A Random Comment

[Jonny_Tapas]

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If I can somewhat consistently fail something with a 70% chance of success 8 times in a row, essentially meaning the 30% of failure won out, shouldn't it be possible that I successfully do something with a 30% success chance 8 times in a row? As anyone who plays this game will tell, that will never happen... ever.

This statement is false.

As many times as I've been enraged about loosing lots of gil to odds that should have been in my favor... I've also had many many wins. Unfortunately what you remember is highly effected by how much it emotionally effected you.

You are more likely to remember loosing a very large portion of gil by blowing up a 90% synth

... 3 times in a row.

You are more likely to forget hitting 6 HQ copper ingots in a row at below 12% because the copper ingots are emotionally insignificant.

As many times as I've complained about mining 3 for 18 at 70% or something ridiculous like that...

I do have a very specific memory of mining 9 HQ umbral rocks in a row at only 32%.
I previously posted this video of me teleporting to a zone and getting an ATMA on my first fate: http://www.twitch.tv/jonny_tapas/c/4443531

The wins happen and they happen just as often (or just as rarely) as the losses do.

But the wins don't piss you off and send you raging to the forums. (Maybe not you specifically but the community in general.)

[Felessan]

Item Synthesis? -20
Materia Melding? -40
Atma Drop? -60

There is no adjustment for any of listed activities, it's just a negative experience overwhelms positive one by significant margin. A number of example here show RNG in FF14 are "fair" and no adjustments made.
I got mine atma in 18 hours, I was interested in this back at the peak time for atma farm so I gathered some statistics from all my friends, fc and lses just how fast people getting atma - and average was around 15 hours. Yes, there are always outliers who got it after a very long time, but there are also people who got it in less than 4-6 hours (and I really *hated* them when I spent 7 hours just to get one atma). People bragged how they got 3 atma in 20 minutes and I wanted to kill them for that.
The same with materia melding/synthesys. I craft for sale and I crafted already items in ten thousands and see no divergence from "fair" distribution of NQ/HQ.
You can't just rely on your memory to make a proper conclusion about your own luck - you need a proper track somewhere else. Because in your mind failures and successes written differently, the failures of the same amplitude given twice the weight of successes. And when you try to "average" based on you memory, you'll always get a "i'm unlucky" feeling on a long streak of events.

I think by that point it's closer to 1 unit. Or negative units... as the person realizes "One down, eleven more to go... for my first Atma weapon."

You can change "happiness" to "excitement", and a lot of people do get excited after finally getting sneaky atma they went for hours.

[Adler]

I think main problem for people crying in forums about unfair success rate for any drop/craft or anything else they have failed and then offering their calculations is concentrating on wrong things. You more or less can't beat machine on math - so instead you should try to observe machine's work and notice little things that can help you. Atma CAN be got fast with all the randomness and crafting has a pattern not so related to success % to get HQ. Instead of writing down numbers and trying to make calculations that usually are false anyway just try to feking watch and learn - there are things and actions that does matter towards chance of success based of if and when you use or don't use them.