So I watched Redline last week, and it is one fine film, definitely worth checking out. But this post is specifically about one of the plot points in the movie: that protagonist JP and his partner Frisbee fix races for the mafia, which they do by having JP hang back until the last quarter of the race, suddenly take the lead, before ultimately losing the race. There will be some minor spoilers.

I got to thinking what kind of scheme the mafia had going that allowed them to profit from this situation, and what they needed JP to do. And it made me realize that, given JP’s capabilities, they could have fixed it a different way which would have allowed them to profit regardless of whether or not JP lost the race.

First of all, what was the mafia’s business model in Redline? At first, I thought it was by being the house and enticing people to make many losing bets on JP by making him look like a sure thing at the end of the race. But towards the end of the Yellowline race that started the movie, the mafia boss’s underling came to him and said that “all their positions on JP” had been “unloaded.” This implies that, in fact, the mafia no longer had any bets for or against JP at that point, so they had no reason to care whether or not JP won. It also implies that there is an after-market for these bets that they could sell already-made bets to.

So I’m not sure what scheme they had going on (if anyone is, please let me know in the comments!). But it seemed like they were pretty dependent on JP’s capabilities: JP needed to be someone capable of both (a) convincingly being an underdog for most of the race and (b) convincingly being the favorite for some of the last part of the race. And, of course, the mafia was quite insistent that (c) JP lose the race.

The fact that JP is conning the spectators twice, first by pretending to be worse than he is, then by pretending to be about to win before losing, should set off an alarm; you only need to con someone once in order to make profit. Indeed, if JP is capable of (a) and (b), there is a pretty safe way for the mafia to fix the race, one that doesn’t care if JP wins or loses.

So here’s the new scheme:

1. Keep JP at or close to last place for most of the race. Make bets for JP as late as possible while he’s still behind.
2. In the last segment of the race, have JP suddenly take the lead. As late as possible, take all those bets you bought for JP and re-sell them in the after-market.
3. Profit! It doesn’t matter who wins the race, because you’ve sold all your bets, and all you’re holding is cash.

How does this work? The key lies in the fact that the bookie must adjust the odds of a bet in a predictable way. And this affects the price at which one can sell bets in the after-market.

First, a quick review of how one accurately determines the value (expected value) of a bet. If you have a ticket representing a $1 bet on JP, its value V is determined pretty simply:

V = Y*Z

where:
Y = payout of the bet.
Z = probability that JP will win.

Betting odds during the end of the Yellowline race

One thing bookies have to do is to try to keep that expected value V fixed, and under 1. Consistency is important so that you get an even distribution of bets for the racers and under 1 is important so that the house is likely to make a profit. Everyone knows this, so the bookie must follow this behavior so that there is no suspicion of foul play. As Z fluctuates throughout the race, the bookie must change Y in the opposite direction to keep V as close to constant as possible (of course, there is flexibility in real life, since no one truly knows the value of Z).

Here’s an example using dummy numbers. Let’s say the bookie wants to keep V at 0.9 throughout the race. During phase 1, when JP is far back in the pack, Z is very low, making Y very high. Let’s say that, when the mafia bets on JP, Z(1) = 1/10,000 – probability of JP winning is 1/10,000. Then the bookie sets Y(1) = 9,000 – the $1 ticket that the mafia bought will pay out $9,000 if JP should win.

But then enter phase 2: JP surges to take the lead. Now, Z(2) = 1/10. The bookie adjusts the odds accordingly so that Y(2) = 9. But the mafia has already bought a lot of bets that will pay out 9,000 instead of 9. So the mafia turns around to the bettors and offers to sell these bets to them, for a premium, of course. These bets are now worth Y(1) * Z(2) = 9,000 * 1/10 = $900.

If bettors were willing to purchase bets worth $0.90 for $1, then they should be willing to purchase a bet worth $900 for $1,000. Let’s say the mafia offers it to them for $900, to entice them with a better deal compared to what the house is offering. In fact, the expected value of the bet is 1 at the price of $900, so ignoring risk aversion, there is no reason NOT to take it (plus, gamblers tend not to be very risk averse people).

