>>546182461
>>546182718
>>546180552
I awoke. First of all, I miscalculated the free shit you get from atlas. The last 5 entries are just stickers. So I had to add them back to the final count.
Second, for hitting lvl 40 you get four vouchers - one courier, one pig, two prismatic (equivalent to one set's final style). I deduct those from the recipes. Then, I consider one voucher = 6 rares, as per trade-up. In reality it's gonna take more than that because they probably have an equal chance of appearing, and you need 10 (minus the free 2) prismatic vouchers as opposed to 4 courier and 4 pig ones (again, minus the free ones) while they have a 33% chance of appearing (presumably) so you're gonna have to do a lot of recipe crafting (3 materials of same type for same rarity). (Although if you can't get back any of the ones you've crafted then I'm guessing putting in for example 2 pig vouchers and 2 courier vouchers would always give you the prismatic voucher. Maybe.) I'm not dwelving into calculations this deep though, I only want to present the final count. There's gonna be a lot of crafting necessary to get the final recipes anyway so whatever the actual number of necessary games will be, you can probably increase by like 20% to temper expectations.

Anyway - the final count, assuming 1 voucher = 6 rares, seems to be:
>259 commons
>566 uncommons
>169 rares xd