Cinemath: The Game Theory Behind the Snow White War [Updated]

     May 23, 2011


It’s probably clear to you from my nightly journalistic incompetence, but my day job (at which I’m equally incompetent) is student research based in math and statistics.  I’ve been looking for an opportunity to introduce a semiregular feature that combines the two worlds (Cinemath!), and Hollywood obliged this past week.

Universal Pictures and Relativity Media each spent the last year developing movies based on the Snow White fairy tale, both targeting a 2012 release.  Relativity scheduled The Brothers Grimm: Snow White to be the first audiences see on June 29, 2012.  Last Tuesday, Universal made the bold — and quite possibly idiotic — move of rescheduling Snow White and the Huntsman from December to June 1, 2012.  This brand of cutthroat competition is hardly novel among movie studios, but the Snow White war serves as an illustrative case study for the strategic reasoning described in game theory.

After the jump, I explain how the battle between Universal and Relativity is mathematically identical to the Cuban Missile Crisis.

[Update: Relativity moved The Brothers Grimm to March 16, 2012.  We must discuss this after the jump.]


a-beautiful-mind-posterGame theory describes the dynamics at play when the best strategy depends on the actions of your competitor, another player in the game.  As moviegoers, your first introduction to game theory was likely A Beautiful Mind.  Russell Crowe played John Nash, one of the most prominent contributors to the field.  The movie focuses on the period when he went crazy, but prior to the schizophrenia, Nash’s work helped lay the foundation for game theory.

The most immediate application of game theory to the movie business is seen in the jostling over release dates.  The essential goal of the modern movie studio is to lure as many of you as possible into the theater.  This becomes more difficult when a rival studio has a convinced a sizable group to see the movie in the theater next door.

There are a limited number of weekends available each year, and even fewer “prime real estate” weekends.  The best weekends ensure the maximum possible audience, when kids are out of school (the summer months) and/or adults are off work (Thanksgiving, Christmas).  The scarcity of weekends and abundance of wide releases turn studios into vultures circling over these weekends.  That’s why DreamWorks announced How to Train Your Dragon 2 for June 20, 2014 more than three years in advance.  That’s why Marvel waited just one day to swoop in when the would-be Spider-Man 4 was delayed.  And that’s part of why Universal and Relativity are racing to get their multimillion-dollar fairy tales in theaters first.

In game theoretical terms, this race is represented in the game of “chicken.”  The primitive form of chicken is itself very cinematic, seen in such movies as Rebel Without a Cause, Footloose, and Faster, Pussycat! Kill! Kill!.  In the most basic variation, two cars drive directly at one another; each driver has the option to continue driving straight or to swerve.  The best outcome for the driver is to bravely continue straight while his opponent swerves like a yellow-bellied chicken.  In accordance with the male machismo, the driver is shamed if he swerves, but this shame is mitigated if the opponent also swerves.  The worst outcome for both drivers is, of course, a fiery car crash.  Each possible scenario is captured in the payoff table below, which lists the value both drivers place on each outcome.  For instance, the first box shows what happens if both drivers swerve: {Driver 1: Tie, Driver 2: Tie}.


The game is not limited to gearheads.  Perhaps the most famous (and certainly the most terrifying) real-life game of chicken is the Cuban Missile Crisis.  Game theory is especially relevant to sports fans right now as the owners and players are threatening a lockout next season in both the NFL and the NBA.  And, as I’m about to argue, Universal and Relativity are embroiled in a game of chicken over Snow White

The Snow White War

snow_white_illustrationAt this stage, both Universal and Relativity are in pre-production with a cast and crew, but neither studio has shot a frame of film.  Either studio can still cease production (“Swerve”), absorbing the moderate losses of pre-production cost.  Alternatively, either studio can plow forward (“Drive Straight”) toward that June release date.  To formulate this as a game of chicken, we’ll briefly simplify with a few assumptions:

  • The two films are interchangeable in terms of market potential
  • The audience is indifferent between which Snow White movie they attend
  • There is not enough demand to accommodate two Snow White movies at the same time — both Relativity and Universal would prefer to release the movie into a market with only one Snow White movie.
  • Disney has its own Snow White film in development, but it will not hit theaters before 2013, probably later.  Snow and the Seven does not factor into this game.