And then, the mafia walks away. It has “unloaded” all its “positions on JP” and is sitting on a pile of cash. It bought bets for $1 that it sold for $900, a nice 89,900% profit. Of course, these are dummy numbers, but as long as the bookie follows this predictable behavior, and as long as the after-market is liquid enough for the mafia to resell all their bets to bettors, the mafia will profit. Using more reasonable numbers, even if the jump between phases 1 and 2 of Z was from 1/50 to 1/10, and V was fixed at 0.5, the mafia would make a 150% profit.

This fix is almost exactly what insider trading is in the stock market. In this case, JP (or more specifically, the probability that JP will win) is the stock, and the non-public information is the knowledge that (as well as of when) JP’s probability of winning will skyrocket. It would be like an insider knowing that a company will soon be bought up by another company and buying lots of shares in that company’s stock before it happens.

Here, the mafia is in an even better situation than insiders, because they are actively manipulating the stock instead of just knowing how the stock will move. The incentives line up so that the mafia wants Z(1) to be as low as possible and Z(2) to be as high as possible. Both are accomplished by having the phases 1 and 2 end as late as possible in the race; as it gets closer to the finish, the odds tend to get more extreme: the probability that someone who’s behind will win gets lower, and the probability that someone who’s in the lead will win gets higher.

It will look awfully suspicious both to bettors and to law enforcement if you see one player buy and sell huge bets at such times. So the mafia would want to hire many bettors to do this, perhaps during slightly staggered times, and on much smaller scales as not to arouse suspicion. So the profit would be slightly variable, and the bettors would have to get their cut. It would also create more possible holes, more people who could talk to the police. Still, don’t you think the mafia boss would’ve preferred to take on that extra risk given to what happened?

This wouldn't have happened if the mafia had adopted this business model.

Of course, if the mafia had done this and hadn’t cared about whether or not JP would win or lose, we wouldn’t have gotten the awesome moment when Frisbee was saved, nor would we have gotten the epic finish with the planted bomb. So all in all, I guess it was for the best.

Sayonara, Zetsubou-Sensei (Goodbye, Mr. Despair) is known for being deeply tied to Japanese culture and current Japanese events. Which makes Del Rey’s end-notes very helpful when reading the manga but sometimes these notes do not answer the question I have. In this case, the central idea to Chapter 32 (in Volume 4) of the manga is that Christmas is ruined for Mr. Despair because it appears he was conceived on that day and thinking about that event makes it impossible to have fun on that day (and the teasing he receives after everyone else worked out the math didn’t help either).

It was a great joke and reminded me of the time – when I was much, much, much younger – that I asked why two of my cousins had birthdays that were only 2 days apart (even though there was several years of age difference between them). It seemed like an odd coincidence to me but it was pointed out to me that their parent’s anniversary was 9 months before their birthdays. Putting myself in their shoes,  I can understand why this would distress Mr. Despair but what bothered me about the joke was that the length of time between conception (December 25th) and birth (November 4th) seemed way too long to be right. It bugged me enough that I wanted to get the correct day that Mr. Despair should have born on to make the joke actually work, even if this dissection killed the humor of it. And since I found the answers interesting, I figured that I’d share my enlightenment.

In the United States it’s customary to say a pregnancy lasts 9 months but in Japan the custom is that a pregnancy lasts 10 months and 10 days (which was alluded to in the manga). I thought it was odd to see such a difference in time; so, I looked to see how long a pregnancy actually lasts and if there’s a difference between Japan and America, on the off-chance there is some big difference in length that I’m unaware of. I wasn’t surprised to find that according to a recent study, an average Caucasian pregnancy lasts 269 days from conception to birth and an average Asian (and other minorities) pregnancy lasts 266 days. So, no, a pregnancy anywhere takes about the same amount of time.

To get November 4 as the date of birth, the manga author used 10 calendar months and 10 days but the reading I did stated that the Japanese custom is for the length of pregnancy to be 10 lunar months and 10 days. Don’t ask me why it appears that the manga author doesn’t know this himself but, even with using lunar months, it’s still too long of a time. (1 lunar month = 28 days for a total length of 290 days, or so I thought.)

