I opened 250 Materiel Crates 3.0 in FFXIV

Full results below--I kept a spreadsheet.

Did you miss out on a minion or mount from ARR, Heavensward, or Stormblood and can't stomach the price on the market board? Don't have the patience or skill to complete the content that drops the minion or mount? Maybe you're the gambling type? Materiel Containers might interest you. You need 20,000 Grand Company Seals and the prerequisite Grand Company level to buy one, and the amount you can buy is limited only by the number of seals you have.

What is a Grand Company?

Your Grand Company is the faction you chose very early in the ARR main story, and is either the Twin Adder in Gridania, the Immortal Flames in Ul'dah, or the Maelstrom in Limsa Lominsa. It's possible to change your Grand Company as well provided you are high enough rank and have enough seals. You keep your rank from your previous Grand Company and any seals, but they don't transfer over. You will also be unable to wear any Grand Company-specific armor, including glamours. But if you change back to your old Grand Company, you will regain the seals and rank you had left behind.

How to increase your Grand Company Rank

Not all Grand Company rewards are available right away. You'll need to rank up in a variety of ways to reach Captain rank, where all available rewards are unlocked. You'll need to finish a class hunting log, a few low-level dungeons, and level your squadron up and have them complete several objectives. Leveling the squadron and balancing their attributes to complete missions is time-consuming. I recommend starting that early on.

How to get Grand Company Seals

Grand Company seals are acquired by trading in unwanted gear at the company headquarters or accrued by completing FATEs, your Grand Company Challenge Log, and through some Duty Roulette activites. You can also send your retainers out on Quick Exploration ventures, where they will often return with a piece of gear. Quick Exploration Ventures only take an hour to complete, so if you send your retainers out regularly, you can get a lot of extra gear to trade for very little effort. You can also trade other types of FFXIV in-game currency for gear, like Hunt Nuts and Allagan Tomestones of Poetics, which you can then turn in for seals. (Finally! Something to do with your Poetics!)

If you want to farm seals from dungeon drops, a max-level character can solo an unsynced dungeon like Shisui of the Violet Tides from Stormblood in a matter of minutes for roughly 12,000 seals gained from trading in gear.

Dawntrail gear pieces are worth over 2000 seals each.

About Materiel containers

Materiel containers can be bought at Captain Level from the Grand Company Quartermaster for 20,000 seals each. The containers come in two versions: 3.0 and 4.0. The 3.0 containers have a single minion or mount from ARR or Heavensward and the 4.0 containers have a single minion or mount from Stormblood. The container loot table is 85 items for the 3.0 container, and 55 for the 4.0 container. The rarity of the original item seems to influence its drop rate from the sample size I collected, but a larger sample size is probably needed to make any definitive conclusions.

What drops did I get?

In the graphic below, the value column represents the number of drops for a given minion. The frequency represents how many minions had the same drop rate.

Out of the 250 materiel containers, the most frequent drop was the Clockwork Barrow with 9 drops. The next most frequent, with 6 drops each, were the Dust Bunny and the Hunting Hawk.

The least frequent, with zero drops, were the Atrophied Atomos, the Demon Brick, Gestahl, and the Night Pegasus Whistle. The Demon Brick is a frequent drop from a chest in the Amdapor Keep dungeon. It's really easy to get, so I can guess that zero drops here may just a product of the small sample size. Gestahl was previously only acquirable through a level 55 Fishing Retainer venture. This requires having the Fisher class leveled yourself to at least level 55 to even have a chance at getting the minion.

The Night Pegasus Whistle unlocks the Black Pegasus mount. The Whistle only drops randomly from a piece of the Accursed Hoard treasure sack which only drops from floors 151-200 of Palace of the Dead, a roguelike dungeon with 200 floors. The Accursed Hoard is a hidden treasure that becomes visible from using an item or miraculously standing on its exact location. Soloing the dungeon to floor 200 will get you the Necromancer title. Personally, I reached floor 100 solo on Machinist and that was enough for me. I don't have a PotD group going, so I was hoping to get that whistle!

Overall, I was able to collect a lot of minions that I didn't have before. The Fat Cat is a great one, and the Wind-Up Estinien fights along you when battling on the world map. I might keep buying these 3.0 containers in the hopes of getting that Whistle, but honestly just buying the mount from the market board with the gil that I earn from selling coke might be the easier choice.