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The odds that a gem will be upgraded increase with each higher level Greater Rift completed in that game. There is also a chance that the gem will receive a double, triple, or quadruple upgrade, boosting it 1-4 levels in total. It's yet not known if anything effects the chances of a double or bigger upgrade, and most fans suspect it's pure [[RNG]].
The Legendary Gem upgrade chances are displayed in the [[tooltip]] , so the following figures are not estimations, but are what the game actually says before each upgrade attempt.[http://www.diablofans.com/forums/diablo-iii-general-forums/diablo-iii-general-discussion/90337-community-effort-legendary-gem-upgrading-effects]
* Rift Level 01 - Upgrade chance 21%
* Rift Level 17 - Upgrade chance 45%
