Clicker Heroes: Who To Gild?

I've been running with all of my Clicker Heroes gilds on Frostleaf for some time now. I've mentioned it in posts twice, and both times people have commented to say it would be better to have someone else gilded. (The Masked Samurai in one case, Terra in the other.) Both times I plugged some stuff into my spreadsheet and determined Frostleaf was, in fact, the best option for me at those precise moments in time. I was posting a comment to Sky about how Frostleaf was still the best for me so maybe he was wrong when I thought about it a bit more and decided Terra probably was better for him than Frostleaf...

My problem so far (and quite possibly Sky's as well) is that we're looking at specific moments in time and deciding who is the best to gild at that time. Once a hero has been established and you've bought all their upgrades they all scale in exactly the same way. For every 25 levels you buy the cost will have increased by a factor of 5.42 and the damage done will have increased by a factor of 4. Under this scaling system whoever is the best choice will flat out stay the best choice for all time. You should gild whoever is best amongst heroes you can afford. There is one catch... Every time a hero levels to a multiple of 1000 they get a damage boost of 10 instead of a damage boost of 4. Essentially, you get a 2.5x bonus for hitting the multiple of 1000. So if two heroes are close to each other in power level then having one of them get a 2.5x bonus can easily swing the balance of power between them.

In the specific case Sky brought up, with Terra and Frostleaf, my Frostleaf with an equal amount of money spent on them does a little over twice as much damage. But my Frostleaf had recently crossed a 1000 barrier, and my Terra was close to breaking her own 1000 barrier. If I removed 300 levels from each hero Terra will gain 17% more benefit from being gilded than Frostleaf would. This is the state Sky is in, as he mentioned his Terra was around level 1500 which is about the same cost as Frostleaf to 2950. But pay just a little bit more and bump them up to 1550 vs 3000 and suddenly Frostleaf gains 111% more benefit from being gilded.

One other interesting thing to note is the above comparison isn't exactly fair. Terra and Frostleaf don't actually gain precisely 4x damage when you buy 25 more of them. You're also adding on 25 more levels which get multiplied through by all your other multipliers... How much of a boost this is depends on how many levels you already have. For example, taking Terra from 1000 to 1025 actually multiplies the damage done by 4.1 while taking Frostleaf from 2450 to 2475 is only a damage boost of 4.0408. This seems like a small difference, but it is a crucial one. Frostleaf at 2450 is 7% better than Terra at 1000 even though it's the same level difference as the 2950 to 1500 comparison and no extra 1000 level barriers were broken along the way.

This does mean that as you keep leveling and leveling the 'right' choice would (very slowly) shift up the depth chart even if there wasn't the weird quantized breakpoints at the 1000 marks. The difference does start getting really small as you get more of them, though, so it wouldn't be enough to swing a huge gap in any reasonable length of time. The 2x gap that Frostleaf owns at the 3025v1575 mark doesn't go away until sometime after my spreadsheet breaks from numbers getting too big. At the 11000v9550 mark Frostleaf maintains a 26% edge over Terra. But at the 10975v9525 mark Terra is up to a 99% edge over Frostleaf!

So now I have a couple questions... Can I work out a more general formula of some kind to actually rank who I'd want to gild at any given cash level? And how much does it cost to switch between two gilded states?

Assuming I never ascend again Terra will be 'right' for 550 of every 1000 levels when compared to Frostleaf. And she'll be 'wrong' the other 450, and she'll be more wrong than she is right, so I'd stick with Frostleaf if I couldn't switch. I have 173 gilds, and they cost 80 souls each to move, so I'd have to pay 13840 souls to make that swap. I have 111805 souls right now. So I'd have to give up more than 12% of my damage in order to pick up the 17% benefit from having Terra gilded during that window. This is a gain, but it's such a significant amount of my damage that it's a terrible idea if I'm going to keep ascending and ever play in a range where Frostleaf is way better. So I think the back and forth swap is right out. (Unless it actually lets me push on to the point where I earn more than 13840 extra souls? At my current depth I'd need to be able to push through 150 more levels to make that much. Since each level has a boss that has double health that's not going to happen by getting a 2.5% damage boost.)

