The Half Monty, Part 2
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, herself included.

..... ."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
Nina Smart
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 titles.

Congratulations, Nina, and Kevin and I thank all of you for participating."

Copyright (c) 2000, 2001 by Laura Lippman.

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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"And I'll tell you right out that I'm a man who likes talking to a man that likes to talk."

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