Below is a hypothetical payoff table measured in profit/loss.  (Please note these numbers are entirely made up for the purpose of ranking each outcome.)  If a studio backs out now, it loses $10 million in pre-production cost.  If a studio goes forward with the production, it incurs a much higher cost.  If there is no competition, the active studio earns $100 million in profit.  If both studios must split the market, both studios lose $50 million on their investment.


One of the core concepts in game theory is the Nash equilibrium, which borrows its name from the aforementioned Russell Crowe John Nash.  A Nash equilibrium predicts the outcome of the game — it is not necessarily the best outcome for either player, but at the Nash equilibrium each player has chosen the best strategy after taking into account the other player’s decision.  In a game of chicken, there are two Nash equilibria, where one player swerves and the other drives straight.  This backs up intuition (or mine, anyway) that there is no way there will actually be two Snow White films in theaters next June.

(As I mentioned, I simplified the scenario to fit comfortably in a payoff table.  I discuss other possibilities in the appendix.)

So who swerves?  Universal’s move to June, in game theoretical terms, is “signaling” — a public display of pre-commitment to a strategy.  In the vehicular chicken, one party may signal their intention to drive straight by disabling the steering wheel, removing the option to swerve.  This signal is a declaration that Universal will have their Snow White movie in theaters first.  Universal’s message: “Your move, Relativity.”

Relativity’s Move

I like to think of game theory as a kind of mathematical soap opera, so let’s back up and flesh this story out a bit.  In February 2008, Relativity signed a deal with Universal to co-finance 75% of the studio’s slate through 2011.  Seven months later, the studios reupped their partnership through 2015.  At the time, Relativity CEO Ryan Kavanaugh remarked, “Our deal has been very profitable to date, and the Universal creative, marketing and distribution team is unparalleled. They are true partners.”  Universal executive Michael Joe added, “We have had a genuine collaborative partnership to date, and we look forward to expanding on our ambitions together in the future.”

snow-white-illustration-2Relativity had ambitions beyond the co-financing business, though — the studio started distributing its own films last year.  In June 2009, Relativity picked up Melissa Wallack’s script The Brothers Grimm: Snow White to produce and distribute.

Three months later, a spec script by Evan Daugherty titled Snow White and the Huntsman sparked a bidding war among the studios, including Sony, Paramount, Fox, New Regency Summit, and, of course, Universal.  In the end, Universal paid a large sum to compete with Relativity, testing the bounds of their “genuine collaborative partnership.”

Since then, Universal has generally pretended that Relativity’s Snow White movie does not exist.  Even in this week’s scheduling announcement, Universal chairman Adam Fogelson and co-chairman Donna Langley attributed to the move to efficiency:

“As [the filmmakers] were finalizing casting and preproduction of Snow White and the Huntsman, we realized that the ambitious and fully-formed world they had promised was blowing away all expectations.  We’re thrilled that Universal will be bringing this singular version of a timeless story almost seven months earlier than anticipated.”

The move is transparently motivated by the competition, but nope, Snow White and the Huntsman is a “singular version.”  There is bad blood between the two studios, and that must be taken into account when evaluating their strategies as an additional incentive to act irrationally.  (Interestingly, irrationality is a good strategy in a game of chicken.  If you are convinced the other driver is crazy enough to drive straight no matter what, your best option is to swerve.)

And so, with that oral history laid out, what are Relativity’s options?

1. Release the film earlier

If the craziest studio wins the game, Relativity could try to out-crazy Universal by announcing a release date before June 1, 2012.  I am rooting for this to happen, to extend the soap opera.  But it’s inadvisable.  Currently, Relativity has just over a year to shoot and add copious special effects to The Brothers Grimm: Snow White.  That’s already a very tight turnaround.  How much further can they push it?  Universal is in the same position, and there’s a reason Fogelson and Langley didn’t promise eight months earlier than expected.

Rushing to finish a film that will eventually be sold as a big-budget fantasy will negatively affect the quality and commercial prospects of said film.  There is a date that is too early, such that it is no longer viable to produce enough for the necessarily awesome two-minute trailer.  I obviously don’t know the exact date, but anything earlier than June approaches that limit.

