Numbercraft (the math behind GCL) page 2

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it simplifies to (S/U)^.53.

 
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Duh, mine was way too complicated. I knew there had to be a better way. Thanks, fractalman.

 
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That means…

X^(1/.53)*U = number of summoned monsters needed

X being desired multiplier
U being unsummoned monsters

with 13,102 unsummoned monsters(9.8 giants * 1337 waves, NOT including the ones that the shadow spawns), it would take about 41,385,667 summoned monsters to beat 71.57 multiplier D:
31K monsters / wave for 1337 waves… might be possible theoretically (as Y/L is imba strong) but i don’t think my computer can take that :P

Edit; refined calculations – average giants / wave is 2.45 (tested in D10 & C2 endurance with x1 monsters, giants only – results were 3,273 & 3,279 monsters killed)

 
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Shouldn’t there be a 1 somewhere? I mean even with 0 summoned u get 1.00x (duh). I guess thats why the lower numbers dont really fit the regression.
So how about (S/U)^X
1?

 
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Interesting: a “+” is seen as underlining.

 
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…hm…maybe ([S/U]+1)^.53…

 
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I did a little bit supergem testing. I tried also to find a formula for the damage increase for low gems but as far as i can tell these numbers are arbitrary.
The damage increase from Gr>12 is 56.9 to 57.5% depending on gem grade (the higher the more increase). Range increases for 8.18% per level, FS for 18.0%. Without FS increase the damage increases ~199% per grade for a Y/L but with the FS increase the dps increases for 211% to 251% (the higher the grade the better).

Y, L and O increase with 38% per grade, R for an awful 9% and B for 25%.
I tried a high R/Y/L gem (gr35) to see the effectiveness of red there. But you need more than 1 million kills for the gem (depending on grade) to reach the damage that a pure Y/L gem does for the same mana (wtf?). Completely useless.

O is useless past 20 or so since u fill the pool once per frame anyway. So the best gem is Y/L dual (has higher damage than any 3-colour gem). But I might try Y/L/B since the slow is pretty much a stun at higher levels.

I managed to manapool ~900 times per frame (with a macro of course) being pretty close to the max of once per frame.
My macro managed 502 duplications per frame (2 frames per duplication) which leads me to believe that a wave is actually 33.5 seconds and not 33 seconds giving 1005 frames per wave (can someone confirm this?). Manually it is possible to do 1 duplication per frame.

 
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how come 199% increase is lower than 2? See, an increase of 2.0 equals to 100% increase, and 199% roughly equals to 3.0.

weird though that damage increases so weirdly, the higher the more, even with those small percentages. But this means that pure Y gem grows faster than 2.0, and it too will require a nerf once it will come to game balance. Bad IMHO.

 
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Right. I first thought increase to 1,99 but its an increase by 1.99. I should read my own formula…

And L needs a nerf too. It’s just too powerful an gems 9+. Especially since it hits the same targets in traps.

 
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What grades are best to anger with? I’m level 219.

 
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If you are going for a summon multiplier (every game except endurance) it probably is worth to avoid the grades in this post http://www.kongregate.com/forums/23-gemcraft-chapter-0/topics/146498-numbercraft-the-math-behind-gcl#posts-3271197 when angering a lot.

Low grade = lots of gems needed to summon a lot of monsters → high HP / armor increase after several angers.
high grade = lots of monsters summoned with a single gem with a moderate Hp increase & low armor increase.

I usually anger with grade 1-3 in normal games as you usually don’t summon more then 10-20 monsters a wave anyway.
In longer games like endurance i summon with as high grade as possible (without making a too big gap in my mana pool/defense), summoning 50 (or 500-2000, lol) monsters in a single wave with a grade 8-9 or with 10 grade 1’s make a huge difference in hp/armor.

 
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also, non-premium, whats left to do once you’ve beaten the game?

 
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Originally posted by Streaks:

also, non-premium, whats left to do once you’ve beaten the game?

pylon levels

 
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how do people get such high summoning multipliers? it seems like you’d have to summon a shit load very early on to keep the number of unsummoned monsters low.

 
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You can try to get all (or as much as possible) journey/challenge amulets.

Beside that… can’t think of much. You could try to beat all maps again on highest difficulty setting for more exp although endurance is the best by far for exp.

