## Tuesday, February 24, 2015

### Finding utility in the Lottery

As reported earlier, I took two boys to Saturday's Gun show.  Being fifteen year old boys they were not able to travel from Eaton Rapids to Mason without requiring food.  The Wooden Nickle sold lottery tickets and keno.  Kubota's friend did his best to convince me that buying lottery tickets is a sound investment strategy.

He quickly lost interest when I started showing him how to calculate the odds.  I hate to waste a good lecture so I am going to recycle it by posting it as an essay.

Consider the Mega Millions lottery.  The first five numbers range from 1-through-75 inclusive and do not repeat.  The sixth number is drawn from a pool from 1-through-15 inclusive and can repeat one of the first five.

Let's look at the first number the customer picks.  There are five chances of it matching one of the drawn balls out of seventy-five total choices.  The chances of also picking the second number correctly is one chance in four matching (remember, you already knocked out one with your first pick) out of a pool of seventy-four numbers.

The odds for correctly selecting the first five numbers are about

one-in-17,000,000 = (5/75) * (4/74)*(3/73)*(2/72)*(1/71)

Multiply in the Mega Ball (1/15) and you end up with about 1/259,000,000 chance in winning.

#### Sharing

So one might assume that the purchase of a one dollar Mega Million lottery ticket is revenue neutral when the jackpot is about \$260,000,000.  You would be wrong because the winner must share the jackpot with everybody else who picks the winning numbers.  This is a case where thinking like everybody else is not to your advantage.

 Excellent article on PIN numbers from Datagenetics

This is a great time to be unpopular, a skill that Belladonna assures me that I have refined to a world-class  level.  In fact, I have raised this skill to a science.

The first rule is to avoid numbers below 32.  When a person chooses "My numbers" they choose numbers that are easy to remember and have a personal connection to themselves.  Dates, for instance.  Months run 1-through-12.  Days of month run 1-through-31.

The first half of this rule (avoid numbers 1-through-12) is the only rule that can be applied to the Mega Ball.

The second rule is to avoid multiples of 11.  That is, 11, 22, 33, 44, 55, 66

The third rule is to avoid numbers like 34, and 67...numbers where the second number is one greater than the first number.

There are some anomalies.  60 is a very unpopular number, perhaps because this is THE milestone birthday when we must kiss the illusion of middle age goodbye. 68 and 70 are not popular but 69 is (for reasons ERJ refuses to speculate upon).  80 is out also an unpopular number but it is outside the range.

#### Sequences

The common perception is that randomly selected numbers must look, well, random.  In fact, any string of numbers is random.  The string 60, 61, 62, 63, 64 is as likely to show up as any other combination of five numbers.  The least sophisticated buyers are unlikely to list strings that appear ordered on the mistaken belief that they are not random.  The downside is that statistically sophisticated ticket buyers might seek out these strings on the belief that they are less likely to share winnings.

One unknown is the easy-pic algorithm.  Does it have "rules" that delete non-random appearing strings?  It would not be that hard to code and it would make the majority of the customer base happier.  That is something to think about.

#### Renting dreams

In the end, the utility in buying lottery tickets is not economic.  There is no way to justify the time and pro-rated gasoline expenditures on the infinitesimal net value of a lottery ticket even when the jackpot is enormous.

The utility in lotteries is their uniqueness.  Where else can you rent a hundred million dreams for a buck?  You have to keep re-renting those dreams, but it makes life endurable for many people.  Lotteries are not "sweet dreams" but "cheap dreams".

The problem is that some dreamers mistake the lottery as a sound investment vehicle and invest more than \$2 a week.

ERJ advice:  Rent the dreams (if you want) but don't buy the hype, don't think of the lottery as an investment.

This is from Mrs ERJ and I have been unable to work it into any other essays.

-Consult a dictionary before using unfamiliar adjectives to describe to your spouse.  The words "penultimate" and "superflous" might not mean what you think they mean.