Is Winning $324M Better Than Winning $1M?

On March 30, a production manager named Richard Wahl won Mega Millions and will be receiving $324,600,000. However, this is not the reality of many people who play the lottery, especially since the odds of winning the jackpot is only 1:302,575,350 according to the Mega Millions website. This was only Wahl’s second time purchasing a Mega Millions ticket, but some people purchase dozens of tickets a year. This brings up the question as to why anyone would play any sort of jackpot that has such a low probability of winning.

The utility theory would suggest that nobody would buy tickets because the probability of winning is much lower than the probability of losing, so the utility would be negative. The utility theory suggests that people will estimate the expected utility and make a choice based on the best option, which in this case, would be to not purchase a lottery ticket.

However, the utility theory has evidence against it since people can make different choices based on something such as wording and availability, which would not impact the equation used to calculate expected utility. The prospect theory of probability tells us that people have a higher weighted probability when the actual probability is low, and a lower weighted probability when the actual probability is high. This means that for most probabilities, other than around the 20% probability mark, people either overestimate or underestimate the likelihood of an event occurring. The probability of winning the Mega Millions is extremely low, yet people are still able to imagine, or even believe, that they could realistically win millions of dollars. This allows lottery players, such as Richard Wahl, to be risk seekers and play Mega Millions.

Wahl described in an interview that he felt paralyzed when he won what he initially thought was $1 million. He and his family are middle-class, so one million dollars would feel extremely good to him, explaining why he felt unable to bring his ticket with him anywhere or leave it at home, causing his Easter plans to be cancelled. Although the CNN article does not discuss how Wahl’s reaction changed when he realized his ticket would give him over $300 million, he likely did not feel too much happier than he did when he thought it was $1 million. This can be explained by the prospect theory of value function.

Since Wahl won Mega Millions, any amount would be a gain. This would mean that his happiness would be higher than it was before he had extra money. However, even though $1M to $324M is a much larger difference than his baseline amount of money to $1M, happiness would not increase as much between when he thought he won $1M and after his realization that he won more. This is because as you have more of something, such as money, it has less value to that person. This leads me to believe that realizing he would be $323 million richer than he thought he would be with the $1 million win, he likely did not experience as much of an increase in happiness. This seems to be confirmed by Wahl’s goals, such as restoring a Corvette, retiring, and helping a few relatives financially; most of which could have been achieved with only the original $1 million.

As long as people are willing to be risk seekers and spend a few dollars in order to potentially win millions, Mega Millions will stay in business because of the prospect theory. Richard Wahl is one of the few people who have won, and the fact that he has been on the news so much lately impacts availability. Many people will remember the last person who won, so they are more likely to predict that they have a possibility of winning as well and purchase a ticket themselves. I would not personally buy a Mega Millions ticket because I see it as nearly impossible to win, which means I have a more moderate probability weighing and the difference between the actual probability and how I act is less than someone with more severe probability weighing.

3 thoughts on “Is Winning $324M Better Than Winning $1M?

  1. Daniel

    Well done; I actually think that material gain might have a satiation point.

    When thinking about gains like that you see a potential gain and that gain will cease to mean something at a certain point. Things such as Food, Sex, and Sleep have natural “end points” where the thing you are referring to means less. Comparing a starving person to a person just leaving a buffet as apt examples.

    Giving a person 1 million dollars will have a huge effect, but giving that person 300 million dollars will have a “leveling” effect. So the outcome in your chart makes perfect sense. Prospect theory is fascinating, but looking at base rate neglect, lack of understanding for probability….and failing that? good old fashioned greed, makes perfect sense as to why the lottery is working the way it does.

    1. swong Post author

      The cheapness of a ticket certainly makes the possibility of winning millions of dollars more enchanting, even though most people realize how low their actual odds are. I’m sure that choosing one’s own lottery numbers plays a role in them believing that their ticket is “worth more” as well, similar to the example from class when people who picked which baseball player was on their card wanted to sell it for a profit, while those who did not pick sold at a loss. I love your comparison to someone who is starving and someone who left a buffet!

  2. Emily Busbee

    I personally would (and have) bought a mega million lottery ticket before simply because they are so cheap to buy, and I almost see it as I have to little to lose, but so much to POTENTIALLY gain. While you do realize the odds are extremely slim to nonexistent that you will ever win, that does not stop hope from creeping through the cracks of your rational thinking.

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