And yea, as slogsdon said, you can try beating all waves in a pylon lvl (although it will give less exp then a endurance game unless you do some insane summoning)

 
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Originally posted by pongi01:

I did a little bit supergem testing. I tried also to find a formula for the damage increase for low gems but as far as i can tell these numbers are arbitrary.
The damage increase from Gr>12 is 56.9 to 57.5% depending on gem grade (the higher the more increase). Range increases for 8.18% per level, FS for 18.0%. Without FS increase the damage increases ~199% per grade for a Y/L but with the FS increase the dps increases for 211% to 251% (the higher the grade the better).

Y, L and O increase with 38% per grade, R for an awful 9% and B for 25%.
I tried a high R/Y/L gem (gr35) to see the effectiveness of red there. But you need more than 1 million kills for the gem (depending on grade) to reach the damage that a pure Y/L gem does for the same mana (wtf?). Completely useless.

O is useless past 20 or so since u fill the pool once per frame anyway. So the best gem is Y/L dual (has higher damage than any 3-colour gem). But I might try Y/L/B since the slow is pretty much a stun at higher levels.

I managed to manapool ~900 times per frame (with a macro of course) being pretty close to the max of once per frame.
My macro managed 502 duplications per frame (2 frames per duplication) which leads me to believe that a wave is actually 33.5 seconds and not 33 seconds giving 1005 frames per wave (can someone confirm this?). Manually it is possible to do 1 duplication per frame.

When combining two identical gems, the minimum damage increases by 54%, and the maximum damage increases by 58%. At low levels, a bit of randomness of +/-1 damage will be added. This is true even for creation of all gems directly, and that’s why there’s variation on damage. It ends up being a binomial distribution of min/max damages. Most of the time the effect is quite minor. All gems of the same color have the same grade 1 stats though. I didn’t really check the increased value of range, since it was so small, but for me it was 8-9%. For firing speed, it’s exactly 18%. (So for pure gems, it’s exactly grade1_value * (1.18) ^ (grade -1)). Combining gems and firing speeds are unknown, and same goes for damage.

Specials increase by 58% for poison, and 38% for Y/L/O (and also purple), 25% for B/C, and 9% for red. All percentages are exact. Red was designed to be useful at lower grades, it just doesn’t scale, which I think is fine.

Gems that are combined with a gem of the same grade that doesn’t have it’s own color, their specials are reduced, depending on the color, doesn’t matter if pure gems or dual gems are involved. Remember that duals and triple gems have only 80% specials. Poison damage is 96% (so 4% reduction), purple is 93%, Y/L/O is 88%, B/C is 87%, and R is 78%. (I also tested poison with combining with lower grades, it’s 97% for -1 grade, and 98% for -2 or more, but the stats are still horrible). An interesting case is that with interesting combining you can actually get slightly more damage and specials (and dps) from combining your gems instead of duplicating and combining the two gems. So I can typically make a dual gem of the same grade have about 18.5% more specials that most dual gems (damage is increased as well). Testing was done with Y/L gems since those are the most popular:

grade 12 pure gems: 871% crit if Y, 778% chain, if L.
grade 13 dual: 613% crit, 548% chain. (combine 2x pure)
grade 14 dual: 846% crit, 756% chain. (combine 2x 13 dual)
grade 15 dual: 1168% crit, 1043% chain. (combine 2x 14 dual)

However, you can get a better grade 15 dual by doing the following:
grade 14-Y: 1153% crit, 482% chain. (13 dual + 13 pure Y)
grade 14-L: 540% crit, 1029% chain, (13 dual + 13 pure L)
grade 15-super: 1284% crit, 1147% chain. (14-Y + 14-L)
There’s a 10% increased damage compared to if you combine dual gems directly.

You can repeat the process, but it maxes out at ~18.5% increased in specials. I didn’t test damage exactly, but at least with this you can get about 1.185^2 ~ 1.40 or 40% damage increase by a combining trick.

There are exactly 1000 frames per wave, which is 33 seconds and 10 frames. It was the same as in GC0. Counting frames was easier in time seige mode. =p The wave bars used to be 50 pixels wide, so they used to move once every 20 frames, but Peter shrunk the bars to 45 pixels for GCL, so they mode oddly now.

 
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Interesting. So it’s better to duplicate the pure gems and only combine for the final gem.

