The only useful thing you are guaranteed to get from crates is gems - so that's what I buy them for.

Don't do crown crates, kids. Stay in school.

I swear the good stuff is programmed to drop for lower cp characters. The "hook" to pull the new players. But us veterns get the shaft.
I had two buddys start playing, they both bought a four pack of crates on day two, each got a mount, one was the apex Skeletal fire wolf.
These two still get mounts every 4 pack they open. Ive witnessed it. Ive bought maybe 150+ crates never one mount.

Bought 15 storm crates, prayed to Hircine in his Hunting Grounds and got storm camel. Worst loot ever, I hate camels and can't even use it (I feel sick just watсhing how they run!). I'd like to change it even for one gem!
Promised to feed Pacrooti to the pack.
In next 15 crates got storm wolf, storm guar, second storm camel, clouded sence, bear-dog and imperial mananaut cap
From 15 xanmeer crates got lizard horse and trap (one I wanted most).

Usually my luck is much worse and I expect just gems.
Maybe I should always have werewolf pack near when opening crates...

I've purchased crown crates for 1500 crowns a couple of times. I got the Lightning Atronach horse the first time and got nothing spectacular the second time. From the free crown crate events, I've gotten a couple of Guar mounts and the Black Camel. So from the Gem collecting, I purchased the Ice Wolf mount. I wish the mounts were sold and rotated in the crown store. I'd readily buy!

The first option is closest to my experience.

I have almost always gotten a few things I am happy with. But I don't go into them with the hope of getting a particular thing.

The only time I have been disappointed was when I bought four crates and three contained the nix-hound, which I already had anyway.

Just don't support it

So, has Baron Munchausen shown up on this thread yet? You know, that one person who will claim to have gotten a Radiant Apex mount that they don’t want from a free Crown crate?

I don't know if it's my luck that is terrible or what, but my average reward for a crate is around 5 to 8 gems each. The more crate you open of a single type, the more gems you get, as you will inevitably unlock things you already have. So you start with a yield of 4-5 gems each, and then up to 10 or more, for an average of 8 if you open about 50 crates. The yield might increase if you open more crates or already own some of the rewards, but this isn't some grand calculation I made with big data, just my own experience with my own crates.

The first crate give you a ton of useless potions and buff items, some costumes you'll never use (I still resent the Winterborns costume, that are simply horrible), and then maybe a decent costume or a non apex mount. And if you keep opening them, you'll find the same sh*tty items and costumes and mounts. Items can be converted to gems. Costumes and mounts are auto converted to gems, which slightly increases the gem yield.

But if you're counting on your luck and that alone to get what you want, then don't. If you really want some apex mount, you'll have to get ready to spend a lot. back when Wild Hunt crates were first introduced, I really wanted the wild hunt horse. And I got it. After opening 49 crates. Mind you, I didn't get the horse in a crate, I did just get pretty much every unlock from every lower tiers several times, and thus enough gems to buy the horse. I knew I'd have to spend big on it, and my situation then allowed me to do so, but I vowed to never do that again. That was a total of 16 500 crown, the price of manor house, which by themselves are already way overpriced. For a mount. The only difference between being me and being crazy is that I knew I was doing something stupid.

Recently I bought some crates to top the gems I had from the free crates so I could get the lizard bear. I had counted I'd need 15 crates with my usual luck, and I actually needed 14. Small wonders. And on those 15 crates, Pacrooti gave me a bonus card ONCE. Just once.

But of course, there was also this one free scalecaller crate that gave me the galvanic horse. Luck does happen. Just never count on it, and never take it for granted. Most of the time, you get shafted. If you really want something, make sure you are ready to pay way more than you first thought. Or maybe, start not wanting it.

Opened 49 storm crates. Got 2 apex mounts and enough gems to bought lightning guar I actually wanted. However more I spent less good stuff I get from the crates. It does seem like there is some kind of algorithm at work here.
I probably will abstain from buying crates in future, since in the end you get only disappointment and shame for supporting these kinds of business practices.

I open 4 crates a month and never fail to get at least one mount. Funnily enough I got the golden eyes guar this time, not a fan but it's one for my ever growing collection. Think I've only got 1 apex in the past year though.

Pretty much had to get just about everything I actually wanted with gems

Working as intended

I've gotten the occasional one-shot nice thing from free crates, and mostly junk - I don't complain, cuz the crates are free, but I will never voluntarily pay money for a crate - I don't even spend my "free" (they're not really free) crowns on crates

Bought 30 crates with ingame gold, thankfully, and the only thing worth it was the atro transformation (hoping it was longer than 3 mins tho, 10 mins at least would be awesome), also got a lot of crap so I finally got enough to buy one of the storm atro mounts.