Most likely for you (and anyone else looking to “finish” traitstones) it is probably explore by a pretty good margin, no matter what type of traitstone you are bottlenecked on. But lets “explore” the other options.
Not so much “Quitting Early” as autopiloting and moving as quickly as possible. If you are after glory especially (or gems) the earlier on in a match, the more your rewards increase for any given move and unit of time because there are fewer types on the board and things cascade easier. As someone that isn’t “good” at treasure hunt, my last test showed I earned about 600 glory and 75 gems with 60 maps in one hour using this method (but no gem keys and only 20 glory keys). Others show still show better gains overall using the “fast” method. Because of the availability of treasure maps almost from the word go on new accounts, going for high moves in treasure hunt has always been bait, but making higher chests than green does pan out to “more rewards” long term if you do it consistently without losing speed. Keeping chests intentionally low hurts you almost as much by restricting your moves, making each move less valuable and wasting time. Basically, you just want to be fast, and if you just want low tier rewards like glory, don’t go out of your way to match into higher chests, especially above green.
That being said, it is unlikely you will get even total arcanes faster from any source other than Explore. If we use even the most efficient conversion of glory to Arcane traitstone, we need 200 glory per traitstone. Explore offers triple the drop rate of arcanes (and celestial, double runic) as other modes (unless they changed it since my last 2000+ battle test), at roughly 1 every 17 battles per arcane on average. An optimized explore team takes about 20 seconds at endgame or 30 seconds at midgame. PvP battles generally run in the 1 minute range on average nowadays for three trophies, but sometimes you find yourself in a good matchmaking pool for one trophy and can get away with 30 second battles fairly consistently. Either way, you are looking at probably about 400-450 glory/hr, significantly less at lower level where your battles will still take about as long but you’ll get less glory, and probably between 60 and 100 battles (with a 1/50 arcane rate).
Given that, lets look at some quick math using what I’ve estimated using my own experiences. For PvP, assuming we get 1-2 random arcane from the battles themselves, we max out at about 2-4 arcanes/hr. Treasure hunt we will estimate at about 600-800 glory per hour, but we rarely go about 45 moves, generally getting about 120 total traitstones with couple random arcanes from the deal, for a total of about 3-6 arcanes/hr. For those wondering, the drop rate of Arcanes from Gem Chests is about 1.6%, so other TH resources obtained here equates to a fraction of arcane at best. Barring battlecrashers and weekly events, those are both at optimal circumstances and mostly “stone of the week” and only on weeks where an epic pack is available. Events using the new troop for extra glory where the troop isn’t bad can get you another stone or two worth of glory per hour, but battlecrashers and gnomes favor explore where the battles go much quicker with pretty much zero chance of escape or loss. Explore gains no glory, but you’ll get about 120 to 180 battles in, which equates to about 7 to 10 arcanes/hr completely of your choosing. Using a controller and having good muscle memory with endgame stats can bring that up even higher by shaving a second or two off each already extremely short battle. If you buy arcanes on a non-epic pack week, you’ll be spending 50% more per stone, making explore even more attractive relative to the other options. Explore also gets you more Runics and Celstials than the other modes by a significant margin (possibly even minors and majors due to sheer speed).
Basically, for Arcanes at least, well optimized explore is almost twice as fast as any other well optimized option under the best conditions, and just kinda poorly optimized explore is still better than most other well optimized options. This is not even mentioning that at this point, a vast majority of your glory should be coming from tributes and glory is far less valuable elsewhere (especially after Spoils of War is capped in the upcoming patch). Explore is the clear winner here if your goal is traiting troops.
Worth noting that treasure hunt can produce those kinds of numbers with no troop collection and very little practice, so if you need, say, a minute or more to clear an explore battle, it probably isn’t worth it unless you have an immediate need. For those that are super early game and running out of maps is a concern, just run with Tyri in team that has good “flow” (I like hero w/ priests hammer +5/lion prince/tyri at high enough level to destroy at least 8 gems/pandasa guard or dragonian rogue) and you’ll get a ton of maps just clearing through quests with what is probably also your fastest available team. The last new account I made was able to trivially finish its first Treasure Hunt event, starting the account on the Friday the event was running, without resorting to any kind of hard map farming/looping Tyri, while also just burning maps as quickly as possible. At this stage of the game, treasure hunt including the time it takes to get the map is better for soul farming than using actual soul generators.