[Update: Since posting, Relativity rescheduled The Brothers Grimm: Snow White for March 16, 2012.  On one hand, this makes sense.  Relativity decided to go all in on Snow White -- depending on how Immortals performs in November, this could be their first major property as an independent distributor.  And if you're going all in, you might as well leapfrog a busy May already populated by The Avengers, Battleship, Men in Black III, and head straight for March where the likeminded Alice in Wonderland earned $1 billion.

On the other hand, this is crazy!  Production will begin in June, allowing just nine months to create a viable blockbuster fantasy.  The studio was reportedly considering 3D, but that cannot still be a possibility, right?  The director, Tarsem, has made three films in 12 years.  Maybe the technology really has gotten to the point where Hollywood can churn out a tentpole in nine months, and Tarsem, post-Immortals, has evolved into the man who can achieve such a feat.  That's a cool idea, and I really would like to see this be a good movie.  However, no precedent comes to mind.

I love the audacity, though.  ("Au contraire, Universal: your move.")  Can Universal go any earlier than March with a movie that was originally scheduled for December?  I'd love to see them try.  I actually think the best move is to move Snow White and the Huntsman back to December.  The studio loses a little face, but the marketing department can react to the success or failure of Relativity's movie.  Clearly, though,  studios have no interest in what I think is best.  So look on the front page of Collider next week for the headline "Universal Moves SNOW WHITE AND THE HUNTSMAN to Yesterday."

To be clear, both studios are still signalling.  There's still time to bail.  Outside of these brackets, I'll leave the post as is for now.]


2. Keep the film where it is

Relativity could keep the June 29, 2012 release date.  I’d like to see the studio try, just to see how audiences would respond.  But I cannot imagine a scenario where this will happen.  Relativity will either announce an earlier release date or…

3. Put a hold on development

I believe either Universal or Relativity will eventually be forced to push the release date back or, more likely, cease production altogether.  Universal has the upper hand, so my best guess suggests Relativity will put The Brothers Grimm: Snow White on hold.  Let Universal be the guinea pig that tests just how much audiences are yearning for a modern Snow White.  Depending on how Snow White and the Huntsman does, revisit Wallack’s script in a year or two.  In the meantime, maybe see if you can get in on the co-financing, or seek compensation for backing out of the game.  I am admittedly a risk-averse individual, but this is what I’d do if I were Relativity.


Studios are not necessarily mathematically rational entities, and that makes this whole process really exciting.  I am not even remotely certain about my best guess.  At this point, I’m more interested in the behind-the-scenes game than either of the movies.

Further Reading

Mathematicians are great at maintaining Wikipedia, so check out the pages on game theory in general and the game of chicken.

Mind Your Decisions and The Quantitative Peace offer a really cool rundown of the game theory in The Dark Knight.

The Baltimore Sun uses Dr. Strangelove to a touch point to discuss the game theory involved in nuclear war.  Included is an interview with Thomas Schelling, a famous game theoretician who consulted Stanley Kubrick prior to shooting the film.

Rebel Without a Cause depicts a game of chicken where the goal is to not drive off a cliff.

The Joker facilitates a game between prisoners and theoretically upstanding citizens at the end of The Dark Knight

Kevin Bacon learns how to ride a tractor to prove his manhood in Footloose


Chris Hemsworth Thor_PremiereIn formulating the game, I treat the movies as essentially interchangeable and the month between release dates as negligible.  In reality, things will not be quite so simple.  Before I continue, allow me a simple test.  These people are all cast in one of the two Snow White movies: Lily Collins, Chris Hemsworth, Kristen Stewart, Julia Roberts, Armie Hammer, and Charlize Theron.  Now, without looking at IMDB, can you link each to actor his or her movie?  I do this for a living, and I can’t.  I have to look it up with every new casting report.  This is anecdotal evidence for movies that still have a year to advertise, and thus entirely meaningless.  I don’t intend this to be condescending (it is), but I wonder how much audiences can distinguish between two movies trading on the familiarity of the Snow White brand.  Individually, Snow White and the Huntsman will draw more Chris Hemsworth fans, and The Brothers Grimm: Snow White will appeal to the Julia Roberts fanbase.  But overall, these movies will be defined by their Snow Whiteness in the public eye.

(In this sense, the Snow White war is fundamentally different than Deep Impact vs. Armageddon or Volcano vs. Dante’s Peak.)

