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

[Scaredgirl]

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

I have been thinking about this a long time now. I talk a bit about it in here (http://elementscommunity.org/forum/index.php/topic,3329.msg32882#msg32882) but this is an important question so it really deserves its own thread.

The mistake many people make is that they take pillars depending on how many cards they have, when they should be asking: how much quanta is used?


There are roughly three different situations depending on how much quantum you produce.

1. You produce too much quanta. Your hand is usually small, and you keep drawing Pillars. "Damn, where is that Dragon?! I'm so unlucky!"
2. You produce too little quanta. You usually have a hand full of high cost cards but no quanta to pay for them. "Wtf, no Pillars?! I'm so unlucky!"
3. You produce optimal amount of quanta. Both your hand and you quanta reserves are empty but your table is full. You play cards as you draw them. "I'm pro".

This QI system tries to achieve situation #3 by adjusting the number of Pillars so that you don't overproduce or underproduce.


I decided to use simple math and the excellent thread Deckbuilding 101: From Noob to False God Slayer (http://elementscommunity.org/forum/index.php/topic,1190.0.html) by jmizzle7. I too all 12 decks in that thread, counted quanta usage, and divided that by number of Pillars in that deck. I call it Quanta Index (QI).

QI Quanta Index

=

Total amount of quanta used to pay for cards + ability costs Number of pillars in the deck

Counting card costs is easy. Where this becomes difficult is when we have to take into consideration the quanta used to pay for abilities. I used this method:

- if the ability happens automatically each turn (for example Devourer) it gets counted twice
- if the ability is non-situational as in player will play it if he has quanta (for example Chrysaora, Hourglass) it gets counted twice
- if the ability is situational (for example Maxwell's Demon) it gets counted once

PART 1 - QI for all 12 decks

Here are the results for all the 12 decks in that thread:

QI = 7.867	QI = 6.75	QI = 6.5
QI = 6.353	QI = 5.875	QI = 5.5
QI = 5	QI = 4.588	QI = 4.5
QI = 4.235	QI = 4* *I counted one Immolation giving +7 and other doing nothing	QI = 2.727

If the QI is high that means there is not enough quanta produced.
If the QI is low that means there is too much quanta produced.

As you can see, the results are quite interesting.

You can instantly see that the Aether deck uses WAY too much quanta. I went to test this and QI is definitely right. When you play this deck, it's very likely that you are in a situation with bunch of high cost cards in your hand but no way of paying them.

The medium seems to be about 5. So we could say that for each 5 quantum you use, take one Pillar. This is of course just a rough estimate and guessing. Further study is required.

PART 2 - Improving the decks using QI

So I decided to take the decks with the highest and lowest QI and improve them using the formula. Decks are Aether and Water.

WATER

Water deck has a QI of 2.727 which is clearly too low. Some people might say that it needs those Pillars to be fast, but those people are wrong.

I played 10 matches with the original deck, and there was clear over production of quanta. after only a couple of turns I had 20+ Death quanta and kept on drawing Pillars.

Code: [Select]

4t3 52g 52g 52g 52g 52g 52g 52g 52g 52o 52o 52o 52o 52o 52o 52p 52p 52q 5i5 5i5 5i5 5i5 5i5 5i5 5i7 5i7 5i7 5i7 5i7 5i7QI = 5

I the switched 2 Pillars to 2 Plague, and 1 Pillar to Arsenic, changing decks QI from 2.727 to 5 and the results were much better. I could instantly see how my quanta production was more balanced and my deck better.



AETHER

Once again started with the original deck. I found it to be slow and sluggish. Annoying to play because I spent my time stalling and waiting for quanta.

Code: [Select]

61o 61o 61o 61o 61o 61o 61o 61o 61o 61o 61o 61o 61o 61o 61o 61o 61o 61o 61s 61s 61s 61s 61s 61s 61t 61t 61t 61v 61v 61vQI = 5.333

After my changes, QI dropped to 5.333. I just took some cards by random because what the cards are makes no difference in this experiment, only card cost is relevant.

Just like with the Water deck, I could instantly see an improvement. The new Aether deck was much faster and more enjoyable to play. No more stalling and waiting, I could play something almost every turn and my hand had only 1-2 cards most of the times. I could probably drop QI below 5 and still have good results.


