u/IkBenDood

With 30 days left (May 27–June 25) and 1 free box per day (assuming you focus at least 60 minutes a day):

Direct collection:

• 42% chance to collect all 11 items (1 cake + 5 macarons + 5 cupcakes) directly

With Stamp System:

• ~99% chance to complete the collection using stamps from duplicates
• You'll earn ~248 stamps on average from duplicate items
• This is enough to buy 3 missing macarons/cupcakes (3 × 80 = 240 stamps) or the cake + 1 item (150 + 80 = 230 stamps)

Most Common Scenarios :

Missing Items	Probability	Stamps Needed	Can You Buy It?
Nothing	42%	0	Obvioulsy
Only cake	15.5%	150	Yes
Only 1 macaron	13.5%	80	Yes
Only 1 cupcake	13.6%	80	Yes
Cake + 1 item	8%	230	Yes
2 non-cake items	3%	160	Yes

Conclusion : You almost certainly don't need to buy extra boxes. The stamp system from duplicates will save us all from wasting gems and coins. Again, if you want to go on!

Edit : For the unlucky few (~1% chance), you might miss the cake + 2 other items. In this scenario:

• You need 310+ stamps (150 for cake + 80×2 for the others)
• But with only 8 collected items from 30 boxes, you have ~22 duplicates → ~264 stamps max (22 × 12)
• 264 < 310, so you can't buy the missing items