Using Quanta Index to determine the optimal number of Pillars in a deck

[Essence]

Random musing on QI theory.

You want 1 pillar per 5CC of casting cost. 

There are 12 elements.  Quantum Pillars produce 3 random quanta.  On average, then, 25% of elements get a quanta per turn -- or, statistically, each element gets .25 of a quanta per turn.  Therefore, with 4 Quantum Pillars, you get the same net effect as though you had 1 pillar of each kind -- statistically.

So, in order to find the right number of pillars in a half-rainbow deck, you need to find the one sub-element that has the highest total CC, divide that by 5, multiply that by 4, and then add that many Quantum Pillars.  Then, with your main element, subtract 1/4 of your Quantum Pillars from the total number of on-element Pillars you put in.



So, for example, if you have a half-Light deck with 46 total CC in Light, and the other half is rainbow with the highest CC being a Toadfish (5), you need

5/5=1x4=4 Quantum Pillars, and
46/5=9-(4/4=1)=8(-1 for a Light Mark)=7 Light Pillars.  Total of 13 pillars, 4 Quantum and 7 Light.


No idea how to take Novas into account; I usually just swap them out 1-for-1 with QPs.

[UTAlan]

Is it feasible for the quanta generation of one card to be calculated based on other cards in the deck? For example, you might base the light quanta generation of luciferin off of the number of ability-less creatures in the deck.

Possible? Yes. Easy? No. I'm currently processing the cards one at a time, in the order they appear in the deck code. This requires a second pass, as it would need knowledge of all cards in the deck, not just the ones it has already processed. I'll think over how I could implement it, though. Once I know how many ability-less creatures in a deck, what would be the estimate of quanta generation? One per ability-less creature? Two? Five?

[Onizuka]

That number would have include any creature with dejavu as its ability as well. 

I'd probably rate each non ability creature as like 2~4 light quanta.

[silux]

1:5 ratio is never right but in a case;
you use that

To get a useful amount of pillars:

• find a nice combo-sinergy;fill in one pillar for every 3-5 cards
• test 3-5 times the deck in the trainer
• add or take away pillars and return to point 1

Or if you feel good at maths you can find best number of pillars using function analysis (you must find the integral of the f(x) written on the card)(I use 7math for this)

[UTAlan]

That number would have include any creature with dejavu as its ability as well. 

Good point.

I'd probably rate each non ability creature as like 2~4 light quanta.

That seems a bit much to me. In reality, you are unlikely to have every ability-less creature in the field of play when you play luciferin. I was thinking 1 light quanta per. This should balance out the creatures that aren't played versus the ones that generate more than 1 quanta in a game.

[tyranim]

i dont know if this has been answered yet or not, but what about towers? how would one change the formula to include the quanta produced when a tower is played?
and pends

[Chromatophore]

i dont know if this has been answered yet or not, but what about towers? how would one change the formula to include the quanta produced when a tower is played?
and pends

How does it factor in things like producing creatures, pests, immolation, nova/supernova, soul catchers, luciferin, pendulums, and upgrades?

QI is COST / # PILLARS, with the assumption that a pillar generates 5 quanta (on average) per game. I modified the formula a bit to account for these other cards, doing COST / GENERATION, which is broken down by element. For example:

* Aether Pillar: 0 cost/5 generation
* Aether Tower: 0 cost/6 generation
* Aether Pendulum (nonupped): 0 cost/2.5 generation/2.5 Mark generation
* Aether Pendulum (upped): 0 cost/3.5 generation/2.5 Mark generation
* Devourer: 2 cost/1 cost/5 generation
* Cremation: 0 cost/9 generation/1 generation for all other elements
* Nova: 0 cost/1 generation for all elements
* Supernova: 2 cost/2 generation for all elements

(In the end, I actually do COST / (GENERATION / 5) to keep the formula consistent with the generally accepted QI values, but the result is the same.)

Not sure if everyone uses the same method but this is more or less what i use

[Xenocidius]

I've been reading this topic and considering the ideas involved.

I think quanta-producing creatures should each be counted as a pillar, but that their casting cost is still added to the total cost of the deck. Applying this to the Darkness deck:

Total amount of quanta used to pay for cards: 10*6 (dragon) + 2*6 (devourer) + 4*3 (steal) + 4*3 (drain life) = 96.