I'll post most findings later. Anyone who doubts the awesomeness of Quanta Index, try this little before-after experiment and see for yourself.

PART 3 - QI Report

What we need now is for someone to make a piece of code, that automatically counts QI.

It would look like Deck Image Creator (http://helltgivre.free.fr/elements/), only instead of an image, it would show the QI of your deck, and possibly even a small report where it would say something like this:

QI REPORT

Deck information:
Cards = 30
Total Cost of Cards = 72
Total Cost of abilities = 12
Number of Pillars = 11

QI
Your QI is 7.315 which is means you have too few pillars.

Fix:
Remove 2 copies of Golden Dragon.
Take 2 copies of Light Pillar.

This will change your QI to 5.152.

Who wants to waste his/her time in doing something like this?

Ok, I need to take a break. I'll write some more stuff later.

I've never studied math in a University level and I would really like to hear some input from all you math nerds out there I'm sure there are many variables that I haven't taken into consideration.

We could potentially design a mathematical formula that tells you the optimal quanta usage without ever even testing the deck (I already did that with the Aether deck). That would be pretty cool.

Discuss.

[Glitch]

=o

Seems good.  I'm confused how lucifrase and quantum pillars would work, and I'm not sure how upgraded pillars get counted, but I definitely see how this could help newbies.

[Scaredgirl]

=o

Seems good.  I'm confused how lucifrase and quantum pillars would work, and I'm not sure how upgraded pillars get counted, but I definitely see how this could help newbies.

Quantum Pillars and all Towers would have their own formula. This one works only with regular Pillars.

And this isn't just for newbies. 99.99% of players don't calculate these things in their head, they just take some amount of Pillars and test it. For example I've built 100+ decks and I've always tested what the optimal number of Pillars is. Had there been this kind of formula (proven to work) it would have saved a lot of my time.

[Astaroth]

Yeah, this is definitely a nice look into how many pillars are needed in a deck. I have a question though. Wouldn't decks with quanta-producing creatures show a much higher index than what it really is? For example, that Dark deck has 6 quanta-producing Devourers. Wouldn't its QI be a bit lower?

[Kael Hate]

Evaluating decks via Cost is good for a basic check, but there are variances that you need to look at when heading to refine. An Example is the Life deck. after you have 5 life pillars on the table there is no more need as you can only play 1 card per turn and no further need to stcokpile. The decks with big Dragons like the entropy deck need more to get to the critical 1 card drop. The Darkness deck is an exception because it generates quanta from devourers. The Aether deck can run a little short because you get a 3 turn stall off of each shield.

[Kamietsu]

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

What? How does that even work? Only one ability in all of Elements happens each turn and costs quanta (Inundation). Devourer doesn't have an ability that costs quanta that happens automatically each turn.

[Cynxos]

Wow...
This is... Pretty usefull.
But I'm not sure regarding the entire "fore each 5 quantum take 1 pillar" thing.
In a way it seems like it wouldn't be efficient enough. And as for the stats regarding the Poison deck, I KNEW IT!

[Scaredgirl]

Yeah, this is definitely a nice look into how many pillars are needed in a deck. I have a question though. Wouldn't decks with quanta-producing creatures show a much higher index than what it really is? For example, that Dark deck has 6 quanta-producing Devourers. Wouldn't its QI be a bit lower?

Yes, you are right. Quanta-producing creatures have to be taken into consideration. They are that "ability happens automatically each turn" I talk about in the original post.

In case of Devourers, I counted them so that each Devourer uses his quantum drain ability twice, lowering the "total amount of quanta used to pay for cards". So if you have

My reasoning behind this is that some Devourers in your deck probably use the ability 4+ times (Devourers in your opening hand) while others don't use it at all (Devourers at the bottom of your deck). This gives us a highly theoretical average of 2 per Devourer.

Evaluating decks via Cost is good for a basic check, but there are variances that you need to look at when heading to refine. An Example is the Life deck. after you have 5 life pillars on the table there is no more need as you can only play 1 card per turn and no further need to stcokpile. The decks with big Dragons like the entropy deck need more to get to the critical 1 card drop. The Darkness deck is an exception because it generates quanta from devourers. The Aether deck can run a little short because you get a 3 turn stall off of each shield.

Yep, this is just the basic framework. It of course needs some fine tuning based on what the actual cards are.

