless he or she was the only person buying the tickets. As more tickets are collectively sold, the odds of winning inversely decrease.

 

Who Plays the Lottery?

Your chances of winning the lottery are exceedingly remote, but that doesn't stop people from playing. Overall, approximately 57% of U.S. adults collectively will spend upwards of $50 billion each year in the hopes of striking it rich (Canadians spend more than $8 billion per year). Time and again, when a lottery was introduced in a state, the local number of adults who engaged in gambling (which a lottery technically is) increased 40%. In certain states, the majority of lottery revenue comes from a small percentage of players. A Minnesota study, for instance, determined that 20% of its lottery players accounted for 71% of lottery income, and in Pennsylvania, 29% of players accounted for 79% of income, according to the North American Association of State and Provincial Lotteries (NASPL).

So what? The lottery is just one of those fun things that we do as a way to strike it rich, right? For some folks, that's true, but for others, often those with the least amount of money to spare, playing for these jackpots can be a serious income drainer. An overwhelming amount of lottery participants seem to reside in the lower economic classes, according to the stats. In California, a study found that 40% of those who played the lottery were unemployed; in Maryland, the poorest one-third of its population buys 60% of all lottery tickets; and in Michigan, people without a high school diploma spent five times more on the lottery than those with a college education. Small wonder that consumer-finance gurus say the lottery is essentially an extra tax on the poor.

 

Feeling lucky? You'd better be if you play the lottery. Depending on which one you play, you have some pretty long odds. For example, the odds of winning a recent Powerball drawing in Tennessee was 1 in 292.2 million. To put this in perspective, you have a one in 2,320,000 chance of being killed by lightning, a one in 3,441,325 chance of dying after coming into contact with a venomous animal or plant, and a one in 10 million chance of being struck by falling airplane parts. Most people would agree the risk of any of these events actually happening to them is pretty slim. 

Let's look at it another way. Assume you went to the largest stadium in the world (which happens to be in North Korea). The stadium was filled to capacity. As part of the price of your ticket, you were entered into a lottery where you could win a new car. In that case, your odds of winning are 1 in 150,000.

Would you be sitting on the edge of your seat in that stadium as they're reading the ticket number or would you believe that, realistically, you're not going to win? To equal the odds of winning the lottery, you would have to fill that same stadium to capacity 833 more times and put all of those people together and have the same drawing for the one car. Would anybody believe they could actually win in a crowd of people that large?

Still not convinced? If they were giving away a new home to just one person and everybody in the six most populated states in the United States entered, that would equal your chances of winning the lottery.

 

Independent Probability

Of course, someone has to win the lottery, and the only way to win it is to be in it, as the ads say. But what's the best way to be in it? The rules of probability dictate you do not increase your odds of winning the lottery by playing frequently; each time you play the lottery there is independent probability—much like a coin toss where each and every toss, regardless of the number of tosses, has a one in two probability of landing on heads. The odds stay the same, in the lottery and the coin toss, regardless of the frequency of playing.

You can, however, increase your odds by purchasing more tickets for the same lottery drawing. Keep in mind, though, that two tickets might increase your odds from one in 14 million to two in 14 million, which is not a significant improvement, statistically speaking. Someone would have to buy a lot of tickets to appreciably increase their odds of winning. Even if a person could afford to, however, he or she could not buy enough lottery tickets to guarantee a win unless he or she was the only person buying the tickets. As more tickets are collectively sold, the odds of winning inversely decrease.

 

Who Plays the Lottery?

Your chances of winning the lottery are exceedingly remote, but that doesn't stop people from playing. Overall, approximately 57% of U.S. adults collectively will spend upwards of $50 billion each year in the hopes of striking it rich (Canadians spend more than $8 billion per year). Time and again, when a lottery was introduced in a state, the local number of adults who engaged in gambling (which a lottery technically is) increased 40%. In certain states, the majority of lottery revenue comes from a small percentage of players. A Minnesota study, for instance, determined that 20% of its lottery players accounted for 71% of lottery income, and in Pennsylvania, 29% of players accounted for 79% of income, according to the North American Association of State and Provincial Lotteries (NASPL).

So what? The lottery is just one of those fun things that we do as a way to strike it rich, right? For some folks, that's true, but for others, often those with the least amount of money to spare, playing for these jackpots can be a serious income drainer. An overwhelming amount of lottery participants seem to reside in the lower economic classes, according to the stats. In California, a study found that 40% of those who played the lottery were unemployed; in Maryland, the poorest one-third of its population buys 60% of all lottery tickets; and in Michigan, people without a high school diploma spent five times more on the lottery than those with a college education. Small wonder that consumer-finance gurus say the lottery is essentially an extra tax on the poor.  

 

Gambling vs Investing: Which Has the Better Odds?

A curious headline was placed on the homepage of the Mega Millions website on March 25, 2011, a day when the odds of winning had gone up to 1 in 175 million (1,166 stadiums in case you were wondering). The headline read, "Save for Retirement." Anti-gambling groups cried foul at this apparent attempt to spin the lottery as a means to fund a person's post-work years and lottery officials quickly issued a statement saying they were running a campaign encouraging people to dream about how they would use their winnings—not offering a financial strategy.

Is there a better, more profitable, way to spend or invest the money you'd otherwise devote to the lottery? Let's look at the numbers. If a person spends $5 per week on lottery tickets, it adds up to $260 per year. Over 20 years (a typical long-term investment horizon for stocks and bonds), the total spent on lottery tickets would be $5,200. Putting $260 per year into stocks earning 7.3% annually (based on equities' historical performance) yields $11,015 after 20 years. But if you just spent the money on lottery tickets and presumably won nothing, you would be out $5,200 after 20 years.

Of course the stock market is never a sure thing; stocks can depreciate as well as appreciate. So let's try a more cautious estimate. One study in Texas found a person without a college degree spent an average of $250 per year purchasing lottery tickets. If that same person were to start an IRA or other retirement account that earned a conservative average 4% annual return and contributed that same $250 to it per year for 30 years, he or she would have $15,392 once they reached retirement age. If they did the same thing for 40 years, that number would jump to more than $25,000.

Although some would argue that in today's economy there is no way to guarantee that the money would earn 4%, there's also no guarantee that it wouldn't earn far more than 4%. But all of that aside, the odds of having $15,000 after 30 years are largely in the person's favor; certainly more so than with the lottery's 125-million-to-1 odds.

 

The Bottom Line

If you ever do win the lottery, you will want to work with your financial advisor, tax attorney and CPA to determine which option is best for you: taking the winnings all at once or in annuitized payments over decades. As a rule of thumb, if you and your money-management team think they can invest to earn an annual return of more than 3% to 4%, the lump sum option makes more sense over the annuity, at the end of 30 years.

Many people see purchasing lottery tickets as a low-risk investment: Where else can you "invest" $1 or $2 for the opportunity to win hundreds of millions of dollars? The risk to reward ratio is certainly appealing, even if the odds of winning are remarkably small. Is it better, then, to play the lottery or invest the funds? There is no one universally correct answer. Much of it depends on what money is being spent. If it is needed for retirement or the kids' college, it may make more sense to invest: A payoff is more certain down the road, even if it doesn't amount to a sexy six-figure check. If, however, the money is tagged for entertainment, and you would have spent it seeing the latest movie anyway, it might be fun to take the chance. Keeping in mind, of course, that you are more likely to die from a snake bite than to ever collect.

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