Every now and then, economist, statisticians, and anyone else in the business of calculating risk will tell you that you have a better chance of getting struck by lighting than winning the lottery. No matter how you argue against this point, the fact of the matter is, it is not worth the gamble. However, if you happen to be filling up the your car at the gas pump and have dollar to spare, why not donate it to the state to spend it on social programs. After all, your State, like many other states are probably faced with budget crisis. So, if you are going to play, play smart and up your chances of winning by a just a hair. Before getting too excited by the miniscule factional basis point increase in the probability of winning, lets go over the basics of why the dollar you spend is a lot riskier than most and almost every other gamble you can think of.
Perceived Risk verse Actual Risk
Which one would you rather risk, a dollar on a lottery or three thousand dollars on a call option of particular technology company? Most people at this point would probably choose the dollar on the lottery over the three thousand dollars on a call option. Without going into all the complexity of a call option, basically a call option is bet that a particular stock will rise above the strike price plus the premium, which in this case is three thousand dollars. For example, a stock is trading at $50 and the strike price is $55. Lets suppose you bought 10 contracts (each contract = 1 Lot or $100, so three thousand dollars equal 3 Lots). In this case the premium is $3. So in other words, the stock has to rise above $55 + $3 = $58 to gain any money from your bet of three thousand dollars. On the flip side, if the stock does not go above the strike price minus the premium, in which this case is $55 – $3 = $52, you lose everything.
It is perceived that losing three thousand dollars on an options contract is riskier than the dollar that you spend on the lottery, but is it really? To answer this question, lets take a look at the expected return of both. Finding the probability of winning the lottery is a lot easier than finding the probability of a certain stock reaching a target price. For one, anyone can go to www.megamillions.com to get the exact probability of winning the jackpot or they can calculate it themselves by using the following formula:
(5/56) x (4/55) x (3/54) x (2/53) x (1/52) x (1/46)
The above formula is based on choosing five numbers 1 – 56 in any particular order and one mega ball number 1 – 49. That gives you a 1 in 175,711,536 chance of winning, a probability of 0.0000006 percent. This also means that you have a 9.9999994 percent chance of losing. So what is the expected return on this gamble? It depends on what the actual jackpot is for that week. To keep it simple, if the jackpot is more than 175,711,536, than the expected return is positive. But wait a minute, what about taxes and time value of money. Okay, we will go over that later but for now, lets go find the expected return of options. The actual formula for calculating the expected return for option is as follows:
However, for simplicity purposes, lets say the average volatility of a given stock price is +/-20 percent, which is pretty realistic for tech companies. Lets further assume that this particular stock has a 50 percent chance of gaining 20 percent, 25 percent chance of gaining 12 percent, and 25 percent chance of losing 12 percent. These are pretty realistic percentage. The simple calculation is as follows:
0.5 x 0.20 + 0.25 x 0.12 + 0.25 x – 0.20
Hence, you have an Expected Return of 8 percent
To complicate this matter even further, we have to consider the ex-alpha rate of return for the investment. That is the risk adjusted return. But to satisfy the average readers, I will leave that for the Journal of Finance or any other paper read by people who actually care about these types of things. For now, lets get back to the topic at hand, the Lottery. As you can see, from a risk perspective, a person has a greater chance of gaining money in an option compared to winning a lottery.
So why do people still believe they have a better chance of winning lottery compared to betting on options? Behavioral finance would say people are irrational and only view a jackpot of several hundred million as a better gamble compared to even the stock market. For one, the reward is perceived to be bigger. However, as illustrated above, people do not always calculate the amount of risk that they take in order to win the jackpot.
Going back to the probability of winning the lottery, it seem that if the probability of winning the lottery is 1 out of 175,711,536, then as long as the prize money is more than 175,711,536, we could pay to get 175,711,536 combination to win the difference. Right? Wrong! First, we have to consider the time value of money. If you win, lets say $200,000,000 on a $175,711,536 bet, it seems as you won the difference of about $24 Million Dollars, a gain of about 13 percent. However, this money will be distributed over the next 26 years. That is approximately 7.7 Million per year and taxed every year. Given the level of inflation, opportunity costs, and among other things, the value of winning will never reach the original gamble leaving you with a negative rate of return.
If you were to choose a cash option, your prize money is a little less than half so that would not work either. So the natural question that you would ask is, what if the prize money exceeds $350 Million? At this level of prize money, a lot more people will play the lottery increasing the chance of, wait for it, splitting the pot. Oh no! Even if the participating States do not have a total population of 175 million, the people who play would spend on average $20 when the prize money reaches more than even $200 Million. Given these facts, the odds are really stacked against you.
But if you still must play, play by these rules:
First, play only when the Jackpot hits above $175,711,536 and never ever spend more than $100 minus the full tank that you put into your car. The best option is to just play a dollar. Yes, buying more ticket will increase your chances of winning, but not by a significant amount. Your money is better off invested elsewhere. Moreover, you have 1 in 40 chance of winning something and at least 1 in 75 chance of winning at least two dollars. If you win two dollars, you double your investment and if not, no biggie. You just donated your dollar to the State.
Second, computer generated random numbers gives you a 70 percent higher chance of winning verses picking your own numbers. This is a time-tested approach, where 70 percent of past Jackpot winners got their numbers through random picks. Furthermore, if you pick your own numbers and win, the more likely you will end up splitting the pot. The science behind this is that people tend to choose the same numbers. For instance, they tend to choose lower numbers under 12 or 31. This is because numbers under 12 or 31 signifies special dates or birthdays. The most popular numbers people tend to choose are 7 or any number that are multiple of 7 such as 21. They also have a tendency to pick numbers associated with the jersey worn by their favorite basketball or football players.
Finally, if you insist on picking a number, pick a mega ball number that hasn’t shown up in a while. This will increase the likely-hood that the number in question will show up. It uses the same logic of flipping a coin. If you flip a coin six times and all six times, you get heads, then on the next subsequent flip, your chances of getting tail is a lot greater.
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