I believe this much is true: both movies would be better off if the other movie did not exist.  But if the audience is split, the movies are unlikely to perform identically.  There is arguably major benefit to being first, evidenced by the race between Universal and Relativity.  I assume the studios would bombard the public with two massive Snow White-centric marketing campaigns from January to May.  In this case, the dual marketing creates one large mass of general Snow White brand awareness.  The first Snow White movie reaps the benefits; by the time the second rolls around, demand for Snow White has largely been satisfied, limiting the potential audience.

Alternatively, a discerning audience may shun the first and opt for the second movie.  Though again, I am skeptical this audience is large enough to make a difference, especially since a movie is an experience good.  There is also an argument that the first movie, if successful, actually rachets up demand for more Snow White.  That seems counterintuitive to me, but what do I know?

Around The Web
  • Marc

    Fantastic article Brendan! It was thoroughly engaging, well written, and enlightening.

  • Twilidiot

    Love it! Nice infographics, too. Thank you for the information in the appendix. I’ll be very interested to learn more about game theory and THE DARK KNIGHT. Those Econ classes were hard work; glad to put them to use for once after 20 years.

    Since so much thought, research and editing obviously went into this, the Sam Claflin factor hadn’t yet emerged at the time of writing. The swoon factor is definitely at work after those beautiful green pools were shown worldwide in 3D IMAX in a record-breaking Pirates of the Caribbean release.

    If Universal can run an intelligent social media campaign, the power of Twilighters + Pirates fans will easily propel SNOW WHITE AND THE HUNTSMAN forward. That should help you remember who is attached to what: Kristen Stewart + Sam Claflin + Twitter = $50 million +.

    •!/colliderbrendan Brendan Bettinger

      It will be interesting to see if Pirates 4 makes Claflin the next hot young thing. I don’t know how big his role is, but we’ll see how prominent he is in the marketing campaign.

      Huntsman does have the edge in starpower. But what will that mean for box office? So far the devout Kristen Stewart fanbase has failed to mobilize enough to affect the box office of her non-Twilight movies. Maybe Snow White, another big fantasy, will be the one to do it.

      How much does Twitter add in your equation?

      • Twilidiot

        Got me there … I’m not as good with math as you are! What exactly is the box office impact of a really well-run social media campaign to market a film? First I need to see one that meets my standards.

        Water for Elephants’ official social media campaign was obviously run by amateurs and Fox missed the boat. Robert Pattinson is #9 on Forbes’ social media influence list and he doesn’t even have a (public) Twitter or Facebook account.

        Disney and Bruckheimer have done a pretty good job with Pirates but it still seemed to be in beta. There are at least three different Disney Pirates official accounts (@disneypirates, @thePOTC4movie, @piratesff) and only the second engages in a notable quantity of conversation. Good contests the day of the premiere and Bruckheimer’s guest-hosting of The Hollywood Reporter blog was pretty good.

        If Pirates had been able to get the cast and filmmakers (Marshall, Rossio, Elliott, Zimmer) to engage on Twitter, that would have been quite powerful. Director Chris Weitz is my model there; he does regular Q&As.

        I also haven’t seen publicized well enough that the ON STRANGER TIDES premiere raised over $1 million for the Boys & Girls’ Clubs and that the special edition of the Pirate’s Booty snack is donating to them as well. With the current generation of armchair philanthropists, that could be a marketing goldmine.

        Justin Bieber is obviously a career made of YouTube and Twitter but Never Say Never was badly marketed IMHO. It’s well-made and told from the point of view of the adults and therefore very enjoyable for them, but that didn’t hit the streets. Eight-year olds don’t go to the movies by themselves.

        Enough babbling by me for now. But you do have me thinking about how to quantify in dollars the value of social media, especially Twitter. Now I have to go read that darn 100+ page report from the Yahoo researchers about who is an influencer on Twitter.

    • Dawn

      What does Twitter have to do with it? Actors in popular movie franchises have large twitter followings but that doesn’t usually translate to tickets bought. Kristen Stewart and Robert Pattinson are prime examples of that logic. There is much written and tweeted about them in the interwebs, but their non Twilight movies don’t do very well. Pattinson’s do a little better than Stewart’s but he’s doing studio films. Water for Elephants is based on a bestseller so box office should be higher. I’m basing this on his domestic numbers.
      I say all this to say that the social media effect is null and void. There is definitely room for something like a Snow White in the summer that will draw a large young female audience. The question is, which one will be the victor in actually going to camera?

