I assumed Tier 60 will be the absolute lowest you'd want to run to still get decent loot and somewhat acceptable experience / key value.

If you're playing on lower Tiers / Paragons, most of these findings should still hold somewhat true (obviously discounting the scaling, so you could probably replace old Caldesann's at ~ +15 ranks already etc.).

To replace a Caldesann gem on an item the new gem should be ~20 ranks higher, else you should max out the 8 / 4 / 2% chances on your main gems first.

Main gems should be 3 above highest farming Tier once you start hitting a wall (not counting tryharding high Tiers for 'gemup runs').

Stopping empower at 77 will save you 8.4b gold (70%) but only requires ~2 more runs (~20 more min on top of ~2-2.5 hours).

My findings (the colored text in the pic):

Bottom right: Comparison of leveling main gems with 8% (and less) chance vs.

Bottom center: Comparison of leveling main gems with <60% vs.

Bottom left: Cost scaling more precisely for relevant Tiers.

Top right: Same but empowered stops at Tier 77.

Top center: Required amount of runs / gold / time (time is a rough approximation for 3-5 weeks into the season) to get a gem to 90 with all empowered rifts.

Top left: Cost for empowering (basically +1 gemup).

If you want to see the numbers, here's my Excel sheet (explanation see below): I assumed ~3.5 months and 200b/h early game, increasing up to 1000b/h near the end of season.

Keep in mind we know neither the exact duration of this season nor the exact XP/h values that people will achieve. I calculated numbers for P1400 / Tier 90 gems with my solo Natalya setup(dual wield, no mainstat on jewelry, full diamonds, nonancient amulet), which will be pretty early in the season but for casuals like me it will still be decently high. It's about when to upgrade which gems and how to use our gold optimally. Here's some math on Caldesann's Despair I did a while ago and I decided to share it now. It gives players a general idea of when to upgrade gems and how to more efficiently use their gold in this activity. Wudijo recently made a thread on our forums sharing a spreadsheet and some numbers on Caldesann's Despair.

16, 2016 Love is in the Air, Legion - Tier 19 Monk Armor Sets, Tweets, BM Hunter Spec Preview Caldesann's Despair Theorycrafting & Math

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Diablo 3 caldesann's despair rank 100