Human beings are notoriously poor at processing risk
information.
There must be some evolutionary advantage to it, or perhaps
we are simply the butt of a cosmic joke.
Our brains evolved to keep us safe from sabre tooth tigers while
encouraging us to hunt antelope. But somehow the wires became crossed.
We tend to overestimate the risk of low probability, high
impact events. Nuclear meltdowns terrify us. Massive natural gas explosions
give us panicky agita. Mass-casualty terrorist attacks make us lock down the
borders.
All have occurred. All can possibly reoccur. The probabilities
are exceedingly low. But that doesn’t stop us from obsessing.
On the other hand, the risk of a high probability event in
which we exercise personal control is vastly underestimated. This is why we text while driving, flirt with opioid
drugs, and ride motorcycles. We think that we can somehow overcome the odds,
because, it seems, that we are “good enough, smart enough, and doggone it,
people like [us].” (Kudos to Stuart Smiley a.k.a. Senator Al Franken).
We fear flying, because we lack personal control, but blithely
leap out of airplanes, since we control the ripcord. Go figure.
Another area in which we overestimate the likelihood of a
low probability event is the lottery. We plunk down our cash, some of us a few
bucks, others betting the mortgage. Some of us weekly, some of us daily. We
share a common aspiration of hitting the jackpot, but do we really understand
the odds of that happening?
Note the table nearby. The odds of winning the jackpot in
our most common lottery games range from small to vanishingly small. But there
is some information that we can tease out.
Listed are the name of the game, the most recent cash value
of the jackpot, the odds of winning the jackpot, the expected value of the
game, and the breakeven jackpot.
This analysis is incomplete. For one, it underestimates the
winnings by not considering secondary prizes. But to the contrary, it
overestimates winnings by not considering taxes due. As a first order
approximation, we consider it to be fair.
First, a few definitions. The most recent cash value is
taken from the game websites. Because the terms of payment vary, making them
all based on cash value equalizes the comparison.
The jackpot odds reflect the random number of tries it would
take to win the jackpot. Whew!
The ticket price is obvious. But the expected value (EV) is
a mathematical portrayal of your average winnings. Note that all of them are
less than the ticket price. Translation – all of these are losing games. Which, of course, they have to be. These games
are rigged to make money for the house (the governments and gaming companies supporting
them).
The last column, breakeven jackpot, defines the amount of
jackpot required to justify buying the ticket. Notice that this value is often
many times the most recent jackpot. (Another hint that this is a chump’s game).
So what are the lessons here? There are several.
Given these particular games, run and hide from Powerball
and Lucky for Life. The only exception is if the Powerball jackpot rises to
$584 million. Then it’s worth the $2 ticket. Lucky for Life, on the other hand,
by definition is never worth it. Its cash payout is limited to $5.75 million
but would need to be over $61 million to be worthwhile. This may be the worst
game on the list.
Mega Millions isn’t particularly bad. If the jackpot rises
over $258 million, give it a go.
Megabucks and Mass Cash are your best bets. Still losing
games (remember, the goal is to raise revenue for the government), the odds are
slightly better in your favor. Megabucks, in particular, is attractive when the
jackpot is $14 million or more.
While we are poor risk information processors, and may well
be the butt of a cosmic joke, God gave us a salutary gift. The ability to
invent computers. That is truly cosmic.
The joke is on the gamers. We now know how to play the odds.
