Thanks for posting the math on this!

It's worth noting that v4.2's Hyper Ultimate Variety Pack sits in between the two options you analyzed in terms of efficiency.

**Per 10,000 Theonite:**
Premiere 10+1 Vouchers: 110 Relics (as ten 10+1 vouchers), with an average yield of ...

- 82
**Bronze** fighters
- 23.2
**Silver** fighters
~~8.2~~ **4.2** **Gold** fighters
- 0.6
**Diamond** fighters
- 4400 relic shards

Hyper Ultimate Variety Pack: 154 Relics (as fourteen 10+1 vouchers), with an average yield of ...

- 114.8
**Bronze** fighters
- 32.48
**Silver** fighters
~~11.48~~ **5.88** **Gold** fighters
- 0.84
**Diamond** fighters
- 6160 relic shards
**Guaranteed** exactly 11 fighters for each character, with at least one Silver-or-better for each

Canopy Coins: 230 Premiere relics (6.25 purchases of 1,840,000 coins = 11,500,000 coins), with an average yield of ...

- 188.6
**Bronze** fighters
- 32.2
**Silver** fighters
- 8.05
**Gold** fighters
- 1.15
**Diamond** fighters
- 9200 relic shards

~~The Hyper Pack gives slightly more natural Gold Fighters for your Theonite on average, but coin purchases more than make up for it with the sheer ~~*volume* of natural-Bronze fodder and relic shards they offer -- both in terms of potential skill points and eventual Gold-to-Diamond upgrade materials. 74 Bronzes and the three extra Silver Relics they give you can be melted down into *four* Golds, compared to the three-ish extra nat-Golds the Hyper Pack offers. Raising even half of those Bronzes to level 30 also gives more skill points than raising three Golds to 50, for much less total experience required.
EDIT: I originally read the 0.82 probability-per-relic for Bronzes as 0.82 probability-per-10+1 for Golds, leading to some incorrect numbers and conclusions. Don't maths while tired, kids. :^P