The chances of a Phase 2 legendary if you buy less than the number for a guarantee
Today's exciting news is two-fold. The airdrop cards for Phase 2 have been revealed! And they look dope.
The other news is the drop rate and the number of packs needed for a guaranteed legendary. Each pack will have a 0.33% chance of dropping each airdrop, with one copy of each being guaranteed for every 300 packs you buy. Although GF cards won't be guaranteed ever, the chance of getting one will be 4% for each cards you receive.
What I want to focus on here, is what are the chances of getting at least one of the airdrop cards if you buy less than 300 packs? Because there are two cards here, and the numbers are different than in previous sets, the math is a little different.
Below is a graph of your chance of getting at least one copy of one of the 2 airdrop cards as a function of how many packs you've bought. I've put in a horizontal line for when your chance crosses 50% (around 105 packs). The near-vertical increase at the end shows the chances going up as soon as you hit the magical 300 guarantee. Even this is somewhat misleading as to its true value, as when you hit 300, you go from a 20% of getting none to a 100% chance of getting 2, one of each.
The main takeaway is that the chances of getting one are not great unless you're buying >200 packs. Even at 299 packs, you still have ~20% chance of getting no airdrops.
As with the pre-sale, this seems to be a case of go big, go home, or hope you get lucky. Buying a few packs is probably the worst way to go, as you're paying a voucher +$4 and you'll likely get no airdrops, when you could get exactly the same thing in a few weeks for just $4 with no voucher needed. And if you are already buying a decent number (like 100-200), you should really consider buying up to 300 to guarantee not one, but two airdrop cards.