What about the start of a general formula? I feel like the first number I need for each hero is their self buffed value at level 200. This is a high enough level that you'll have all of their upgrades, and is also where the 4x multipliers start showing up. None of the other multipliers should matter since they'll impact every hero by the same relative factor.

Ok, I get that value, and it isn't very interesting. Each hero is better than the one before it except the truly terrible ones (Betty, Midas, Amenhotep). So then I tried dividing by the base cost of the hero, but that wasn't any better. Now each hero is worse than the one before with a couple exceptions. Mostly around the terrible ones again, though The Masked Samurai performs a lot better than the two before him.

What I really care about is comparing how two heroes would perform if I could spend all my money on just them. Which means I want to be comparing the cost efficiency of each hero at that gold value. So I added a cell to my spreadsheet for each hero to work out how many levels I could get for a given amount of gold using the formula for summing a geometric series.

...BREAKING NEWS...

It also turns out there's a cap on the hero multiplier. 4100 is the last level where you get a 4x boost! So once a given hero is getting above that value they really fall off the cliff in terms of usefulness. Like, to the point where I'm thinking you'll almost never want to buy level 4101.

...BREAKING NEWS...

Ok, but I still don't have a simple formula for who to gild... But now that I have all this stuff plugged into my spreadsheet I can just enter in an amount of money to see what hero is best at that money level. And because I'm still obsessed with Frostleaf I also want to look at how much better the best hero would be compared to just leaving all my gilds where they are on Frostleaf.

And now that I did that, I don't think it's very useful to post. The problem is there are so many different values I could use, and the 'best' actually changes a lot between them. I tried doing every multiple of 10^20 and then every multiple of 10^5 and things would swingly wildly. 1x10^125 had The Masked Samurai on top, but 1.5x10^125 has Orntchya on top with Frostleaf almost equal. Once Lilin becomes a reasonable option she seems to stay on top, but that's likely just because her breakpoints line up well with the ones I randomly decided to look at. Even by 1x10^130 Lilin is almost 4 times as good as Frostleaf, and she runs almost exactly 3000 levels behind him so they're never going to get offsync on the 2.5x multiplier. So if I ever reach the point where I can have Lilin up after I ascend it'll be right to gild her up for sure.

What does this all tell me? Well, I've been pretty lucky to always have Frostleaf math out to be the best when I've checked since he doesn't seem to be showing up as the best in my random samples. It's entirely possible he's just frequently the best in the little chunk of the leveling curve where I've been playing the most. Which certainly implies that gilding him up was a good choice.

What confuses me a little is I've been trying, and I can't find any times when Dread Knight, Atlas, or Terra are the best. Even at the 1500 Terra mark where Sky rightly pointed out she's beating Frostleaf... She's worse than Orntchya, Ivan, Treebeast, Aphrodite, and Brittany. Ok, I found one... At 4.2x10^129 Terra gets to buy level 2000 and marginally jumps ahead of Orntchya to take first place. But Orntchya is at level 979 at that point, so she'll take the lead back by 1.8x10^130. And while Terra was barely ahead at her 2000 mark, Orntchya has a _commanding_ lead at her 1000 mark.

I think the main thing that's going on is some of the earlier heroes are just really good and the new heroes like Dread Knight and Atlas are stuck competing with those heroes when they're breaking into their primes. By contrast when Orntchya gets up to 1000 everyone from Natalia and earlier has wasted multipliers thanks to the 4100 cap.

Ok, I fiddled with it a bit more and now I can easily have it give me the amount needed for a given hero to hit a given level. Like, say, 1000. Some heroes are the best at the precise moment they hit 1000 - Treebeast, Ivan, Brittany, Fisherman, Samurai, Forest Seer, Frostleaf, and then every hero from Phthalo on up.

