The Freakest Links

Is illegal downloading responsible for the music industry’s woes? Felix Oberholzer-Gee and Koleman Strumpf say nope.

The I.R.S. will give you a pile of money if you help them catch a big tax cheat. Too bad they weren’t this generous with John Szilagyi, who was one of their own.

These three guys look pretty thrilled to have produced the first three-way tie in Jeopardy‘s history. This A.P. report says that the show “contacted a mathematician who calculated the odds of such a three-way tie — one in 25 million.” Does this seem high to anyone else?

(Hat tip on Jeopardy: Matt Hertz)


Considering that each person essentially controls their own final score (since the Final Jeopardy question allows each contestant to risk all of their money), these odds are waaaaaay too high. If the assignment of points during the game was random, the odds are probably much closer to the 25mm.


I guess it would depend on what type of mathematician calculated the odds. It seems to be more of a behavioral question a straight mathematical question.

I enjoy watching Jeopardy and have seen it many times over the years, and there have been many times where all contestants have a chance to win. It seems plausable that the mathematician could calculate the odds of the scores before final Jeopardy, and the odds of the two finalists guessing the correct answer and wagering all of their money. But how do you calculate the odds of the finalist with the most money not wagering enough to give himself the same amount as the other two? If we consider him to be an intelligent person, he must have done it on purpose. This is especially possible if there isn't a reduction in his winnings for allowing the tie, which looks like it may have been the case (lots of assumptions!).

Overall, I would say the number is suspect, as the end result came down to the gaming of the system of the finalist with the most money (because the system did not penalize him for doing so). Because the system was gamed, the mathematical answer becomes very suspect.



The odds on the three-way tie on Jeopardy were calculated by Dr. David Levine at Washington University in St. Louis, based on a completely arbitrary and unrealistic assumption that two players tied with $5,000 each bet a random amount of money: 5,000 x 5,000 = 25,000,000.

The actual amounts on the show differed, and the tie really depended on the non-random decision by the leader to offer the tie, rather than betting to pass his opponents' maximum possible total by $1.


My own theory on the whole P2P file sharing/music theft scheme is that record labels and the RIAA haven't adjusted to the paradigm shift that occurred ten years ago as the P2P service rose up. The water marking schemes were available but they didn't act on them, because they spent more time listening to their attorneys and not enough to the music fans, artists, and most importantly the people that had the actual technical knowledge to properly advise them. The recording industry could be enjoying it's most profitable era ever right now, instead of suing their customers and blaming their own sluggish pragmatic reaction on technology they could easily be harnessing now.


Doesn't this bring up the possibility of collusion for three players to remain on the show indefinitely? Interesting bit of game theory, perhaps.


The odds seem reasonable to me, because it's really the odds of an individual being smart enough to be leading on Jeopardy going into the final question yet being dumb enough to not know how to bet.


Any calculation of odds makes certain assumptions that distort the numbers.

To use an example, just because Harvard only accepts 10% of applicants doesn't mean that each applicant has a one in 10 shot. Some are better, some are worse. Just because you got in didn't mean you got lucky.


Math isn't my thing, but it seems to me that one might want to take into account the fact that apparently the jeopardy tie happened because the guy who was in the lead (mefi says he's a puzzle whiz and computer scientist, although I don't know if that's true) did it on purpose. In his own words from the jeopardy forum: "I've never had a philosophical objection to tie games, although I understand the strategic reasons why you shouldn't bet to tie. Making history seemed like a very special reason to bet to tie." (

I wonder how you work intent into odds.


Is it just me? I tried to read the Jeopardy and music industry stories but both seem to have busted links.

Josh Millard

Doesn't this bring up the possibility of collusion for three players to remain on the show indefinitely? Interesting bit of game theory, perhaps.

What bgriff said—that's the first thing that struck me, too. The grin on Mr. $13400's face in that clip was tellingly mischievious.

How would the folks at Jeopardy react to that sort of conspiracy? Do you suppose they anticipated it? Anyone have access to an official Jeopardy rulebook, or whatever?



It's normally called the Slashdot or digg effect and it appears this blog is big enough to have a Freak effect*.

* The traffic generated by a link on the referring site is enough to overwhelm the server hosting the linked content.


Collusion before the show is definitley prohibited by the rules.

"The grin on Mr. $13400's face in that clip was tellingly mischievious."

As reported on the Jeopardy board, during a commercial break someone in the audience asked Alex a question about a triple-tie. When the leader found his opponents tied at the end of the game, he decided to take the opportunity to make history.

The Jeopardy rules also state that each of the winners, in this case, get the full $16,000, instead of splitting it three ways, which would effectly discourage any impulse to offer the tie. Sony is free to change the rules, if they consider this a problem.


Hey! It seems the authors of the file-sharing survey wrote something very similar to what I wrote here in this blog on the topic of illegal book downloads:

"While downloads occur on a vast scale, most users are likely individuals who in the absence of file sharing would not have bought the music they downloaded."


