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Is there a complete list of the things luck changes?
Equip monsters that boost research drop chance. You can find them by going to Party -> Main and then the middle of the screen there is a text box. Type "Research" or select "Research Drop Chance" from filters.
For research drop amount, it is better to bring summons with high luck than summons that boost research drop amount, so bringing your AAA team is usually way to go to farm new summons (I guess intended ?)
Of course always train Tamer passives for drop chance and amounts
Another boost is in Will -> Train Insight
And do not forget about Familiar -> Arrogant Fairy for research drop chance
Can also bring summon that boosts Arrogant Fairy effect (Fallen Angel from The Arbitrator)
I have a party one-shotting the cobra. With 8 members in the party, 10.6k research drops.
Now, if I add the Goblin Elite (RDC 80%), I get 20.6k research. And if instead of the Goblin, I add the Griffon (RDC 100%), I get 17.3k research.
So clearly, RDC is not simply acting as an RDA buff as well, because if it were the Griffon would buff MORE than the Goblin, but it doesn't.
So for my next test, I removed the Goblin and Added the Robbery Condor. Notably, that ally has NO luck, RCD, or RDA. Guess what? 18.6k drops - a huge boost, more than the Griffon but less than the Goblin. This is, interestingly, the same order as their power levels.
So, new hypothesis: Ally power level influences research drop amount.
One more test. I use the 9-ally team as above with the Goblin, and confirm that it gets 20.6k research. Then I remove the Sludge Slime (100% RDA), which takes me down to 10.3k Research. This says that whatever mystery factor is involved here, it's multiplicative, not additive, with the RDA number. Adding the Condor back into my party takes me back up to 14.1k. But adding the Ceasefire Saint, I get only 10.3k, no boost at all. Same for Barbaric Fool. Same for Fallen Angel (without using Arrogant Fairy, obviously if I'm using it things will be different).
This leaves me with my current hypothesis: Ally power level influences RDA, but this excludes Guardian-summoned creatures.
[Edit: I also tried a guardian summon with 2.15k luck in the ninth slot, replacing the goblin. This took me down from 20.6k to 13.2k - or up from the 8-ally party's 10.3k, a ~28.15% boost. So luck is a decent boost, but not good at all compared to the condor or goblin. And finally, I tested with Iari (Norn had a hangover and wasn't available). 10.3k, no boost at all, just like Guardian summons with no luck.]
Goblin Elite Max Luck: 65.6k
Robbery Condor Max Luck: 52.4k
Ceasefire Saint Max Luck: 590k
Barbaric Fool Max Luck: 590k
Fallen Angel Max Luck: 590k
More Luck means more Research per Drop. This is why the Goblin Elite and Robbery Condor gave more Research per drop than the Griffon did. As for why the three Guardian monsters gave less, I would assume that is because you have not maxed out their Luck as otherwise they would be outperforming your Zone 8 (Valley) monsters in terms of Research per Drop. A monster that has not hit Maximum Level has a Luck value of 0 and will not contribute to Research gain.
Your main Research gathering team should consist primarily of high Luck monsters from the latest Zone or Guardian as well as a couple with Research Drop Amount bonus to make it go nuts.
could you show us the team that you use, maybe thats why I dong get any drops what soever because all my team member are guardings (they are the strongest cause I havnt leveled my monsters yet ^^; )
Ah, now I see! Thank you!! For some reason, I totally missed that the Luck you get from boosting max-level allies is the same luck everywhere else. Of course, that makes perfect sense.