For what colours is this also true? I tried L/O (nothing) and Y/L/O (the last added was a little bit stronger and one of the other weaker (i don’t know which, there seems to be ranking of priorities???).

Edit: Now I see. I guess it’s because the last added pure colour gets a bonus. The effect is even stronger if you do this twice (combine 2 grade 15-super with gr15 pure Y and L and then combine to gr17-super-super). I don’t think it works with 3 colour gems since the third colour will get a penalty.

A grade 12 with 5 of these steps has a ~18.2% increase of the specials and a grade 18 with 8 steps has a ~18.5% increase. Not much difference anymore but you can squeeze out another 8%.

 
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Originally posted by frostlion:

If we do all this, we get the following base effectiveness (shown in both a linear and a log graph):

formula used: 60 * [mana gain per hit] * [firing speed] / {[gem cost] + 200}
Note: I didn’t actually have the firing speed for orange on hand, so I cheated and used the one for yellow gems. A fair approximation because yellow is around 10% faster, but it scales roughly the same.

So what we see is, to keep this gem gaining the same amount of mana per minute, you need to double the mana pool multiplier going from grade 4-8, double it again by grade 12 (to 4X), get it to 8X by grade 15 and to 16X by grade 18.

Overall, an orange gem scales acceptably, but it won’t make you rich without some serious investment in mana pool (and if you can invest in that, what do you need the gem for?)
It doesn’t get really interesting until you throw it in a trap combined with a lime gem and get a chance to multiply your mana gain by the number of chains as well!

Do you have a graph for lime/orange gem scaling?
And also, does anyone know the formula for the cost to extend your mana pool?

 
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Did this a while ago (without graph though). DPS is damage per second, MPS mana gain per second (if the gem fires continuosly). DPS/cost MPS/cost is clear I hope. DPS L/O O is the damage difference between an orange and L/O of the same grade. The MPS is of course without the mana gain multiplier.

Notice that these values are for traps with deadly traps @max. For towers you have to halve the MPS and double the DPS of Orange. The DPS of L/O reduces not by factor 2 since the chains increase dps. So its hard to calculate. But L/O should always be in traps since the chains only hit the same target twice when in traps (AFAIK). (BTW: Which causes massive lags for high grade L/X since the game has to calculate 1000+ chain hits. At least thats what I think is the reason.)

Notice that with the trick above you can gain another ~39% MPS (at least for the higher gems).

 
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Originally posted by Streaks:

Do you have a graph for lime/orange gem scaling?
And also, does anyone know the formula for the cost to extend your mana pool?

Extend mana pool (regardless of mana pool mastery):
Next value = current value + round((current value + 773)/200)*10
The round function rounds to the nearest integer. I think 773 is correct, but it’s like close to it.
It also maxes out at 95% of your max mana.

 
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Originally posted by fractalman:

it simplifies to (S/U)^.53.

this has to be wrong , because the easiest datapoint is : 0 summoned and mult is 1.0
for S = 0 you would get a mult of 0… has anyone already some more data ? and i saw a pic somewhere here with
Summon = killed ==> mult = infinity which tells me that you could reach a mult close to infinity if S is really really big and killed = S +1. i hope i could help

 
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Originally posted by karstenSchrank:
Originally posted by fractalman:

it simplifies to (S/U)^.53.

this has to be wrong , because the easiest datapoint is : 0 summoned and mult is 1.0
for S = 0 you would get a mult of 0… has anyone already some more data ? and i saw a pic somewhere here with
Summon = killed ==> mult = infinity which tells me that you could reach a mult close to infinity if S is really really big and killed = S +1. i hope i could help

If you get a multiplier of infinity, then there was a division by zero.

 
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here is what i got ( nonpylon – if theres a diffrence)

Killed

 
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Killed Summoned SummonMultiplier

238 132 1.54
111 5 1.02
136 30 1.14
181 75 1.33
165 59 1.26
106 0 1.0

 
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I think it could be a little more than 0.53
The formula Multiplier = [Killed/(Killed-Summoned)]^0.53 it’s right
if summoned = 0 => Multiplier = 1
If summoned = killed => Multiplier = (killed/0)^0.52 = infinity (killed ≠ 0)
if (summoned-killed = 1) => Multiplier = killed^0.53 (high number)
If summoned > killed => Multiplier = complex number (but there will be a special case in the code)