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The Jewel of Rhaelyx is one of the two component pieces of the Crown of Rhaelyx (the other being the Circlet of Rhaelyx) which provides a 10% chance to preserve resources when training non-combat skills.
The base drop rate of the Jewel is [math]\displaystyle{ \frac{1}{10,000,000} }[/math] per action taken. The drop rate increases by [math]\displaystyle{ \frac{1}{2,500,000,000} }[/math] for each Mastery level you have in any skill, to a max of [math]\displaystyle{ \frac{1}{100,000} }[/math] which is reached at 24,750 total mastery level. After that point, additional Mastery levels will not increase the chance further.
Crown of Rhaelyx (the other being the 
Circlet of Rhaelyx) which provides a 10% chance to preserve resources when training non-combat skills.
750,000
Firemaking, 
Cooking, 
Smithing, 
Fletching, 
Crafting, 
Runecrafting, 
Herblore, 
Summoning, and 
Archaeology. The chance of getting a Jewel depends on your total 
Mastery level, which can be seen on the Statistics page.
Circlet of Rhaelyx
Jewel of Rhaelyx
Combat:
