The value of a Hearthstone pack

Hi! Recently I’ve been wondering about one thing. How much value can you expect from a single Hearthstone pack? There are many quick answers to that. If you are unlucky and all the cards (one rare and four commons) in the pack are already in your collection then you get the proverbial fourtyduster, the bane of pack openers everywhere. On the other hand, you might just hit the jackpot . Obviously, the value depends on luck. But since there is no such thing as luck, let’s talk statistics. According to some nice people who tracked opening of hundreds of packs and recorded the results , the expected amount of dust you get when you disenchant all cards in a pack is 108.
This, however, assumes you disenchant all cards you get. And while that might be true when you are opening your thousandth pack, the situation is much different when you are on your first. In the first pack, all the cards are new, so you are not dusting anything. As a consequence, each card has the value of dust required to craft it. In this situation, even the lamest fourtyduster is worth 180 dust. ( edit: actually, more than that. The average fourtyduster with four different commons is worth 260 dust, while the most lame and dastardly one with four copies of a single common is only 190 dust. Thank to comments for pointing it out
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So the average value of the pack is dependent on the size of your collection and it decreases as the number of packs increases. The remaining question is: How?

To satisfy my curiosity, I have mopped out a quick analysis. Here it is. Let’s say we are trying to obtain a full collection and we are opening the packs with that in mind. That means we are automatically dusting all golden cards and all multiples (we don’t need to dust them immediately, but we hoard them with the sole purpose to dust later). On the other hand, we are not crafting anything. At least, not until we decide to stop buying packs and craft the rest of the collection from the dust we had. The value of each pack is then composed of two parts. The first part is the value of cards that are not yet in our collection. These contribute with their full value and also increase the value of our collection. The second part is the value of the dust we get from disenchanting golden cards and multiples.
The ratio between these two parts depends on the current size of our collection and decreases over time. If you now run the numbers and plot the results, you get this:

There are two kinds of values shown in this image. The effective dust per pack (dpp) is the total amount of dust the opened pack contributes. Cards not yet in your collection contribute the full value, the remaining cards contribute their disenchant dust value. The total disenchant values are represented represented by the disenchant dpp lines.