The 1000 level mark feels like it has to be the time when a given hero has hit their power apex relative to the others. It has an edge compared to the 2000 mark because there's no one further up the food chain close to hitting the 1000 mark and blowing you away. Terra is the best at 2000 as mentioned above, but only for a _very_ brief period of time. And then it tails off even more at 3000 where she gets passed by Cadmia, whoever is after Cadmia, Orntchya, and Lilin.


Anyway... What conclusions can I draw from all this rambling and numbers? I think if you're not even the best when you're at level 1000 you should never be the primary gild focus. As time ebbs and flows it feels like quite a few heroes are reasonable choices, and they happen to be the ones who are the best at 1000. I can see a case being made for any of Treebeast, Ivan, Brittany, Fisherman, Samurai, or Forest Seer when you're at the stage where buying Frostleaf is non-trivial. I think I'd lean towards Brittany myself, but Samurai is also a fine choice. Perhaps the best plan is to spread out your gilds amongst all of those bottom heroes to smooth out your boost from gilds. You'd need to level them all up, but that's fine. I do think once Frostleaf becomes an easy buy he becomes the dominant choice, mainly because I like only having to buy one hero on an entire ascension. (I click once to kill a unit and advance to level 140 thanks to Iris. Then I click the holiday trinket to make some money, buy some Frostleafs, and win. (I do buy 200 of everything just to make sure I get all the relevant buffs.) It's easy, and while Frostleaf does get passed for top spot by different heroes as time goes on he always stays near the top in power. Or at least, he did. The new heroes shake things up a bit. But the cheapest of the new champions are stuck competing with previous good heroes, including Frostleaf himself, and I don't think you can justify switching off of him to one of them. Phthalo might be where things change. Certainly if you're reaching the point where Frostleaf is running over level 4100 you have to make a change to something further up the chain. Even at something like 3900 Frostleaf he's still the 5th best option and only off the best (Cadmia) by a factor of 5.

So, I think the right strategy is to gild a bunch of the low level heroes. Then switch to Frostleaf. Then switch to something higher up when you reach the point you can afford that higher up hero pretty trivially. And I think I'm going to wait until at least Phthalo and maybe even Orntchya before I made a switch.

Clicker Heroes Update

Earlier this week Clicker Heroes came out with a new patch that added in 9 new heroes. I'd stopped playing recently but having some new things to enter into a spreadsheet was enough to bring me back. More numbers! Must make them bigger!

Unfortunately it doesn't seem like a whole lot of interesting thought went into these new heroes. Each one costs 1x10^15 times as much as the previous one. It does 7.37x10^12 times as much damage as the previous one. They all have the exact same upgrades, with the same cost progression, and all of the upgrades only work on the individual champion.

In short... Not a whole lot to figure out, sadly. Each one is worse than the one before it because the cost escalated more than the damage did. It'll probably shake out the same as Frostleaf did... Overpriced for a while, but eventually you get enough souls to make it trivial to get a bunch of a new hero when you ascend and then you'll want to pile all of your gilds onto that one.

On the plus side they did add in a shortcut where you can pay a little more to guarantee you gild the hero you want with a single click. You expect to spend 66 souls by doing it manually or you can pay 80 souls and get it done in one click instead of 33. That is a price I will _gladly_ pay should I ever decide I want my gilds on someone other than Frostleaf.

Will this update keep me playing? Well, it got me back into the game... And I can't buy some of the new heroes so maybe I want to stick around until I can do that... Or maybe I'll just quit again soon. Time will tell!

Clicker Heroes Wall

I'm finding myself running into a bit of a wall in Clicker Heroes. I want to have all the ancients because that seems like it might be a reasonable spot to say I've beaten the game. (Or maybe I need all the achievements?) But I don't want to just buy them, run out of souls, and say that's that. I want to buy them when it might make sense to do so. I've actually bought them all except for three: Thusia, Juggernaut, and Morgulis.