Josh Millard

The Jeopardy rules also state that each of the winners, in this case, get the full $16,000, instead of splitting it three ways, which would effectly discourage any impulse to offer the tie.

Do Jeopardy losers take home their non-winning positive balance? If not, how would a full-rather-than-divvy plan discourage the impulse to collude?

Assuming losers don't keep their balance: with (potentially disqualifying) collusion, each player generates $16000, in this case. Without collusion, and with all contestants confident of their answers (rightfully, on such a gimme -- Bonnie Parker?) both of the $8000s get nothing, and $13400 nets $26800.

Obviously, there's the safe incentive for $13400 to bet it all and be assured $26800 over $16000 -- but if he and the 8K twins recognize this, a forced tie that yields a total of $48000 to be split disproportionately to 13.4K (say, $32K to him and $6K to the twins) is a win for everyone, if 13.4K can trust the twins.

But I may have the essential loser-takehome rule wrong. I haven't been watching enough Jeopardy, I suppose.



bgriffs, I don't see how you could realistically collude to produce a 3 way tie without being blindingly obvious about it. In this case, the only reason it worked was because there was a tie for 2nd place, so the 1st place player made the assumption that the 2nd place players would bet all their money in a last ditch attempt to beat him. That is a reasonable strategy to expect, since only the first place finisher keeps any money, so there's not a big incentive for the other players to bet more conservatively. But even then, in order for the tie to work, all 3 players needed to know the answer to the final jeopardy question. And in order to get to a point where there's a tie going into final jeopardy, or even just an arrangement where everyone's score is close enough that they wouldn't lose too much money by considering a tie, you're going to have to control who answers which questions correctly throughout the entire game. on categories & questions the players don't know ahead of time.



Re: the tax whistleblowing--

What would hold someone back from reporting ANYONE they know earning at least $2 mill. to the IRS? I'm guessing the IRS has a system to see how credible a source "tip" is... but what would happen if they got something like 80% of the list of names of people earning $2mill a year... wouldn't the IRS realize everyone just had their name submitted?

Josh Millard

Comment eaten: trying again.

The Jeopardy rules also state that each of the winners, in this case, get the full $16,000, instead of splitting it three ways, which would effectly discourage any impulse to offer the tie.

Why would that discourage the impulse?


1. Losers don't take home their balance, but rather some consolation prizes of nominal value.
2. All three players were confident that all three players knew the answer. (And "Bonnie Parker" was a gimme. If *I* know the answer, random Jeopardy contestent certainly will.)
3. All three players understand the game theoretical implications of a tying for a tripled, not divvied, pot.
4. 13.4K can trust the 8K twins to make it worth his while if he plays to the tie.

Given all that, 13.4K is in a position to turn total winnings of $26800 distributed solely to him into total winnings of $48000 distributed equally among the three players, to be later redistributed in his favor (perhaps $28000, or $32000, or...)

A lot of assumptions there, but if (1) holds (I'm not up on the Jeopardy fine points), 2-4 are plausible. And in fact it seems like the anti-collusion disclaimer in the rules attests to that—Jeopardy has to provide a disincentive to collusion specifically because it would profit colluders otherwise.

So I guess it was pretty doe-eyed of me to doubt that they'd have a hard prohibition in place.




I agree it would be then the crux of the matter is how quickly the rules could be amended to cap or otherwise limit the number of shows in which 3-way tie contestants could participate without legal issues arising.

As for the common knowledge factor, as the final answer approached, a contestant who didn't know the answer could signal, subtly somehow, that he didn't know, and then all three could wager whatever mount they have and guess incorrectly. I can think of a lot of other interesting ways to cheat if the three players are all in on it, but i don't want to get too far afield of the topic.


Correct me if I am wrong, but don't they have to wager before they actually see the final question. (I believe they see the category, then wager, then get to see the question.) This makes collusion quite a bit more difficult.

As for the strategic wisdom or folly of the tie bet, what if the player in the lead is confident he is better than both of the other two players? Then betting so that IF he answers correctly and IF they bet everything and IF they get the question correct there is a tie may not be a bad idea. He wins money and gets to play again the next game against players he feels he can beat. Then he might also get the benefit of reciprocity if the next night he is behind going into final Jeopardy in a future game.


Perhaps I wasn't clear. The rules as they are now say that each contestant gets the full amount in a tie. 3 x $16,000, in Friday's case.

I was suggesting that the show could amend the rules so that each in this case would get $5,333.33 ($16,000 / 3). While the leader might feel generous enough to make the wager that gives each of them $16,000 at no cost to himself, he'd more likely prefer to increase his bet to $16,001 to win the whole pot, rather than taking home only $5,333.33 as his share.

Whether it's in one's self-interest to face the same opponents again or to face new opponents without the buzzer experience is another subject being fiercely debated, but the vast majority of contestants choose to go for the win, often with the "win by $1" wager.