TaBoo's Free Will Versus the Sports Book Paradox

The Second Riddle

Published on February 9, 2005 By TaBoo Tenente In Entertainment

I encountered a slightly different variation on this riddle once again in LABYRINTHS OF REASON by William Poundstone. Anyone with the slightest interest in logic and the concept of paradox should read it.

A man by the name of Bernard Lowell, at the age of twenty, moved from his home in a small town in Ohio to Las Vegas, Nevada. He was fascinated by the games of chance, and by the people who thought they could beat the games. Games like craps and roulette held little interest for him. He played some poker and made some money, but he lost interest quickly.

Instead he gravitated toward the sports book, and began placing wagers on baseball and basketball and football. Before long, the Las Vegas community became aware of Bernard Lowell. Bernard Lowell was making money. The other sharks watched him carefully, and determined that, for whatever reason, this man was predicting nine out of ten games correctly!

Month after month the authorities studied this man, and month after month his percentage remained more or less constant. They sent private detectives to follow him, hoping to uncover some fix, some cheat to his method. They found nothing. Ten years after he had first arrived in Vegas, Mr. Lowell had amassed a great fortune, and was famous across the country--even among non-gambling citizens.

Jay Leno invited Mr. Lowell on to the show, on the exact day of the ten year anniversary of Lowell's sports betting. After joking about this and that, Jay finally asks the question that everyone has wanted to ask him for years. "Tell me, Bernie," he says. "How do you really do it?"

Bernard Lowell is silent for a moment. Finally he says, "All right. I'll tell you. Not that it matters, because my track record has been proven, proven to be 90% over many years of betting. Still, I suspect your audience will not not believe me. The answer is this: I see it."

"Er, you see it?"

"Yes. It's as if I get a blurry version of ESPN Sports Center running across my eyeballs when I consider a game."

"ESP is more like it. Then tell me: Why do you ever guess incorrectly?"

"Well, as I said, the channel comes in a little blurry. I know it is hard to believe, but as I say, my track record is proven. So I would like to make a proposal. In two weeks, I will be opening the "Lowell's Den" Book and Casino on the strip in the greatest city in the world, yes, Las Vegas, which, among other reasons, is why I am appearing on your show tonight. If you are willing, I will select a member of your audience tonight to participate in a special contest of prediction."

Jay Leno looks up at his producer, who is nodding his head and giving two enthusiastic thumbs up. "I'm sure no one will object," Jay laughs, and the audience cheers. "So long," he adds, "as we can film it live here on my show, what do you say audience?" Of course the audience erupts in more cheers. "Now, Bernie, what contest do you propose?"

"Jay, I propose this: you may select any member from your audience tonight. You will invite them back tomorrow to particpate in the following game: this individual will sit at a table, and on the table there will be two boxes, one labelled "A" and one labelled "B". I tell you now that I will put a ten thousand dollar check inside box "A". Box "B" will either contain a check for one million dollars, or it will contain absolutely nothing! You see, the contestant knows that there is certainly ten thousand dollars in box "A" no matter what else happens, but he/she cannot know what I have decided to do with box "B".

"Now, the contestant will choose between two options: either the contestant may choose to take box "B" only or to take both "A" and "B". Do you understand?"

Jay Leno thinks about it. "I understand that only a nut job would take only box "B". Why shouldn't someone choose both?"

The man named Bernard Lowell smiles. "Well," he says, "there is, of course, a catch. If I predict that the contestant will take both boxes, then I will put nothing in box "B". If I am right, the contestant will get the ten thousand dollars that will always be in box "A" and the "nothing" I put in box "B", and we'll call it a day. On the other hand, if I predict that the contestant will choose only box "B", then I will put the check for one million dollars in that box. Of course, the contestant will get the contents of the box or boxes selected, regardless of what I predict."

Jay says, "Everyone will think you're a bum if you decide not to put the money in there, you know."

"I don't care about that," Bernard says. "My concern is simply to protect my reputation. While it's true that one out of ten times I guess incorrectly, I will only get this one shot of publically proving that my reputation is well-earned. I will make my prediction, and I will predict correctly. Now, if everyone understands, Jay, please choose your contestant, and after the show is over, and the cameras are off, I will make my decision."

Jay strolls through an audienced packed with people screaming to be chosen as the contestant, and he finally glides to a stop . . .

. . . in front of you! You have been chosen. Jay sets you up in a nice hotel for the night, chats you up through the pre-show, and assures you that he has no clue as to what Bernard Lowell has predicted. The moment comes. Jay sits you at the table, and just as Mr. Lowell suggested, there are two boxes, clearly labelled "A" and "B", but it is impossible to see the contents.

Mr. Lowell approaches, and restates the rules. You must choose either box "B" or both boxes. "A" has ten thousand dollars but whether or not box "B" has a million dollars in it, only Lowell knows. If he has predicted that you would choose both, there will be nothing in that box. If he has predicted you would only take box "B", then there will indeed be one million dollars inside.

"Can I have a glass of water?" you ask Jay Leno. Good for you. You got a laugh from the audience. But how much money will you get from the boxes? Will you get zero dollars, ten thousand dollars, one million dollars, or one million dollarsand ten thousand dollars?

It is time to make your selection. What do you choose?

Copyright ©2004, ©2005, ©2006 Joshua Suchman. All rights reserved.
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Comments (Page 2)

TaBoo Tenente

on Feb 09, 2005

and after everything is said and done, free will discussion had or not, i would do the same thing danny would. for some of the reasons i suggested in the game theory, i would bury my head in the sand and say, "either we sink or swim together. lowell, you want to be correct? well, you'd better put the money in box B or you're screwed like me."

thanks, danny. we'd both go down in infamy together.

it still confuses me though. the money is in the box or it isnt, right? does my decision really affect the odds?

tbt

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