My next ancient is going to cost me 50000 souls, and Morgulis is likely the best of the terrible options left since I don't actually click very often. Morgulis makes all your hero souls 10% better. Which means that in order to break even on buying him for 50000 souls I need to have 550000 souls on hand when I buy him. Considering I only have 92077 souls right now, that's a long way off.

I can scoop up around 30000 souls in a very short run where I just go until I'm not one-shotting pretty much everything, but this requires pretty active playing for an idle game because I need to actually buy more copies of Frostleaf pretty regularly or my progress sputters to a halt. Alternatively I can push on and on, further ahead, but that really doesn't earn me many souls. I've now gone 4 days since ascending (figuring that while playing World of Warcraft I can alt-tab over to pull a full combo to pass a couple levels every now and then), have hit level 1739, but I'm only going to get 67k souls when I ascend. That's twice what I can get in under an hour, and a terrible rate of return. I am getting more Frostleaf gilds which is nice, I guess.

Mostly I'm just finding my motivation to play waning and I'm getting annoyed at how CPU intensive a Flash idle game seems to be. So maybe getting all the ancients is a pipe dream and I should just pack it in now. It's not like I have any interesting numbers to crunch anymore...

Clicker Heroes: Atman

One of the ancients in Clicker Heroes is named Atman and he costs a large number of souls to level up. His impact on your game is he makes it more likely to have primal bosses spawn as you're playing. Primal bosses are one of the two ways to earn more souls so he felt like a pretty good guy to have. Spend some souls now, get more souls later! The problem is not spending those souls makes you do more damage, which means you get to kill more things, which might well generate more souls themselves. Almost certainly I shouldn't have bought him when I did, but that ship has sailed. Now I want to at least figure out how many souls I expect to gain from an additional level in this guy so I can decide if I want to sink more souls into him now or not.

Typically on a soul farming run I'll get to level 145 and then reset. This gains me 8 souls from other sources and then some number of souls from primals I find from 105 to 145. My gut feeling is that's been about 4 extra per run. How does that stand up? Well, by default each boss has a 25% chance to spawn as a primal and is worth some number of souls based on the level. In this level range I have 4 shots at 1 soul, 3 at 2 souls, and 2 at 3 souls. Which actually averages out to 4 per run. Anyway, that also means that adding an extra 1% chance of spawning a primal on each level will gain me a whopping .16 souls per run. I can do a run every half hour, so if I were to spend the 23 souls on the next level I'd expect to make them back after 144 runs. So about three days to break even, assuming I didn't lose any time by giving up 10% of my damage, anyway... Which all seems pretty terrible, actually.

But what if I go deeper? My longest run ever killed the boss of 260 who is actually worth 13 souls. The total of all those souls could total 194. Getting an extra 1% of those would get me almost 2 souls per run, but that run took me a day. That's 11 and a half days to break even, which is worse than the fast run case.

I'm all about long term rewards, but a week and a half to break even on the cost even if it didn't drastically reduce my damage is a bit much. Until I really ramp up my ability to farm for souls I don't think I should be sinking any more souls into leveling Atman up any further.

Clicker Heroes: Reload

Clicker Heroes has 9 abilities you can learn as the game progresses. Each ability does something and then goes on cooldown for a set length of time before you can use it again. One of those abilities, reload, has an hour long cooldown and reduces the cooldown of your previously used ability by an hour. We were chatting about the game the other day on Skype and were trying to find ways to make good use of this ability.

First of all, 6 of the other abilities all last 30 seconds, have durations ranging from 10 minutes to an hour, and give you a combat relevant buff. It clicks for you, or your clicks are more powerful, or you make more gold when you click... They're all multipliers that stack with each other and the best way to use them is to pop them all for the same 30 second stretch of time. Initially it seemed like the thing to do would be to figure out which ability of those 6 was the best one, reset it, and pop it again in the same window. Unfortunately it turns out that doesn't actually give you a second application of whatever ability you reset. It probably refreshes the duration but it doesn't give you any extra power. And since 2 of these abilities are on an hour long cooldown there's no way to use reload to sync them all up for a different 30 second window.