      • lulu

        ive always believed that just because an actor is in a movie with a large fanbase doesn’t mean that fanbase will flock to see all their movies. having chris or kristen in a movie will not guarantee that the twifans or thor fans will go see snow white. with water for elephants the movie that just came out with pattinson. it wasn’t the pattinson fans that made that movie a hit. fox was smart. water for elephants had a small budget, and they promoted the movie to all ages. its rumored that both snow whites are going to have a budget that is over 100 million, and i’m not sure who their target audience will be. i thought kids and family, but after reading the synopsis im not sure.

  • Lame Duck

    Good read.

  • Rovena

    I hope they cast famous comedians as the seven dwarves in all the films!

  • Lame Duck

    We should expect the following comedians to play the dwarves….hahaha jus kidding! But im sure that troll will pop up here spewing that nonsense any minute now :(

  • oddandy

    The Universal movie obviously has the best chance at success. Tarsem Singh isn’t known for his ability to shoot a movie quickly. Also factor in Relativity not having the resources and money that a major like Universal studios brings to the table. Kristen Stewart has never tried a big studio film of this magnitude since her Twilight fame began. She may very well bring big box office in an easily accessible family film. You also have to look at Chris “Thor” Hemsworth who is bound to become more famous by next year. Charlize Theron brings her own fanbase and maybe a few more adults. Sam Claflin is the oddity here, but the three leads are strong enough that he doesn’t have to be an option. I see Relativity backing out and making an announcement soon. If this movie does a half a billion next summer get ready for more Snow Whites.

  • elikias

    Fun read. I see a number of different ways that this situation could develop other than a simple prisoner’s dilemma. I feel like as with the Deep Impact vs. Armageddon and the Volcano vs. Dante’s Peak example which you mentioned, the key difference between them was quality. One of each pair was a mess, and the other was mildly acceptable to movie going audiences. In this case, if both films go ahead with production then next May the reviews will start rolling in, and one of these movies will be the deemed the clear winner. One of them will be lauded and the other will be panned. People will only want to see one, so they’ll pick the better reviewed film, and the other will fall into obscurity.

    •!/colliderbrendan Brendan Bettinger

      I definitely simplify — perhaps too much.

      The scenario you lay out is definitely possible. I came to the conclusion it is not the most likely. We don’t know that one will be significantly better than the other. And it remains to be seen if people will “pick the better reviewed film.”

  • win-win

    So Relativity got their script first and had the first June release date but they should back off because Universal came along to challenge them with an earlier release date? That’s all your got after that LONG essay and analysis? You didn’t really give a good reason as to why Universal should win this game. You didn’t question if moving the release date up to June 1, 2012 Universal will have a poorer product rushing post production. If we follow your game of chicken, Relativity should go full speed ahead without backing off. They get $50 Million Domestic, double overseas, then DVD and t.v. rights.

    •!/colliderbrendan Brendan Bettinger

      You were right!

  • Terri

    I’m seeing the Kristen Stewart version. She looks like more Snow White, and Julia Roberts is annoying to watch

  • ken

    i read over at boxoffice mojo someone posted that now that universal and relativity have their movies coming out at the same time it can blow the budget up on both movies, and the quality of the movie can be effected. i thought universal was smart in putting their movie out in december, and not going up against the summer blockbusters. i’m sorry i don’t see snow white as a blockbuster contender. i also don’t believe that just because of the cast of them movie will mean that it will be successful. yes, chris is hot right now, but that’s because of thor not because of him.

    • ken

      mistake….i meant that i don’t see snow white as a summer blockbuster contender.

  • oddandy

    There are some unanswered questions I have. What does each movie cost? 3D? Will the directors stay on board if they are forced into tighter scheduling?

  • nina

    I think now that Universal’s Snow White is going for a summer release instead of a holiday-family-friendly release, making the huntsman all hot and young was a smart choice over making him so pepaw figure. Universal is obviously sexing theirs up more with hot new actors and Charlize for the Queen for basic summer release fare.

    • lulu

      that could backfire on them though. “sexing” up a fairy tale that is supposed to appeal to kids and family. look at what happened with little red riding hood.

