Grinding: What am I missing?

(If this is in the wrong forum, I apologize.)
I've been searching for Orbs of Alchemy for a while, but haven't been finding anything. What I wanted to ask is what am I supposed to be expecting from grinding, days (or possibly more?) of work based on pure luck in finding loot? Or is there some kind of strategy I'm not aware of...?
Usually grinding is related to leveling up, a progression. However it seems that this is based purely on chance (and a small one at that) and it's leaving me confused. I've got no idea how to form a plan for this, so I'm asking for advice from people who have done all of this before.

Are you grinding for orbs? Then this is a "how do I find orbs" thread, which is very common. My prepared answer, including links to data sets and other advice is here. If you're grinding for something else, then you might want to read some of the other FAQs on that page. I hope that this helps.

I have a farming strategy that works everytime.
First: find an arcade gate -it's preferred to go tier 3- that has a random floor on the 2nd or 3rd floor
Second: speedrun the first floor and go to the next -or after next- floor and pray for a vault (sparks/fire crystals/orbs) or a grave (crowns/heat)
Third: after you finish the floor replay the gate

Okay, so I too have been grinding orbs for a while now (all of us, apparently).
This is test for ELITE ORBS only.
Here's my case:
I wasn't online for awhile say, 1-2 weeks, but I started grinding even before*. I happen to have 2 Elite orbs and I was grinding for a 3rd one (again) but figured I have enough crowns to buy from the Auction House. So, bought my third orb, crafted my 4* gear.
(*Note: I was grinding for a third one even before my period of absence.)
Long story short, I depleted all my supply of orbs and I started to do Missions & Arcade and lo! Behold! It dropped 2 elite orbs on the first 30 minutes of my runs! (One was a normal elite arcade run and one was at IMF levels), so the idea got stuck to my head..
[Add. info: If you'll see though, there are 2 kinds of orbs: the tradable one (bought off the Supply Depot) & the untradable one (for grinding). They are separated from your inventory.]
There is obviously no limit to stacking orbs but perhaps once you reach a handful amount of orbs the drop rate decreases? I'm not really sure.
It may just be a out of sheer luck. Who knows? :D

Yes, your experience might just be "luck". To tease out a signal from this noise, we'd need a lot more data. But thanks for sharing.

I kind of get the same sort of experience as Trickish. Typically when I get back into the game after a long time, my orb drop rates seem to be a lot higher than usual... or at least I seem to get a whole lot of drops during that first day back in. To be honest, it really is just all RNG. I don't think Grey Havens (or even OOO back then) would have bothered to code in some sort of increased drop rate at any point. Pretty sure they just have some fixed chance and stuck with it.
"pretty sure"" is useless information. Get some real facts.

@Monsieur Bunduru
If you want to disprove every new theory about orbs dropping then that'd be swell...
I'll even provide you with some baseless claims to debunk:
Orbs drop more frequently on Tuesdays
Orbs drop less frequently when a blue player is in the party
It's possible to find 5* orbs in stratum 3
Have fun with endless statistics!
What rank are you? This will dictate where you grind.
In Spiral Knights, you should generally try to grind the places with the most crowns or rarities. That way if you are unlucky and don't receive Orbs of Alchemy from these levels, you still should have enough crowns to buy some.
For example if you grind at Royal Jelly Palace, you have the chance to find 3* and 4* orbs. If you're not lucky with the loot boxes, you will have enough crowns at that point to buy some.
You will really want to grind boss levels that give lots of crowns as well as have a lot of prize boxes. The best in T2 is Jelly King and best in T3 is Vanaduke.
TLDR; Grind levels that give lots of crowns and just buy orbs yourself. If you are lucky the levels should give orbs.
This strategy will be staple throughout most of the game.