I wanted to double check the math so I put 10 lunar months and 10 days into Google’s calculator and it told me the length was ~305 days long. Turns out that I’ve been wrong all my life (and everyone else that I’ve ever heard stating that a lunar month is 28 days long), a lunar month is actually 29.5 days long. This leaves more then a month’s discrepancy between the length of pregnancy based on the saying and the actual length. Surely, in the primordial time that predated the formation of the saying “10 months and 10 days”, people could count more accurately.

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Or maybe not; either way, this was distracting me from my purpose.

If Nozomu Itoshiki, aka Mr. Despair, was conceived on Christmas then he’d have been born on September 17th, assuming an average pregnancy length, that he’s Asian, and that it’s not a leap year. If he was Caucasian then the date would be September 20th and if it was a leap year then the date would be September 16th. A peek at wiki to see who was born around here was, at this point, irresistible.

• Born September 16th – Nick Jonas, Orel Hershiser, Ed Begley, Jr., Mickey Rourke
• Born September 17th – Hank Williams, Sr., Phil Jackson, David H. Souter, Rasheed Wallace
• Born September 18th – Greta Garbo, Lance Armstrong, James Gandolfini, Jada Pinkett Smith
• Born September 19th – Jimmy Fallon, Adam West, Twiggy, Trisha Yearwood
• Born September 20th – Kristen Johnston
• Born September 21st – Chuck Jones, Stephen King, Bill Murray, Faith Hill, Ricki Lake, Nicole Richie

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As many people know, in Japan, New Years is considered the family holiday and Christmas is the holiday for the young, party people. Which is reversed from how it’s in the West so for fun, I calculated the dates if he had been conceived on New Years Eve. If this was the holiday then he’d have been born on September 23rd, or September 26th if he was Caucasian, or September 22nd if it was a leap year. Born around here include:

• Born September 22nd – Scott Baio, Bonnie Hunt, Joan Jett
• Born September 23rd – Ray Charles, Marty Schottenheimer, Bruce Springsteen
• Born September 24th – Jim Henson, Kevin Sorbo, Rafael Corrales Palmeiro
• Born September 25th – Kikuko Inoue, Michael Douglas, Mark Hamill, Heather Locklear, Scottie Pippen, Will Smith, Barbara Walters, Catherine Zeta-Jones, Robert Gates, Jamie Hyneman
• Born September 26th – Johnny Appleseed, Linda Hamilton, Olivia Newton-John, Serena Williams, T.S. Eliot, Pope Paul VI
• Born September 27th – Meat Loaf, Mike Schmidt, Samuel Adams

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In both cultures we celebrate St. Valentine’s Day and chocolate is not the only thing exchanged on that day (for many); so, for my final calculation I thought I’d figure out the birth days from February 14th.  If this had been day of conception, Mr. Despair would have been born on November 7th, or November 10th if he was Caucasian, or November 6th if it was a leap year. Born around here include:

• Born November 6th – Rebecca Romijn, Arne Duncan, Sally Field
• Born November 7th – Marie Curie, Rio Ferdinand, Billy Graham
• Born November 8th – Gordon Ramsay, Tara Reid, Courtney Thorne-Smith, Bonnie Raitt
• Born November 9th – Spiro Agnew, Adam Dunn, Sherrod Brown, Lou Ferrigno
• Born November 10th – Roland Emmerich, Neil Gaiman, Brittany Murphy, Sinbad, Tracy Morgan
• Born November 11th – Fyodor Mikhaylovich Dostoyevsky, Kurt Vonnegut,  Jr., Barbara Boxer, Leonardo DiCaprio, Calista Flockhart, Demi Moore

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I hope, in presenting these dates that I haven’t caused anyone to fall into despair.