Keep in mind that you can also currently finish off Arcane Lights by farming The Warrens if you haven’t leveled it too far (3 guaranteed arcanes for 4-6 minutes is better than any explore). If you have a good level 20 farming delve you can complete quickly, delves in general can hand out a decent amount of total rewards, but probably aren’t the best otherwise if you mostly want stones because they don’t give random stones after battle, just a few specific rooms give something notable. Multiple delve rooms actually hand out Runic stones that you can get 2 or 3 stones clearing depending on your multiplier going in, this is overwhelming skewed toward Runic Magic with five total rooms, most being Epic or blow, then Earth being available in a couple Epic Rooms, with Water being available in three legendary rooms and Nature only having one specific legendary room drop them, and with none of them so far offering Runic Wind or Fire.
I also haven’t run the calculation in a while, but there was a time where just glory pack purchases and keys from guild tasks introduced more traitstones (of every type) into the economy than new troop releases covered. Play long enough, and you can definitely do this with Arcanes, especially if you use your spare Wisdom orbs on mythics 2nd and third traits, get at least a few legendary tasks per week and buy a lot of glory packs every week. Unfortunately, because Arcanes in glory packs tend to repeat a lot, RNG is super streaky, and arcane number requirements are seriously imbalanced, “long enough” could be quite a while. I had a few month stretch where Arcane Venom were “in the red” by a few after having finished all traitstones a long time ago because of multiple troops being released in quick succession that needed that stone and no associated glory pack, and now I’m back up to +40 without any farming.
One last thing to mention is that Orbs of Wisdom seem to have estimated about a 30% drop rate from chaos orbs, and, spent at their peak value on mythics two last traits, 2 of these saves you 42 arcanes. That is four to six hours worth of speed farming explore, or two to three hours per Wisdom orb, or 36 to 54 minutes per potential (chaos) orb. If you can pick up an Orb of Chaos at no personal cost and you can spend less than 36-54 minutes doing so, this is also technically faster than explore on average, if you still need to trait mythics. Otherwise, rolling an Orb of Wisdom just makes up for some of your wasted time for not getting an Orb of Ascencion (at least it wasn’t growth), unless, of course, you finished all traits, in which case about half of Wisdom orbs are useless since Ascencion bottlenecks you for Zuul’Goth if you bother going for that.
All that assumes your current bottleneck is Arcanes, which it is for most people, but different levels of activity in different guilds can make that otherwise. If you run into a problem with:
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Minor Stones: Gold Keys/Explore/PvP for gold for keys If you have a ton of unopened gold keys, go ahead open them. If you need a specific minor only, you are better off exploring over repeating challenges so you can get more Arcanes and Runics for later, but if you are really bottlenecked on minors (all colors), you are still better off just farming the gold from PvP and getting the gold keys. There is an 18.75% drop rate of minors from gold keys, so a, say, 500k gold 1hr farming session is worth 312 random minors (+~35 from battles) while a similarly good explore session of 100k gold in 1hr would net about 62 random minors from the gold and ~88 specific from the battles (YMMV on gold earnings, but generally more total quantity of minors is earned by PvP > gold > gold keys, more specific minors from explore). Repeating challenges will only be very slightly faster than the respective explore for a specific minor due to slightly increased drop rate for minors vs Runic/Arcane/Celestial (est ~106/hr and almost no gold gain with really good optimization) and generally not worth it due to the opportunity cost of everything else. Don’t craft minors.
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Major Stones: Any Battles/Open Keys Every source that gives majors gives way too many of them relative to other types, so these should never be a problem. If you bottlenecked here, you probably crafted them away. You can make some of these into runics in the soulforge if need be, but don’t go overboard. If you are low, any battles or opening gold keys will suffice.
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Runics: Explore. If you need Magic or Earth, recommend delving in a farm delve at least for your daily delves. Otherwise, explore a kingdom with a dual color arcane that you need (unless you really need mono colors), as Runics have double frequency in explore over other modes, and explore is of course much faster than PvP. You can craft some of your spare majors into these if you don’t need souls, but don’t go overboard.
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Arcanes: Explore. You can get Arcane Lights from the Warrens, and glory packs whenever you can (I’ve been doing 16 packs of each troop per week for years and had more than I need for about couple years now), but if you want anything now, you want to explore. Try to rotate kingdoms, you don’t want to farm 200 stones and then get a glory pack the next week. Or, depending on your guild, simply keep playing and wait until you pass the threshold where you no longer need them through attrition from incidental key openings and legendary tasks where they are considered filler loot. Don’t craft them, it is bait.
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Celestials: Explore. Just explore a kingdom where you need the Arcane/Runic. VIP chests have these in ridiculous ratio as well, if you happen to have the need to open VIP for some other reason (new mythic). Wouldn’t recommend crafting them, we might need those jewels down the road, and a weeks worth of dungeons certainly isn’t worth a single celestial.
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Farm glory for glory troop packs vs farm stones: Farm stones (in explore). Tribute glory should be enough to supplement pack purchases and have you trending upward on Arcanes. Farm glory if you need more of the troop.
tl;dr: Explore with a fast team.