The next ability is energize which has an hour long cooldown and doubles the power of the next ability you use. It interacts with reload in odd ways. For one, you can never actually reset the cooldown of energize. Reload skips energize and resets the cooldown of the ability used before the energize. Reload can be energized and if you do so it knocks an hour off the cooldown of your previous two abilities used, skipping the energize itself. In an interesting turn of events if reload itself was one of those two abilities it will consume the buff but it won't actually reset the cooldown of reload. This means if we could find two things worth refreshing we could do them both at the same time. I guess you could actually use this to reset the cooldown of both hour long buffs from the previous paragraph to allow you to pop your combo 2 times every hour and a half instead of once an hour. I'm pretty sure just using the energize on the combo itself would be a better thing to do, though.

The last ability is the one that really screams for a reload. Dark ritual has an 8 hour long cooldown and gives you a permanent 5% damage boost. Extra damage is good! If you could target your reload on an ability of your choice things would be easy and you'd just use it on dark ritual. Unfortunately only having it impact your most recently used ability means you need to be careful about your clicking order and it means you can't just spam the reload on dark ritual. If you time things careful you can pull off two reloads per dark ritual, though. Use dark ritual, use reload, and then do nothing else. In an hour come back, use energize, and use reload. This will reload your two most recently used non-energize abilities which happen to be reload and dark ritual. This only works once (try it again and you're reload two reloads) but it does work. Getting to use dark ritual every 6 hours instead of every 8 hours is totally worth it. I don't think there's another relevant use for reload, but this one use is pretty good.

It gets even better once you unlock some ancients! One of the ancients permanently reduces the cooldowns of all your abilities. At max rank (where I have him) he takes a full 75% off of the cooldown for every ability. This means my dark ritual only has a 2 hour cooldown and my reload only has a 15 minute cooldown. I can use an energized dark ritual every 30 minutes! (Energize, dark ritual, reload... energize, reload... Repeat.) I can even use my other abilities as bookends right before the first energize and right after the second reload. It's pretty sweet. I was trying to figure out a way to do better than that, but the problem really is that you need to use the second energize on reload or there's no way to get the dark ritual cooldown under an hour. So you can do one 10% buff each hour while using your full combo 3 times in the hour or you can do two 10% buffs each hour and never do your full combo. If you really need to use your full combo on a boss you could leave dark ritual unused for an extra 15 minutes and do one 10% buff and one full combo every 45 minutes as a compromise between the two. Or you could just not buff one of the dark rituals I guess... Do a 10% and a 5% each hour. That's better than the last option. So, yeah... Always reload the dark ritual, always energize the second reload, and maybe energize the dark ritual or your combo depending on your current boss killing needs.

Clicker Heroes

Possibly the worst thing you could do with a hand injured through repetitive strain would be to start playing one of the browser clicker games. Well, I'm pretty stupid, so I started playing Clicker Heroes as soon as Sthenno posted about it. But I'm not playing with my right hand, so it's actually not such a terrible idea as it could be. It's also a game where playing without clicking seems pretty reasonable. My left hand is starting to get pretty good with a mouse, but it's sure not super fast at clicking, so that's a good thing.

Normally these clicker games have you click to earn something (like a cookie) and then you start spending that something on things that make more somethings. Numbers getting bigger, woo! In this game you click not to generate a resource directly but to do damage to a monster. Do enough damage to the monster and it explodes in a shower of gold. You can spend the gold to make your clicking do more damage or to do passive damage over time. Sure, the end result is you're spending gold to earn more gold but adding that extra step in the middle makes things novel and fun.

I really want there to exist a game that combines something like Progress Quest with Cookie Clicker. This isn't quite there since it's missing random (and I mean RANDOM) loot drops but it's a step in the right direction. Maybe it's a step that will convince me to work on one of my own? I doubt it, but it is something to mull over some more.

I'm enjoying this game, anyway. If you like browser clicker games you should check this one out.