The Half Monty,
A Tess Monaghan Diversion
(Click here for Part 1)
by Laura Lippman
..... .Tess and Sal stepped outside
into a perfect June evening, full of sweet smells, with a deep
blue sky that could have been a stage backdrop. Tess inhaled
happily, while Sal looked from the title in his hands to the
car parked across the street, and back again.
..... ."So what was the
con?" he asked.
..... ."No con," Tess
said. "Although he misled you when if he said it was a 50-50
shot you had the right cup. It was only one out of three."
..... ."No way. I know probability.
I had 800 on my math SAT."
..... ."Which means you
had only 740 on your verbal. A shocking lapse for you, Sal."
..... ."Which I'm still
not convinced was right --"
..... ."You know, it's not
fatal to admit you're wrong about something. Or," she added
pointedly, "to say thank you when someone bails you out
of a jam."
..... .He sat on the curb, brushing
it off first, so as not to get dirt on his immaculate khakis.
The silver VW glowed beneath the street lamp. From this day on,
it would probably be a little tainted for Sal, a reminder that
he wasn't as smart as he thought he was. Well, that was a good
thing to remember every time one turned a key in a car's ignition,
and Sal had learned it with less pain than some others Tess knew,
..... ."I'm so confused,"
he said at last, and she recognized this for the concession it
was. "What happened in there?"
..... .She sat on the curb next
to him, began refashioning her hair in its customary braid. She
didn't like all that hair flying around her face. It made her
feel like Cousin It on "The Addams Family."
..... ."You were a victim
of the so-called Monty Hall paradox. It looks like a straight-forward
probability problem, but it's not. It fooled some of the best
math minds in the country when it appeared in Parade magazine,
in that column by the woman who claims to have the highest IQ
in the world. The problem was so controversial that the New
York Times wrote about it, tracking down the real Monty Hall,
who ran simulations of it. We even studied it in my math class
at Washington College. You would have been in third or fourth
grade about then, so you can be forgiven for not knowing it.
Which is what 'Monty' is banking on, I guess."
..... ."But it's one out
of two. You flip a coin 30 times, 50 times, the odds will even
out. Why not this problem?"
..... ."Because it's not
one out of two. And, more importantly, it's not random. Anything
but. Monty Hall knows where the die is. Whatever shaker you pick,
he'll always choose to show you an empty one you didn't
pick. In essence, the one you don't pick absorbs the probability
of the one that was eliminated. Add one out of three to one out
of three, and you'll end up with two out of three."
..... .Sal was unconvinced. "Let's
say I pick cup #1 --"
..... ."Monty will show
you an empty cup #2 or #3. Don't under-rate the importance of
that first step. The problem doesn't work if he opens a cup at
random. He always shows you an empty cup, and it's never the
cup you picked. That's what Monty Hall does on the show. He shows
you the door you didn't pick, and it's never the best door."
..... ."Still, it's one
out of two --"
..... ."Nope. Trust me,
Sal." She tapped the title. "There's your proof. Monty
gave it up, because he knew how the game would play out. If he
had a chance to win, why wouldn't he go for it? He had nothing
to lose. Except his name, which probably comes with a rap sheet
for larceny and fraud all over the country. He was ready to play,
until I told him I was going to take the 'switch' strategy."
..... .Sal was thinking so hard,
it looked as if he were in pain. He grabbed a twig, sketched
three circles in the dirt. "If I pick #1 and the die is
in #2, he shows me #3. I have to switch to win. If I pick #1
and the die is in #1, he shows me #2 or #3. I switch, I lose.
If I pick #1 and the die is in #3, he shows me #2 --"
..... ."You switch, you
win. See, two out of three? And it will play out the same if
the die is in cup #2, or cup #3."
..... ."But I still don't
get it." His smooth speaking voice, another of Sal's vanities,
cracked for the first time in five years, as if he were going
through puberty again.
..... ."Then maybe you should
stay out of coffee bars when you get up to Princeton."
..... ."Oh I don't know,"
Sal said, smiling for the first time, finally able to see the
humor in his situation. After all, Tess was the only one who
knew, and she would keep his confidence. "I'd like to see
how far I could get with that immaculate conception question.
If it's not the birth of Jesus, what is it?"
..... ."The conception of
Mary, the first person born without original sin, and therefore
suitable to be the Messiah's mother."
..... ."And that works?"
..... ."Almost always,"
Tess said, wondering if she dared to hug him, then doing it anyway.
"Just make sure your mark didn't go to parochial school."
And the big winner is
Laura writes: "Your readers are quite
intelligent. As always, however, the immaculate conception question
is a spoiler. (You'd be surprised how many Catholics get it wrong.)
Some people who solved the puzzle eliminated themselves from
competition by insisting it referred to the birth of Jesus.
One extremely honorable contestant disqualified
himself, saying he had read the solution in The Straight Dope,
a popular syndicated feature and wondered if I did the same.
Actually, I had learned about the problem from a New York
Times item. (July 21, 1991, Page One). I'll let Tess explain
it in detail, but the key element in understanding the puzzle
is realizing that it is not random. One mathematics professor
noted, in a subsequent letter to the Times, that this is a problem
in conditional probability. I realized, reading these entries, how difficult
it is to describe a mathematical solution in prose. I'm not sure
I did it very well.
All winning entries were written on scraps of paper,
and then placed in the hat of my colleague Gerry Shields. My
co-worker Joan Jacobson picked out the winner.
I always learn a lot from readers. This time, I
learned just how smart readers can be. Thanks.
Nina will receive a $100 gift certificate to Mystery Loves Company,
a Baltimore-based mystery book store with new and used mystery
Congratulations, Nina, and Kevin and I thank all
of you for participating."
Copyright (c) 2000, 2001 by Laura
Laura Lippman has now written five novels about Tess
Monaghan. She has won several awards -- including the
Edgar, the Anthony, the Agatha and the Shamus -- and cheerfully
admits she "may have even deserved one or two of them, but
probably not." She lives and works in Baltimore. She wanted
to be hardboiled but, to paraphrase Jessica Rabbit, she just
wasn't drawn that way.
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