There’s a lot of discussion about Premium vs Normal packs in dusting, and quite a lot of kinda illogical discussion about it. I think a common mistake is that some people assume that the utility received from a card is proportional to it’s dust value — which is actually quite obviously incorrect. If we were looking purely at dust values, the normal packs are obviously more efficient (since you have a 10% chance to get a free upgrade from silver to gold; whereas premium packs have no such chance). Cards also have a very clear diminishing return: if you have 90 unique commons then the 91st is absolutely worthless to you (in fact, commons are almost always worthless). This makes the problem complex, but still workable.

Let’s say you were permitted non-integer dust values, with arbitrary precision — and your goal was to win the Fantasy Challenge (as in, you wanted to open enough packs to win). Let’s also assume that instead of golds appearing in normal packs wasn’t a 10% roll, but instead each normal pack had a 0.9 silver card and 0.1 gold card. Since a premium pack costs 50 dust, and a normal pack costs you 10 dust you have the following equations:

[1] premium pack= 4 silver + 1 gold

[2] 5x normal pack = 20 commons + 4.5 silvers + 0.5 gold

[3] 1 common = 1 dust, so 20 commons = 20 dust = 2 normal packs.

Statement 2 becomes a geometric sequence as we dust the commons and buy more normal packs, which ultimately converges at:

5x normal packs = 7.5 silvers + 0.83333 gold

so would you rather have 4 silvers + 1 gold (from the premium pack) or 7.5 silvers and 0.833333 gold? Let’s re-arrange and simply this a bit:

Would you rather have 1 gold or 21 silvers? Even this is a super confusing choice not one you can make immediately. This situation led me to think about the problem in another way: from what we want to end up with.

Let’s say you wanted to have 4 of 5 for your top 6 teams, 3 out of 5 for teams 7–12 and 2 out of 5 for the remaining 6 teams. You want them all silver, but at least 1 gold per team. Any commons you dust; and you only keep the best silver you have for a player.

To solve this I wrote a simple Monte Carlo, running the simulation 10⁴ times for both premium strategies and non-premium strategies (although a hybrid strategy might exist). Here’s the outcome: