* image selected simply based on my love of halflings
A recent discussion over on the Basic Fantasy RPG forums got me thinking about ability checks (you can go read it here http://goo.gl/2rLYuG ).
In BFRPG many of your basic checks are resolved using a single d6: opening doors, checking for secret doors, etc.
BFRPG follows along in this manner with trap detection as well:
And yet again with secret doors. You seeing a pattern here?
Now in all these examples someone with a high ability score gets a modifier, but the user entr0py posited the idea of instead giving the player additional dice to roll. So you would need to roll a "6" on a d6, but if you received a +1 modifier due to a high ability score you get to roll 2d6 and try to get a single "6". I think the number play out close enough in probability to make this a viable comparison. Please note I am not a math guy, in fact I hate math, so I did a few quick Google searches and called it quits. Probabilities appeared pretty close - not perfect - which I am ok with, this is a game and not rocket science.
Let's say that for every 3 levels you get an additional die when performing actions that logically your character would have experience with over their adventuring career. For those who think every 3 levels is too quick, use ever 5 levels or every 6. My campaigns seem to putter out around 5th or 6th level so I do not think every 3 levels is too fast. Your mileage might vary. GMs could easily add or remove a die to control the difficulty of the situation, I would say never dropping below d6.
I think if you have added backgrounds (see http://basicfantasy.org/download.cgi/BF-Background-Skills-r1.pdf ) or simply had players come with a biography for their characters, this could be used as a guide as well. Character's background says his parents were fishermen? Give that guy an extra die on any check involving the ocean, boats, or fishing.
Wulfgar is running from skeletons and comes across massive boulders blocking his way. The player wants to move a few boulders out of his way to allow Wulfgar to escape certain death. Wulfgar gets the standard 6 on a d6 for this check. His high Strength gives him an additional die, so he can roll 2d6. Wulfgar is also 3rd level the GM deems that feats of strength would be par for the course for a Fighter and provides the player with an additional d6. Wulfgar's player now gets 3d6 to attempt to get a single 6.
I think you could even replace Thieving skills with it. Another "homebrewing thieving skills" example-
Kenric attempts to pick a lock. He gets the base d6 roll, needing a 6 to be successful. As a GM I would argue that picking a lock "fits" within the scope of his class so I offer him another die, now he rolls 2d6, still needing just a single 6 to succeed. The player notes that he has a +1 for his high Dexterity score. He now has 3d6 to roll and get a single 6.
Cleric is digging through ancient texts to try to find an obscure prayer to help combat some evil creature terrorizing his town?
Heimlich wants to find an obscure passage in the church's library. He gets the normal d6, but his exceptional Wisdom gives him an two dice. He now rolls 3d6 on his check.
This process might not be perfect but I think it provides a viable method of utilizing natural ability AND experience is a super fast method that a GM can easily manage at the table without comparing tables and charts.