Your adventure stone will gain stats as you successfully complete more and more LDoN adventures. From my experience I have seen an "increase in power" after every 10 adventures. Now my stone has some +HP and +Mana adjustments, but other stats *might* be added as you progressively complete more adventures.
Also, in order to get the stat benefit, I think you have to augment your adv stone to a charm. That is, get your favorite charm (some decent ones can be had cheaply at the adventure merchants for low amounts of points) go the "birdbath" augment pool, click the pool, put the charm and the adv stone in the container that pops up, and hit combine.
Also, you may need to zone once, or unequip/re-equip your charm to get the stats to show up.
Edit: Also, try befriending the search engine here. Far more wisdom that I have imparted can be found
here after a quick search.
Edited, Thu Apr 1 09:37:12 2004 by VWDiesel