## Posts tagged ‘lottery’

### Venn Would Be Good 4 You?

Given my surname, I suppose it was predestined that I’d like Venn diagrams. But nowadays, it seems that everyone likes them, especially the humorous kind. You can find a whole whack of them at www.thisinindexed.com, or just do a Google search for funny Venn diagrams.

Earlier this spring, Reader’s Digest featured *6 Questionable Relationships Stuffed Into Venn Diagrams*. I particularly enjoyed this one:

Of course, it’s based on the idiom “fools and their money soon part,” but it reminds of the following Oscar Wilde quote:

The lottery is a tax on the mathematically challenged.

Though perhaps not as succinct, W. V. O. Quine was more eloquent in describing the phenomenon:

We can applaud the state lottery as a public subsidy of intelligence, for it yields public income that is calculated to lighten the tax burden of us prudent abstainers at the expense of the benighted masses of wishful thinkers.

Not wanting to be left out of all this fun, I decided that I should attempt to create a humorous Venn diagram. How’d I do?

### Math Coinky-Dinks

I’m a math guy, so I know that most coincidences are nothing more than people making a big deal out of something that, in fact, is quite likely. I’m not impressed when two people at a cocktail party have the same birthday or when nearly 30% of the people at that same party have a street address that begins with the digit 1.

Nor was I impressed when the Oregon newspaper *The* *Colombian* printed a winning number for the state lottery *in advance*. The probability that the number they accidentally printed on June 27, 2000, which was 6-8-5-5, would actually win the Pick 4 game the following day was 1/10,000. Not likely, to be sure, but not out of the question.

But is it just a coincidence that Douglas Adams claimed that 42 is “the answer to life, the universe, and everything,” and that Oreo cookies can be obtained by pressing 42 on the vending machine in my office?

And is it just a coincidence that ELEVEN + TWO = TWELVE + ONE?

Well, yeah. Probably.

**But something happened yesterday that was so strange, it cannot be brushed aside as mere coincidence.**

My son Alex was home sick from school. Around two o’clock, he said, “Daddy, I smell blood.” I checked to make sure he wasn’t bleeding… then I checked to make sure that I wasn’t bleeding, either. There was no blood to be found. A couple of hours later, we went to pick up his twin brother Eli at school, and Miss Vanessa at after-school care told me that Eli had an accident.

“He fell and hurt his knee,” she said, “and there was blood everywhere.”

Blood? I asked what time that happened. “Around two o’clock,” she said.

*Freaky.*

With twin boys, I suspect that there will be similar coincidences in the future. For instance, I suspect that I will one day receive a call saying that both boys were caught in a co-ed dorm after curfew. How weird would that be?

But I’m not phased. Coincidences are very common in my family. For example, my mother and father got married on the same day!

To check out some truly random statistical coincidences, click on over to www.coincidenceithinknot.com.

The following joke is based on a fun math coincidence.

Saul: It’s -40 outside.

Paul: Fahrenheit or Celsius?

Saul: When it’s that cold, it’s impossible to tell the difference.

It’s just a coincidence that -40° F = -40° C.

Or is it?

### P(Winning Lottery) > 0… but Just a Little

I know a fair bit about the probability of winning the lottery.

State-run lotteries are a tax on the mathematically challenged.

Given the odds of winning, then you might wonder why I occasionally buy scratch-off lottery tickets. Lord knows, my wife often wonders aloud about it. Believe it or not, there are three reasons that I buy these tickets:

- First, I’m from a rural town in the-middle-of-nowhere Pennsylvania. The rural poor are infamous consumers of lottery tickets. Consequently, I believe that buying lottery tickets is part of my genetic code.

- Second, it’s a guilty pleasure that is easier to indulge than buying PowerBall or Daily Number tickets. When you buy one of those, there is a human interaction, and I imagine that the clerk selling me the ticket is thinking, “Loser! Don’t you know how low your odds of winning are?” For the scratch-off tickets, you insert your money in a vending machine, and the tickets are dispensed. Sure, you may get a disapproving eye from a passer-by, but at least there’s no formal exchange with another human.

