Splinterlands - How rare are black foils really?

I have seen a few conversations in discord and elsewhere that have people thinking a black foil will be more regular than a max regular or gold foil, I find that hard to believe so I thought I would run the numbers - sorry going to be a few tables of figures here.

So lets start with the basics, ignoring starter packs as there are no gold or black foils.

Total Packs & Cards

Pack Type	Packs Available	Cards per Pack	Total Cards
Standard	5,000,000	5	25,000,000
Alchemy	1,000,000	5	5,000,000
Legendary	500,000	5	2,500,000
TOTAL	6,500,000	—	32,500,000

If we completely sell out we will have 32,500,000 cards in circulation plus additional commons and rare regular foils from starters.

But how do those 32.5 million cards break down by foil?

Expected Black Foil Cards

Pack Type	Total Cards	Black Foil Rate	Expected Black Foils
Standard	25,000,000	0.025%	6,250
Alchemy	5,000,000	0.25%	12,500
Legendary	2,500,000	0.125%	3,125
TOTAL	32,500,000	—	21,875

Expected Gold Foil Cards

Lets break this one down:
Standard
25,000,000 cards
2% Gold Foil chance
Expected Gold Foils = 500,000

Alchemy
Guaranteed 1 Gold Foil per pack = 1,000,000 Gold Foils
But 0.25% of the cards will be Black Foils = 12,500 Black Foils which replace Gold Foils
Adjusted Gold Foils = 987,500 Gold Foils
Remaining cards expected Gold Foils = 4,000,000 * 2% = 80,000
Expected Gold Foils in Alchemy Packs = 1,067,500

Legendary
2,000,000 cards
2% Gold Foil chance
Expected Gold Foils = 50,000

Which gives us a total of 1,617,500 Gold Foils and we can assume everything remaining is Regular Foil.

Foil Type	Expected Total Cards
Regular Foil	30,860,625
Gold Foil	1,617,500
Black Foil	21,875
Total	32,500,000

How do those Foils Break down by rarity?
Assuming evenly split across rarity

Rarity	%	Regular Foil	Gold Foil	Black Foil	Total
Common	75.2%	23,207,188	1,216,360	16,452	24,440,000
Rare	20%	6,172,125	323,500	4,375	6,500,000
Epic	4%	1,234,425	64,700	875	1,300,000
Legendary	0.8%	246,885	12,940	175	260,000
Total	100%	30,860,625	1,617,500	21,875	32,500,000

So how many max CC cards will there be, if we sell out and combine all cards?

Rarity	Regular Foil	Gold Foil	Black Foil
Common	58,018	32,008	16,452
Rare	53,675	14,680	4,375
Epic	26,838	6,459	875
Legendary	22,446	3,230	175
Total	160,977	56,376	21,875

Obviously these numbers can be affected by potions but even then... and yes we may see a number of black foils on the market that outweigh the number of max cc common cards but that is down to common cards not being combined over the number of black foils being more available, it should be easier to combine 400 common cards than find a black foil.

Please check my math but it feels like some people are under estimating the value of a Black Foil.