Basically, like pokemon, Maple and Gasha Nuts are not really random.
This site got me pointed in the right direction.
http://forums.legendsalliance.com/topic/17347-crackin-the-nut/
After farming a few Soft Soil spots, I can confirm this info is accurate.
Long story short, Maple shows up the very first time you change a screen outside of dungeons, outside of buildings, and not in Subrosia, every 30 enemies you kill. If you've got the Maple ring equipped, it's every 15 enemies.
Gasha Nuts appear after you've planted a Gasha Seed in a Soft Soil spot and killed a bunch of enemies (30 or so? idunno). If you've got the Gasha Ring equipped, it's half that.
The prize you get from a Gasha Nut is determined when you walk into the screen it's in AND hit it with your sword. The prizes you get from Maple are determined when you walk into the screen, she appears, AND you bump into her.
Restore Points (tapping the bottom screen, NOT saving your game) can be used to choose the prize you want from Maple or a Gasha Nut. If you create a Restore Point while standing in front of a ripe Gasha Nut, and immediately walk up and harvest it, you'll get the same prize every time. Read that link for more information on which Soft Soil spots give which prizes at what percentages. Maple is similar, although apparently she doesn't have the limitation of only providing certain rarities of rings in certain areas. If you create a Restore Point, before killing just enough enemies to cause her to appear, after causing her to appear, she'll give you the same prizes every time.
There are multiple ways to change the prize you get. The easiest way I've found is just to change the screen. But if you check that page, they list quite a few actions that alter your prize, so keep that in mind and try your best to not do random stuff while you're abusing or you'll screw up your prize.
Once you've made your Restore Point, 2 screen changes will always give you whatever it happens to give you. 4 will do the same. And 6, and 8, and on and on. But when you set up a new Restore Point, after getting whatever prize you want, the list will have changed. So, 2 doesn't give the same prize indefinitely. Neither do 4, or 8, and so on. But when you create a restore point, 2, 4, 6, etc will always give you what they happen to give you until you do a random action (kill an enemy, change a screen, etc) and set up a new Restore Point.
The advantage of Gasha Nuts is that they're super easy to harvest and reset on. The disadvantage of Gasha Nuts is that certain Soft Soil spots only give certain rings, and the best spots are super far away from the ring shop.
The advantage of Maple is that she gives any of the random rings, AND you can easily cause her to appear right there at the ring shop. The disadvantage of Maple is that she can be a beach to harvest from, especially when she drops good loot (she speeds up and heads for the best loot first). Also, if you let her encounter you a lot, and she scoops up enough of your rupees, she upgrades her broom and gets really, really fast and hard to harvest from.
If you're going to try Gasha Nuts, and you're playing Ages that link has a great list of the best Soft Soil Spots. If you're playing Seasons, I know from experience that the spot at the Mayor's house is most likely a L1 spot. The spot just north of Impa's house is most likely a L1 spot. And the spot with the Red and Blue Darknuts in the Temple Remains (North West Corner-ish) is definitely a L3 spot. I haven't even made it to the 3rd dungeon yet, so I haven't found the best spots in Seasons yet, and I haven't been able to find a guide yet.
So here's how to use all this information to your advantage.
Once you have a ripe Gasha Nut, make sure you kill any enemies, have any items you need equipped, and know your way back to the Ring Shop. Create a Restore Point. Harvest the nut, trek back to the Ring Shop, and see what it gives. If it's what you want, keep it and save. If not, load your Restore Point again, walk out of the screen, then back in, THEN harvest the nut again, trek back to the ring shop and see if it's what you want. If not...reload the Restore Point, walk out of the screen, then back in, this time more times, then see if it's what you want. Repeat till you're happy with what you've got.
For Maple, once you've killed 29 enemies, or more than 15 and have the Maple Ring
but not equipped, create a Restore Point. Either kill that 30th enemy, or equip the Maple Ring, walk out of the screen, the music will change and she'll fly by, bump her, grab the loot, take it to the Ring Shop to see if it's what you want. If it's not what you want, reload your Restore Point, walk in and out of the screen once, activate her again, and see if it's what you want again. Repeat until you get what you want.
Even if it's not what you'd ideally want, write down how many advancements give you what, because what you're looking for could possibly be really, REALLY far off and you might just decide to settle on something you found before.
Happy Ring hunting!
[edit]
I forgot about, and just came across, the Shop down in Subrosia. You can buy a total of 4 rings from there, pretty dang cheap. The same process applies. I've only seen L1 and L2 rings from a few minutes of resetting, but I haven't seen anything to suggest that higher level rings can't be obtained from there.