People who know me know that I have an interest in physics.  A few weeks ago, I saw this post at Mazui fansubs that calculated the size of some fireworks fired in To Aru Kagaku no Railgun.  On a similar note, if you’ve watched Sora no Woto episode 12, you know that Kanata hears a signal from quite a long distance away.  Some people have expressed skepticism that she could have heard it at all.  Inspired by that post from Mazui, I decided to investigate the conditions myself.  I do not claim to be an expert in physics, but I’m going to give this my best shot with the information I have at hand.  I invite all corrections to the following.  Now, let’s get underway.

Now now, don't jump the gun.

The first thing we must establish is the sound level of Rio’s trumpet.  Obviously, if she doesn’t play loud enough, the sound will never travel the distance to reach Kanata’s ears.  We need to start with the maximum loudness.  I found this post at Trumpet Master that states the maximum sound level for a trumpet is 140 decibels (dB).  The figure is impressive, but there’s two qualms with using this figure.  First, as the maximum, it’s unlikely that you can get much music out of the instrument.  In my head, I just imagine someone blowing as hard as possible to make the loudest sound.  Second, the pain threshold for the human ear is about 120 dB.  Above this, we might hear sound, but we can’t really interpret it well.  It sounds distorted.  Thus, we can’t directly use the maximum, but it does mean that we can be liberal when selecting a point to experiment.  I think 100 dB is a reasonable value, so that is what I will use.

Rio does play a pretty mean trumpet.

The second thing to establish is the speed of the tank Rio rides.  The fastest armored vehicle of World War II that I could find is the M18 Hellcat.  The speed tops out at a blistering 60 miles per hour.  The measurement is quite impressive, but there’s a fault with the choice.  This is not a tank in the traditional sense.  They used it to take out tanks, but it lacked much of the armor and protective features we think of in a typical tank.  Therefore, I also selected the Cromwell to use in this experiment.  This British tank had a maximum speed of 40 miles per hour, though they restricted it to 32 in practice to maintain structural integrity.  The difference in speeds makes a difference, but probably not for the reason you think.  A faster tank actually puts Rio’s trumpet playing skills at a disadvantage.  Why?  Because I’m going to assume that Rio moves at top speed all the way to the front.  This means a faster tank must start further away from the battle.

Really, these bulky things don't look too fast...

With these parameters established, we also need to think about the conditions.  I’m not going to spend weeks of my life becoming an expert in the physics of sound just to write a post.  Therefore, we’re going to assume ideal conditions for this experiment.  This means that the energy of the sound waves is conserved, it continuously travels, and no amplification or interference occurs.  We know from the episode that once the Colonel escapes, he plans for the battle to commence in 10 minutes.  From the time the troops start moving until the time that Rio arrives, 3 more minutes elapse.  The total time is 13 minutes.  As stated earlier, Rio must move at top speed all the way to the front.  This means at 60 miles per hour, she starts 20900 meters away, and at 40 miles per hour, she starts 13900 meters away.  Her trumpet plays at 100 dB.  You can find the formulas here, or you can just plug it into a prebuilt calculator here.  Let’s get started.

Clear as mud, right?

So what does it all mean?  First, the starting distance doesn’t make much of a difference.  However, I think we can agree that even the small change in decibels could potentially make or break something like this.  Second, to interpret this properly, you need some sort of baseline to compare it too.  A lot of sites state that 15 dB is about what you can expect from a whisper.  That gives you an idea of what exactly she hears.  The work means that it is plausible with ideal conditions.  Kanata could indeed hear Rio’s signal.

And there was much rejoicing!

We do need to note two things.  First, the curve for diminishing intensity remains the same no matter where you start.  What this means is that if Rio plays 10 decibels higher, it stays 10 decibels higher across the board until it reached Kanata.  That difference roughly correlates to doubling the loudness, which greatly increases the chances of this plan working.  Second, decibels are objective.  We got to these formulas by taking the averages of many people.  What an actual person experiences is subjective.  Some are more sensitive to sound, and others less.  This explains why Kanata hears the signal while Kureha has no idea what’s happening.  It also means that Kanata’s genetics can pick up a little slack by making her more sensitive to sound.  With this, I think I have pretty well wrapped up the post.  Again, if you have anything to add or I’ve made mistakes, please comment.  I’m actually really interested in this topic.