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

What? How does that even work? Only one ability in all of Elements happens each turn and costs quanta (Inundation). Devourer doesn't have an ability that costs quanta that happens automatically each turn.

See part 1 in this post.

Wow...
This is... Pretty usefull.
But I'm not sure regarding the entire "fore each 5 quantum take 1 pillar" thing.
In a way it seems like it wouldn't be efficient enough. And as for the stats regarding the Poison deck, I KNEW IT!

I listed proven deck that have a QI of 5 or even less. It's enough.

What the optimal QI is, I have no idea. That 5 was just guess, and it sounds better than 4 or 6.

[Boingo]

While I applaud the effort to objectively justify the number of pillars/towers in a deck, I think the answer will depend to a great extent on what type deck (and/or player) you are facing.  In other words, the optimal number of pillars may shift dramatically when playing a T50 PvE as opposed to playing the actual T50 player PvP. 

1. Some of this will depend on how many "dead" cards you have where the card will not get played as it won't have an major effect on the outcome of the game, as with plague against an deck or a given shield against a deck with momentum.

2.  Can you treat rainbow decks in the same way as mono decks?

3.  Other important variables may include cards like fractal--for example, how will fractal alter the number of pillars you need in a pest/fractal deck?  Does it depend on the number of fractal cards in the deck?  What about pharoah or FFQ?

Finally, the number you calculate gives you an idea of how much you'd need to play every card in the deck and not how well the deck will do in a given match where rarely are all the cards played.  I fear the optimal number of pillars may only be determined for a given opposing deck.  As such, there may be an optimal number for performance for each of the decks you've listed against a standard shrieker deck, but there's no telling if these numbers would be different for the same decks when facing flying titan deck or a water poison deck.

This is not proof one way or the other, I just raise some speculation on the premise of the exercise.

[Thalas]

Nice Scared Girl.
I think best is try number of pillars in game and you don't have to calculate it.
There are some factors that are unpredictable like opponent's deck, randomness and many other things.

[Scaredgirl]

While I applaud the effort to objectively justify the number of pillars/towers in a deck, I think the answer will depend to a great extent on what type deck (and/or player) you are facing.  In other words, the optimal number of pillars may shift dramatically when playing a T50 PvE as opposed to playing the actual T50 player PvP. 

1. Some of this will depend on how many "dead" cards you have where the card will not get played as it won't have an major effect on the outcome of the game, as with plague against an deck or a given shield against a deck with momentum.

2.  Can you treat rainbow decks in the same way as mono decks?

3.  Other important variables may include cards like fractal--for example, how will fractal alter the number of pillars you need in a pest/fractal deck?  Does it depend on the number of fractal cards in the deck?  What about pharoah or FFQ?

Finally, the number you calculate gives you an idea of how much you'd need to play every card in the deck and not how well the deck will do in a given match where rarely are all the cards played.  I fear the optimal number of pillars may only be determined for a given opposing deck.  As such, there may be an optimal number for performance for each of the decks you've listed against a standard shrieker deck, but there's no telling if these numbers would be different for the same decks when facing flying titan deck or a water poison deck.

This is not proof one way or the other, I just raise some speculation on the premise of the exercise.

1. What your opponent has of course affects what your optimal number of Pillars is. Unfortunately you can never know what your opponent is going to play so you cannot really prepare for that. All you can do is try to find the optimal number in most cases.

2. Probably not. Rainbow decks seem to require less Pillars than mono-decks.

3. That's where advanced math comes into play. I'm sure there is some complicated formula that would do this but we don't know what it is. This is just the beginning. The formula needs special rules for each special card.

Nice Scared Girl.
I think best is try number of pillars in game and you don't have to calculate it.
There are some factors that are unpredictable like opponent's deck, randomness and many other things.

Like I said there earlier, you cannot prepare for everything so why should you even try? There is no perfect amount of Pillars but there is a number that gives you the best results on average. And using math to determine that number is what we are trying to do here.

[kintar]

An important factor IMO that is not taken into account is the speed of the deck. Faster decks have less time to produce quanta, so they need more pillars. I've farmed AI5 with mono-aether before, and it generally doesn't run into quanta issues even though it supposedly uses way too much quanta, because it's a slow deck so it has more time to produce quanta.