# Winning The Lottery, Branding, Prospect Theory, And Confirmation Error

by: Michael Lonier

## Summary

You need to spend \$2,257 on Powerball tickets to buy the same odds of winning that \$1,000 buys from Mega Millions; why would anyone buy a Powerball ticket?

Prospect theory posits that people will value the chance of a high gain more than the equal chance of gaining less even if the cost is significantly higher.

Cadillac pricing may feed your ego but it lowers your returns - unless you believe that the higher-priced active manager will win, justifying paying a 10x-35x higher cost.

Driving around the country you stop at a lot of food mart gas stations, each with a lottery machine prominently positioned on the counter. Unless you've been out of the country for a long time, you probably know the two big games Mega Millions and Powerball attract millions of people to their twice weekly drawings.

Periodically, some huge jackpot attracts additional millions of people to buy ever more tickets, raising the pot until someone finally gets the big winning ticket.

Why two games? Is it just so there's a drawing four nights a week? Well, yes, that's surely part of it, though you could turn the crank twice as often on a single game. It's a particularly interesting question because Powerball raised its ticket price from \$1 to \$2 some time ago, while Mega Millions remains at \$1.

It turns out the games are quite similar. The infinitesimally small odds of winning are close enough that for all practical purposes they are the same for both. One in 259 million for Mega Millions, and slightly worse, one in 292 million for Powerball.

Powerball has slightly worse odds, but it costs \$2 a ticket to play instead of \$1. Adjusted for risk, A Powerball ticket is 2.26x more expensive than a Mega Millions ticket. You need to spend \$2,257 on Powerball tickets to buy the same odds of winning that \$1,000 buys from Mega Millions.

So why would anyone buy Powerball tickets instead of Mega Millions' tickets? A couple of things come to mind.

Some of it is pure branding, but there's also the way the branding takes advantage of prospect theory to lure ticket buyers.

Branding

Mass communication is a powerful force and it has tremendous sway in commerce, culture, politics and finance. Even without a Mercedes-Benz style ad campaign, there's often an assumption that higher-priced things are better than lower-priced things.

Sometimes that's true. But not with lottery tickets. An infinitesimal chance to win is worth exactly what the math says - no more, no less. So part of it is that lottery buyers are duped by the higher ticket price into thinking Powerball is a premium game.

And of course, you only have to sell half as many tickets at \$2 to generate the same revenue as a \$1 ticket. Which means you can build a bigger jackpot faster, and big jackpots attract ticket buyers. So part of the Powerball brand is bigger jackpots, never mind that you're paying more than double for an equal chance to win compared to the other game. So the higher ticket price is part of the brand's "premium" appeal of bigger jackpots.

You're savvy enough, I hope, to understand that the size of the jackpot and the number of tickets sold has no effect on the odds of winning, so the higher revenues generated by higher ticket prices and bigger jackpots go right to the bottom line of the gaming company. You still have virtually no chance to win, no matter how big the pot.

Prospect Theory

Maybe the biggest part of the Powerball strategy is that people value higher jackpots in a game of chance more than smaller jackpots, even if they have virtually no chance to win either game. People typically feel that the chance to win the higher Powerball jackpot is worth the extra cost compared to a smaller Mega Millions pot. Prospect theory posits that people will value the chance of a high gain more than the equal chance of gaining less even if the cost is significantly higher.

The extreme difference between the impossibly large gain and the small cost to play is difficult to keep in a logical context. So you spend a hundred bucks on \$2 tickets for 50 chances to win, which at 292 million to one means you have pretty much the same odds of winning as if you had bought one ticket for \$2 (or \$1!). But now you're short \$98 for a tiny adjustment in probabilities - a huge incremental cost for little perceived gain.

By now you should understand that this has some parallels with investing. Costs matter, branding does not. A share of Apple (NASDAQ:AAPL) sold to you by Merrill-Lynch is worth no more or no less than a share you buy from E-Trade or Fidelity. The 3.5% you are paying Merrill or JPMorgan Chase (NYSE:JPM) to manage your money, on the other hand, compared to 0.10% for a broad market index does make a difference.

Find a good, low-cost money manager if you need one. Cadillac pricing may feed your ego but it lowers your returns. Unless you believe that the higher-priced active manager will win, justifying paying a 10x-35x higher cost. S&P Dow Jones research gives you a 1 in 3 chance of that being true in any given year, and a less than 1 in 10 chance of persisting over multiple annual periods. Good odds for Powerball, but not so much for investing your life savings.

Jumping into the market when it is surging like a lottery jackpot is an even worse idea than buying a lottery ticket when the pot is huge. At least with the lottery ticket, the odds don't turn against you as the pot grows (you're still not going to win!), but buying a stock after it's surged to new highs means you have bought high instead of low, and will forever see lower returns from that holding than if you had bought it when it was more out of favor.

Confirmation Error

The lottery games are fond of showing winners with big checks, feeding your prospect weakness and creating a confirmation that you too could win big. To overcome the confirmation error that you too will win, you need to recognize that winning a game of chance is totally random with impossible odds. It's a stroke of lightning, not a retirement income plan.

The same confirmation error causes investors to buy last year's stock or fund "winners" at the urging of their well-paid investment advisors, when this year's winners will likely be nearly as random as lottery winners. No one knows the future, even just next week or next month. Avoid confirmation error and value-average into a broad market portfolio over time. Saving early and often is a bigger factor to your long-term investment success than picking winners. The odds of winning following a frequent savings strategy, unlike the lottery, are very much in your favor.

By the way, the Saturday Powerball jackpot paid almost a half-billion dollars over the weekend, and will start building again. Now that you understand how you are being played by the lottery, go ahead and have some fun. Buy a ticket, but just buy one!

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.