Oh boy, one of these!

Let's look at 4chan's growth over the years, taken from my post commemorating our billionth post: https://www.4chan.org/news?all#106

In 2008, 4chan was accessed by 30 million unique visitors, and served 2.4 billion pageviews.
In 2009, 4chan was accessed by 60 million unique visitors, and served 4.4 billion pageviews.
In 2010, 4chan was accessed by 130 million unique visitors, and served 7.5 billion pageviews.
In 2011, 4chan was accessed by 190 million unique visitors, and served 7 billion pageviews.

And I'll throw in 2012 and 2013 YTD for good measure:

In 2012, 4chan was accessed by 229 million unique visitors, and served 7.2 billion pageviews.
In 2013 YTD, 4chan has been accessed by 222 million unique visitors, and served 5.8 billion pageviews. (Note that pageviews have gone down considerably due to us migrating a lot of page refreshes over to our read-only JSON API.)

Despite growing considerably over the years, the site has historically only made money in two ways: donations and advertising. And it should be noted that we haven't accepted a single penny in donations since the fall of 2005. So basically just advertising. I've ranted about why I hate donations on 4chan in the past, but it boils down to my belief that ongoing donations (a la Wikipedia's fundraisers) are unsustainable for large websites, and their ambiguous goal of "keeping the site alive" creates an implicit and non-mutual understanding of what a user should expect in return for their donation. The last fundraiser we did (in 2005) had a very specific goal of raising funds to purchase servers, colocate them, and pay for one year of hosting -- and so I felt more comfortable with it. But make no mistake, I've always hated donations, which is why I've chosen not to accept them for the past 8 years.

4chan's ad inventory consists of three ad units per page. All three unit sizes are deprecated by IAB standards (728x90 and 468x60 have been phased out by most every major publisher, and are no longer recommended), and none appear in the content. They're at the top and bottom of the page, where users spend little time. Adding them inside of threads would probably increase click-thrus and thus command a higher price, but I don't like the idea of scrolling through ads while I browse.

Not only is 4chan's inventory not lucrative from a technical standpoint, but it's primarily not lucrative to 99% of advertisers due to the site being the epitome of "not brand safe." It's both all user-generated content, and has tons of adult content, which means we've always struggled to find companies willing to advertise (our longest running advertiser is a Japanese import toy company -- hardly a Unilever or Macy's). We can't use ad networks or exchanges, and what little direct inbound we get comes from small advertisers with low ad spend. Which is precisely why we introduced the self-serve advertisements you mentioned, but only back in July 2013. If you take a look at the CPMs we sell ads at, you'll find we charge well below market, and in fact most of the ads you see on the site were sold at a fraction of a cent CPM (or sometimes for free!). Not to mention the novelty factor wore off quickly and self-serve sales plummeted, but I digress...

You also mention 4chan "heavily relies on the freemium model," and reference our 4chan Passes. 4chan Passes were introduced in September 2012, a little more than a year ago. They've certainly helped right the ship, but haven't exactly sold like gangbusters. This is for a few reasons, but primarily because they do very little -- their sole purpose is to remove CAPTCHA. Why? Because as explained in their announcement (https://www.4chan.org/news?all#109) and subsequent posts, I have an intense distaste in the idea of fragmenting the community into "those who pay," and "those who don't" (a la Reddit Gold), and so 4chan Passes do one very specific thing, and nothing more. Which is reflected in their modest sales numbers.

Which leads us to what probably the main reason 4chan is a shitty business: because I choose for it to be one. If I'd decided to rape 4chan for all it was worth, as many would have, I'd probably be sitting on a pretty pile money from now, but as someone who has browsed the site daily for the past 10 years, the thought of seeing it littered with ads and other garbage makes my stomach sick. If that means scraping by for another 10 years, so be it.

I wrote this more for myself than you, but I appreciate your skepticism (and I find it extremely amusing).