Total number of pillars in deck: 12 pillars + 6 Devourers = 18.

So, the QI would be 5.33, a much more realistic indication of the deck's quanta balance.

Now, by analogy, towers can be calculated. They are effectively pillars with a casting cost of -1. So, if that darkness deck had all pillars upgraded, then:

Total amount of quanta used to pay for cards: 96 + (-1*12) = 84.

Total number of pillars in deck: 12 pillars + 6 Devourers = 18.

So, the QI would be 4.66, which means there's room for some of those dragons to be upgraded as well.

Marks are another issue - I'd count them as two pillars. Seeing as they are usually splashed to power 6-12 quanta, which would give a QI of 3-6, this seems about right. It would lower the QIs for each of the decks in the OP, and would also lower the average, "standard" QI. Applying this to the above darkness decks gives 4.8 for the pillars version and 4.2 for the towers version. Considering that previously their average was 5, the "standard" QI, the new "standard" QI should be the average of 4.8 and 4.2, i.e., 4.5.

Alright, moving on to abilities. Using the classic example of Inundation, it uses 1 quanta each turn. It effectively negates one pillar. So perhaps you should take one pillar from the total number of pillars in deck count (no need to compensate for multiple Inundations, as you'll only play one at a time)? Note that this also applies for abilities that you will use each turn no matter what.

Of course, the flaw here is that Inundation is situational (you won't always play it). This also applies for cards which you won't always play (like Steal). In fact, maybe their costs should be halved for the purposes of QI? QI is a fairly crude concept, so it probably doesn't matter too much, but if we wanted to really get technical about this, it could be an option.

So, to summarize in a formula, we have:

QI

=

Anything that affects the quanta pool just once Anything that affects the quanta pool each turn

Marks are counted as two pillars. The standard QI is 4.5.

As for decks with more than one element, the only reasonable solution seems to be to calculate their QIs separately. Here's how it works:

• Pendulums count as half a pillar for each element they generate for
• Upped pendulums are like normal pendulums, but with a casting cost of -1 for the element they belong to
• Quantum Pillars count as a quarter of a pillar for each element
• Quantum Towers are like Quantum Pillars, but with a casting cost of -0.25 for each element
• Other cards cost q/x for each element, where q is their cost in , and x is the number of elements for which quanta are being generated

Unfortunately, this doesn't quite work for rainbows, as they have cheap cards and they usually have a lot of quanta left over, which leads to a much lower QI than is realistic. So I won't talk about them here.

Applying the above principles to a simple Darkness/Earth denial deck:

Code: [Select]

593 593 593 593 593 593 5um 5um 5um 5um 5um 5um 5uv 5uv 5uv 5uv 5uv 5uv 606 606 606 606 606 606 606 606 606 606 606 606Total cost of cards and abilities in Darkness: 2*6 (Devourers) + 5*6 (Gargoyles) = 42
Total "pillars": 12/2 (pendulums) + 6 (Devourers) = 12
QI: 3.5

So there's a fair bit of quanta going around, and could be optimized further.

Total cost of cards and abilities in Earth: 3*6 (Earthquakes) + 12 (abilities) = 30
Total "pillars": 12/2 (pendulums) + 2 (Mark) = 8
QI: 3.75

So there's also a fair bit of quanta going around, and overall the number of pendulums could be decreased.

So that's my two cents on using QI for duos and trios. The only thing that's left is making it work for rainbows.

Edit: The QI program (http://www.quantum-index.com/) seems to take some of these things into account. Sorry if my ideas are repeats of what other people have come up with.

[Blues]

"- if the ability happens automatically each turn (for example Devourer) it gets counted twice"

That's confusing.
When an ability happens automatically each turn, why count the card with this ability twice?

[Xenocidius]

"- if the ability happens automatically each turn (for example Devourer) it gets counted twice"

That's confusing.
When an ability happens automatically each turn, why count the card with this ability twice?

Only the ability cost is counted twice (Devourer's ability "cost" is -1, Flooding's ability cost is 1, etc.). As I've said above, I prefer to put them in the pillar count.

[Camoninja]

I think you count the automatic skills twice because you're assuming that the average of the duration of whatever card it is, is assumed to be two turns.

[Camoninja]

How do you count QI for quantum usage of Nymph's Tears?