This week’s Mega Millions $1.5 billion jackpot, the second-largest lottery prize in the history of the world, brought the lottery into the national consciousness with levels of hysteria rarely seen. The lottery is a psychological game just as much as a probabilistic one, and nearly half of American adults will play the lottery each year, for myriad reasons as diverse as the population itself. Yet according to Math With Bad Drawings author Ben Orlin on Vox, these players will generally fall into one of 10 categories.
The Gamer: The Gamer plays for the sheer pleasure of it. Any discerning player knows that their ticket is far more likely to be worth nothing than win the jackpot, but even the most mathematical mind will come to the conclusion that the value of the average ticket sold in terms of winnings is far lower than its $1 price. The Gamer isn’t in it for the money; they are in it for the entertainment value, which to them is well worth the $1 spent. The thrill of possibility is well worth the price.
The Educated Fool: In certain lotteries, where nobody wins a big jackpot and it is then rolled over into the next week’s contest, the average value of a ticket in terms of potential winnings could eventually exceed the face value. For example, in this week’s $1.5 billion drawing, the average value of a ticket in winnings was over $5, far above its $1 face value. This is where the Educated Fool joins the hunt. The Educated Fool relies on that single statistic — the average winnings for a $1 ticket — to determine its playability, largely ignoring the fact that the vast majority of those winnings will be placed on a single ticket.
The Lackey: This guy is always a winner, because somebody else is paying him some kind of wage to purchase tickets for them. The lackey is a dying breed, however, as lottery rules have changed due to the machinations of the next guy.
The Big Roller: The Big Roller is a calculator. When an opportunity arises in which the average value of a ticket exceeds its cost, The Big Roller is ready to pounce. Armed with a massive bankroll and an army of lackeys to execute the plan, The Big Roller seeks to purchase a ticket with every possible combination and walk away with a significant profit. This actually happened in the 1992 Virginia State Lottery, in which mathematician Stefan Mandel led a syndicate of 2,500 investors that sought to purchase a ticket for all 7 million potential combinations. They won, taking away millions in profit. Today, with the Mega Millions and Powerball offering over 250 million possible combinations, it would be a logistical impossibility to purchase enough tickets to satisfy every potential winning combination.
The Behavioral Economist: For psychologists, economists, mathematicians, and the like, a foundation of almost every theory is how people deal with uncertainty. While most research into this subject is nearly impossible due to the complications of life, the lottery provides a simple environment with plain outcomes and clear probabilities in which social theories can be tested. One of the more intriguing psychological patterns to emerge belongs to the next guy.
The Person With Nothing Left To Lose: Prospect theory, a model of human behavior, suggests that people are risk-averse when it comes to potential gains, but risk-seeking when it comes to avoiding greater losses. Thus, for people who live under dire financial circumstances, where every day feels like a perpetual loss, people are then willing to engage in the risk-seeking behavior of buying a lottery ticket.
The Kid That Just Turned 18: Every adult was this guy once.
The Dutiful Taxpayer: The state knows of this veritable certainty: its citizens would rather pay for a lottery ticket than pay their taxes. If the state can make 30 cents off each $1 ticket by offering a state-run lottery, it can make a lot more money than it can by levying a 30 percent tax on something. Lotteries generate key state revenue, and are a lot more enticing than paying taxes.
The Dreamer: For this type of lottery player, the ticket doesn’t represent a chance to win as much as it represents a fantasy. Having that ticket in hand with the potential to win life-changing money gives The Dreamer an opportunity to imagine all of the cool things that they will do with their potential winnings, and $1 is a small price to pay for a special trip to Fantasyland.
The Enthusiast For Scratching Things: This guy just loves taking a quarter and scratching some material off a piece of cardboard. To each his own.