- Third, and most importantly, I know a bit about probability, but I also know a little about the intersection of math and psychology. As it relates to the lottery, the idea is fairly simple — make every third or fourth ticket a winner, and people who buy scratch-off tickets will win often enough that they’ll keep coming back for more. Truth is, the winning tickets usually have a prize equal to the price of the ticket or twice the price of the ticket. For instance, if the tickets cost $5, then the winning tickets usually have a pay-out of $5 or $10. When four tickets are sold for $5 each, the state collects $20 and only pays out $5 or $10. Good work if you can get it, eh?
This last point is actually the one that hooks me in. If I buy four tickets at a time, I can almost guarantee that one of them will be a winner. Consequently, I’ll only be giving $10 or $15 to the state instead of $20. (What a bargain, right? I walked into the store with $20, and I get to leave with $5 or $10. Who could pass that up?) But on the off chance that there are two winners in this group of four, or if one of the tickets is a big winner with a prize of more than double the price, well, then, this could work out all right for me.

Yes, I am fully aware that my argument is irrational and that I am slightly delusional. Recognizing my irrationality and delusion, I don’t buy scratch-off tickets very often; but, I do buy them occasionally.

So, why am I telling you all this? Because this morning, I bought four scratch-off tickets at the local supermarket.

**First Ticket:** It had a “5 Times” logo next to $10. That means I won $50.

“Wow!” I thought. “I’m already ahead $30.” And then, of course, I realized how unlikely it was that the other three would be winners.

**Second Ticket:** I matched not one, not two, but *three* of my numbers to the winning numbers for $5 each. That means $15 in winnings on the second ticket.

“Holy schnikeys!” I said out loud, though probably too soft for anyone else to hear. (I hope.)

**Third Ticket:** I matched two numbers for $5 each. That means another $10.

**Fourth Ticket:** Nada.

But, whatever. I was up $55, so who cares about that stupid fourth ticket?

I collected my winnings, and I walked across the street to Panera and ordered a chai tea latte and a bagel. I handed my MyPanera card to the clerk — indicentally, I hate the recent trend of naming something as MySomething, because then it’s really awkward when I want to refer to the MySomething that belongs to me by calling it my MySomething; but, I digress — and he told me that I had earned a free bagel. “You can have this one for free, if you want,” he said. Well, hell yeah!

A few hours later, I went to lunch with a new professional acquaintance. Even though *I had asked her* if she wanted to meet for lunch, *she* picked up the tab!

Can you believe it? Fifty-five dollars in lottery winnings, a free bagel, and a free lunch. Financially speaking, this could have been the luckiest day of my life. (Well, except for the day when I learned that an essay I’d written had won a honeymoon in Oaxaca for my wife and me. But that’s a story for another day.)

Yep, the chances of one good thing happening in a day are low. But the chances of three good things happening in a day? Infinitessimal! Guess I’m just blessed.

My former boss, Jim Rubillo, knows a thing or two about probability and statistics, too. Somehow, his favorite line seems appropriate for this post.

If you don’t believe in the power of random sampling, then the next time your doctor requests a blood sample, tell her to take it all!

### Skill-Testing Questions and Captcha

All lotteries have three major components:

- There is a value associated with the prize;
- The organization running the sweepstakes benefits financially; and,
- The winner is chosen at random.

To avoid being an illegal private lottery, at least one of the three components must be removed. Canadian sweepstakes law requires that the third component (winners chosen at random) be removed. That is, the sponsoring organization cannot use pure luck alone to determine who wins. There must be some element of skill involved.

Hence the disclaimer on lotteries open to residents of Canada, such as the following from the Bizrate sweepstakes:

If a Canadian resident wins a prize, that person must also answer correctly within a 5 minute time period a mathematical skill-testing question (STQ)…

Apparently, Canadian courts have determined that a mathematical expression containing at least three binary operators is sufficient to qualify as an STQ. Hence, a person whose name is chosen at random might have to determine the value of the following before being awarded the prize:

8 × 6 – 5 + 9

The expression above is an actual STQ that was used in a Tim Horton’s contest a few years ago. (A woman with a learning disability gave the incorrect answer of 51. When she appealed, she was given a second chance, and they gave her the same question. Again, she answered 51. Amid much protest, Tim Horton’s eventually relented and awarded the prize to the woman anyway, though it’s unclear to me how they got around the STQ requirement.)

Similar STQ’s are now being used as captchas on web sites. I was presented with the following math question when submitting a comment to a site the other day:

I really thought they missed a golden opportunity, though, so I submitted a second comment with the following image attached: