Gem rerolling is limited to the amount of lunar souls you can spend, so it is important to not waste them with suboptimal rerolls.

Abbreviations

CD = Critical Damage

CH = Critical Hit

MH = Maximum Health or % Maximum Health

MD = Magic Damage

PD = Physical Damage

Strategy

I use MH to represent both types of maximum health stats since there is no need to distinguish them apart. You will not need any boosts to CH in the long run. You should also have 3 boosts on the gem to get the most stats from it.

The target gem is CH CD MD with no boosts to CH. Each table will have an alphabetical version and another version that is ordered by expected value.

1 stat not boosted

1 stat not boosted (Class Gem)

2 stats not boosted

2 stats not boosted (Class Gem)

Class gems are different because you cannot switch between MD and PD. Expected value represents the average amount of rerolls needed to reach the targeted stats using the strategy. I didn't include Health Regeneration, but you can take 1 + the average of the possible outcomes from rerolling it to figure out the expected value.

Example:

Suppose you have a 1690 PR normal stellar gem with 1 boost to CH , 2 boosts to PD, and no boosts to MH. The pairs are in alphabetical order, so you should look for MH | CH PD in the table. The decision is to reroll PD. After rerolling, suppose you get CD. Look for MH | CD CH, and the decision is to reroll CH. Suppose you get MD. The missing stat is CH, so reroll MH until you get it.

Sometimes there are actually 2 choices for the decision, but I only pick 1 because it is better to keep the dps stat. Suppose you have a gem with CD PD and CH, where only CH is boosted. The decision is to reroll PD, but you could also reroll CH and the expected value would be the same. The only difference is PD doesn't contribute to dps for a magic damage class, so I decide to reroll PD instead of CH.

Sample Calculation

This information is for people who are interested in how to calculate the expected value.

This shows the possible outcomes for rerolling a normal or empowered gem with CH, MH, MH, and no boosts to CH. For CH | CD MH, you can reroll MH to 3 possible outcomes: MD, MH, or PD. The probability of success is 1/3, so the expected amount of rerolls is 1 / probability = 3. We don't know the expected value of CH | PD MH yet, but you can continue to reroll PD until you get CD or MD. One way to think about it is to consider CH | CD MH and CH | MD MH as successful combinations and CH | PD MH as a failed combination. The probability of rerolling to a successful combination is 2/3, so the expected value is 3/2 = 1.5 rerolls. After getting a successful combination, the expected amount of remaining rerolls is their average: (3 + 2) / 2 = 2.5 rerolls. Therefore, the expected value for CH | MH MH is 1.5 + 2.5 = 4. Since CH | MH MH and CH | PD MH are interchangable, they have the same expected value.

However, we must also consider other ways to reroll CH | PD MH. If rerolling MH, then we get:

The expected value is 1 + the average of the of the remaining expected values. 1 + (3 + 4) / 2 = 4.5. Since 4.5 is greater than 4, it is better to reroll PD instead of MH.

Here is a guide for optimizing DPS: How to Optimize Your DPS by Balancing Stats