After watching this Vsauce video on youtube about the Newton-Pepys problem regarding dice rolling probabilities, I got to thinking about pack odds with pulling diamonds. So if you're hellbent on sinking 37,500 stubs down the toilet, you're better off buying 25 standard packs instead of the total 5 headliner packs available to each person.
Scenario A is like rolling five 11-sided dice (5 headliner packs with 1:10 odds of a diamond)
Solution: 1-(10/11)^5= 37.9% chance of pulling a diamond
Scenario B is like rolling twenty five 51-sided dice (25 standard packs with 1:50 odds of a diamond)
Solution: 1-(50/51)^25= 39% chance of pulling a diamond plus a gold or better card in the 20 bundle
The math is better explained in this Wikipedia article, but there is essentially a 1.1% higher chance of pulling at least a single diamond from 25 standard packs over 5 headliner packs