      • nina

        That was a bit of hyperbole on my part. What I mean by “sexed” up was the huntsman was suppossed to be a dad figure, ala Viggo Mortensen where it’s clear they wont’ end up together. Now making the huntsman younger and with Chris Helmsworth? Well, it does a couple things, include make the movie more attractive action wise to male viewers who weren’t really excited about seeing that twilight chick do a fairy tale. It’s not exactly sexing it up with Chris Helmsworth and Stewart, but making the dynamics more sexy and young and more generally appealing for summer audiences.

  • anne

    I’d go with a third option. Relativity should move their release to Nov/Dec 2012, a date that fits this genre of film better anyway. A Julia Roberts led 3D fairy tale opening during holiday season would clean up. Universal should’ve left their film where it was. There was enough time between the two releases that both could’ve prospered, and imo, first or last isn’t as important as the time of year. For this, I think holiday season would trump summer.

    What’s most puzzling to me in all of this is why any of these actors want to sign on. It seems clear that one way or another, there’s going to be more release date shuffling, they’re all going to be filming in a rush, the budgets are going to blow up, and the Snow White wars are quickly becoming a running joke in the media. All of these actors have better options. Jackman, Depp, Fassbender, Viggo, Hardy, and Jolie were the smart ones for dodging this bullet.

  • Mello

    Universal did a calculated risk based in their experience with Fast 5, that finished production in late of Nov 2010 and was released in May 2011. 2D movies have sn easy pos-production, in general. So they know that it is possible to do it, without lost quality. The December release could be also a mess, with Kristen Stewart having to promote also Breaking Dawn II, at the same time. I think they had chosen the December date for marketing and time of the year reasons, not because pos-production time.
    Relativity has more difficult with the 3D option, in the production and pos-production, for obvious reasons, with one more factor, the slow pass of pos-production for what their director is famous. An early date for them would really affect the quality.
    Universal did a bold but not too risk decision, in my point of view.
    (((Sorry for English but it is not my first language and I am also posting through the Galaxy Pad. It is very difficult to make spell check before post it.)))

  • Jim

    Why do people automatically think that Chris Hemsworth equals Box-Office draw? THOR is a much loved comic book character with an already built in fan base, somehow i don’t see fans of THOR flocking to see Snow White. Kristen Stewart has no Box-Office draw outside of Twilight, Charlize Theron? What was her last fiscal success?. It seems to me as though Universal are banking on this being a huge Box Office hit, certainly given the budget, when infact i can see them ending up with egg on their faces. Say what you want about Julia Roberts, but the woman has fans who support her movies, BIG. If i was put on the spot i’d say that Relativity will win out when it’s all said and done. I won’t see either btw LOL

  • helen

    Julia Roberts is a big BO draw..oh okaaayyyy..thats why her last few movies have made so much money..

  • Nick

    This is actually all rather stupid. I’m so tired of this Hollywood marketing BS, one of them needs to swerve and now. But I doubt they will, it’s just another step towards everything being the same movie. I mean seriously, when I saw Pirates 4 the trailers for Conan and Immortals were played back to back and the entire theatre was murmuring “didn’t we just watch this” when the Immortals trailer came on. Let’s focus on making movies that are actually good please?

  • amy

    Julia Robert’s box office draw is dwindling. I was one of the few who paid to see Eat, Pray, Love and it was awful! So, suffice to say I’m not paying to see Julia’s Snow White, plus I ready to see Charlize on the big screen again. Kristen is interesting to watch and I was intrigued enough to see the Huntsman on her alone, but now that they’ve added Chris Hemsworth-I’m way in. Critics loved Chris’ performance in Thor and he’s fanbase is getting huge. Then adding Sam Caflin as the prince was the cherry topper. He’s in Pirates with Depp so even though he’s a newcomer by the time Snow White and the Huntsman comes out viewers will want to see him also. Hate the politics of it all, but I’m pulling for Universal!

    • lulu

      eat, pray, love grossed over 200 million on an 80 million budget. plus chris has a fanbase because of thor. that does mean that those fanboys are going to go watch snow white.

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  • Tracy

    Brilliant read Brendan – thanks!

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  • pat

    man, this was a fascinating read. i’d love to see more articles like this on the site. definitely something unique compared to other blog sites as well as viewing films from a different perspective than what we’re used to seeing.

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