In Burning Wheel (Gold, also Revised), there are some stats — specifically, Perception, Faith, and Resources — that only advance when you succeed at a test.
This makes advancement much more difficult, since you need to actually pass Difficult and Challenging tests — by definition, tests that you're likely to fail, and tests that you have no hope of succeeding without extra effort, respectively; whereas with other skills you merely need to attempt them (well, attempt them and survive the consequences of failure).
However, this is Burning Wheel, so artha is limited and tests don't happen without something at stake. The game's ethos is that you should put something on the line and face danger head-on, but also put some thought and strategy into your approach in order to actually persevere. Doubly so for the "only successful tests count" stats because there's no consolation prize for failure.
For instance, I've been able to advance Perception at the same rate as Will and Power while actively trying to advance and shade-shift Perception while largely ignoring those other stats (and rolling them significantly less often than Perception). Meanwhile, advancing Resources seems like a delicate balancing act because failing tough tests leads to tax, which can actually permanently drain your Resources if you're not careful.
So, what's the best way to pick up the successful Difficult and Challenging tests needed to advance Perception, Resources, or Faith in real play, where artha is scarce and failed tests have real consequences?
(If it involves using a limited resource judicially, tell us how. If it involves setting up certain specific fictional situations, provide some guidance on how to do it awesomely. Et cetera.)
Best Answer
Gaming the Help System
1. Follow the Leader/AKA the Gandalf Effect
Take the person with the highest stat, have them deal with the higher obstacle things, have the rest of the group each throw in Helping dice in order to get the advancements. The leader often will get nothing beyond a Routine test at best, but everyone else gets a good advancement out of it.
2. The Leapfrog game
Let's say you have two characters close or identical in a stat. One will take the test, using as many ways to get extra dice as possible - Linked Test, FORKs, Working Carefully, etc. etc. The other one puts in a Help die. Notice that the Helper isn't penalized for all these extra dice - as long as it passes, it counts as if they met that Ob with their given stat.
Next time, switch roles.
3. Someone needs my Help!
Find an NPC who is has the higher stat, is doing tough Obstacles, and offer your Help. This is easiest to do with Resources, since nearly no one turns down financial assistance. Perception is harder, by it's nature. Faith is the hardest to find someone, but of course, if they share the same Faith as you, they'll probably be happy to take on a disciple and then the tests should come easy.
Practice
Obviously, not easy to do during an adventure, but between adventures, or while waiting for someone to heal up, it's a great time. In general, if you're not doing anything particularly useful, it's always a good time to ask the GM if you can get practice. "Hey, we're going to be riding on horses for weeks at a time. Can I get part of that as Forte practice and part as 'Horse-wise'?"
For things like Perception or Faith, it's a little tougher but not impossible, you just have to be creative or at least have an NPC who can tell you how to practice them.
Artha, the gambling way
You can always spend Artha. If you have it. The thing to remember is the more dice you're rolling, the more likely you are to get a benefit from open-ending a roll. That said... Artha doesn't come quick enough to really pull one of these kinds of tests more than once every 2-3 sessions at best.
Greed, the one exception
Spend a persona point, add your Greed to a test involving the things you have Greed over - the dice count as Artha dice, so you can start making big rolls without having those dice count against you. It's pretty easy to see how this can work for Resources rolls, a bit harder for Perception, and unfortunately, Dwarves don't get Faith at all.
Eleven Grief takes a full Deeds point, which makes it too rare to be that useful, and while Orcs can roll Hate in place of other skills or stats, the advancement only counts towards Hate.
The Fact is...
Practice and Help are the ways to go. Remember Burning Wheel also is built on the assumption of the long term, old school campaign length - it may take dozens upon dozens of sessions to advance these things. You should probably assume that unless you have a game group like that, that a lot of these stats will stay static for the entire campaign.
Resources: Easy to find situations, easy to Help, can't practice.
Perception: moderate to find situations, moderate to Help, can practice.
Faith: moderate to find situations, hard to Help (that is, hard to find other people with Faith), can practice.