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

[miniwally]

Wow I can't believe I've only just realised you used commas instead of decimal points. I feel like an idiot now.

[Hobnob5000]

I think Essence has a point with his method. It works similar to my method of using towers.
For every 5 towers, count as 6 pillars. If there is 4 towers, I count as 5 pillars, but for a group of 3 or below, I just count as pillars.
 For example, with one of my decks

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7jo 7jo 7jo 7jo 7jo 7jo 7jo 7jo 7jo 7jo 7jo 7jo 7jo 7jo 7jo 7jo 7jo 7jq 7jq 7jq 7jq 7jq 7jq 7js 7js 7ju 7k0 7k1 7k2 7k2
Using my method, including the mark a a pillar, the QI of my deck is 5.48 (2 d.p)
Using Essence's method, including the mark as a pillar, the QI of my deck is 5.44 (2 d.p)

I prefer my method because, well... I made it
Essences would be easier to do though

[gutsyDuck]

Hi all, I'm not exactly a math nerd but I often work on this kind of problems.
Your approach is good but at the same time it's false.
good : you got a kind of objective view of the proportion of quanta in your deck. You add some variable to have a better guess.

Bad : most of time people think their deck as a block. got 40 cards, got 3 nova -> got 3/40 chance to draw nova.
A better way of thninking a deck is water. You got a flow of cards, and what is important is the way the card come.

All of this is only probability. conditional probability to be exact. When you try to guess if you got enought pillar, you are asking for something very very complicated. Your question could be "after taking 7 cards, what is the probability to draw the card I need".

Let's try something, just divide card into three classes : pillar, creature, spell. with a 40 cards deck as follow : 10p/20c/10s.
probability to successively draw pillar is : 10/40 (first draw), 9/39 ( second draw ), 8/38, 7/37 and so on....
if you understand all, probability to successively draw a creature cards is : 20/40, 19/39, 18/38 ....

so the probability to draw 3 pillars as the three first cards is : 10/40 * 9/39 * 8/38 = 720 /59280 = 0.01214
but probability to have 3 pillars in your first hand is very different :
you can draw pillar like this (the possibility area ) P is for pillars, C for other cards
P P P C C C C -> this one is 0.01214
P P C C C C P
P P C C C P C
P P C C P C C
...
C C C C P P P

probability of the second line is :
10/40 * 9/39 * 8/34 -> 720 / 53040 -> 0.01357
Probability of the last line is : 10/36 * 9/35 * 8/34 -> 720 /42840 -> 0.01680


This is not exactly what we want to know. Go back to the question : your are right  when you put your QI,it'is the number quantun I need to play. I element there is something diffrent from MTG, your quantum is a pool were quantun stay until it's used. Appear another question : how many time can I wait to play my card ? Does it make a difference if I can play my card in the second turn instead of the third one ? answer to this question depend of how the game occur. In the first turn you can wait. In the last turn you can't.
an easiest question : knowing the probability to draw a pillar in the eigth draw knowing that I already draw X pillar ?

I don't what to tell you that your idea is wrong, it seem to be a good tool to estimate a deck. But if you want to be very accurate in deck building the road is long and complicated. Two things worth knowing : richard garfield (mtg) build is game when he was studying probability (and now he is a mathematic's doctor, speciality : probability ) . Most of Pro MTG player are now pro poker's player.

PS: I write all of these in a raw without coffee, It's (surely) confuse, I'll try to re-write it latter...

[Svenningen]

Weird how I didnt see mark mentioned in the first thread o.0

Anyhow when I do QI, I count mark as 1pillar, wich is quite obvious.

I was also thinking about the mentioned doing each element apart.. I believe its not correct for duo/trio decks to do them all in one bulk. then u wont know wich ur high/low on.

[Hobnob5000]

I was also thinking about the mentioned doing each element apart.. I believe its not correct for duo/trio decks to do them all in one bulk. then u wont know wich ur high/low on.

Yeah, I do all of my elements separately in duo decks. I find it works better

[Thelonesun]

What about Firefly Queens? They produce monsters that produce  quanta every turn. How would I count those if I use Light?

[Xinef]

What about Firefly Queens? They produce monsters that produce  quanta every turn. How would I count those if I use Light?

I'd take the average number of Fireflies you end with, calculate the square root and consider it to be the amount of light pillars you have, but that's a rough guess.

[RavingRabbid]

Is there a Damage Index, too?

[midg3333]

I know Some of my suggestions would be silly to implement into what is supposed to be a rather quick and easy calculation, but these are just some ideas as to what could be done to make QI more accurate.

For those who don't want to read the large wall of text, here's a quick summary of what I am saying:
To estimate the QI more accurately, you should take into account:
-how many turns (on average) your deck will take to kill a 100hp or 200hp opponent, and how that affects quanta usage
-what your deck consists of, and whether or not you will want to play those cards straight away or not
-how often you will use creature abilities and which will overlap
-take into account a mark (i suggest is counts as about 2.5 pillars)


There definitely has to be something different for the mark... it is much better than a pillar. Would it be more accurate to make a mark equal 2 pillars, maybe more? On average, you get any given card approximately halfway through the game on average, so on average a mark, which you get at the beginning of the game every time without fail, will generate 2x that of a pillar. It would probably generate more though for 2 reasons:
1) you hardly ever go through every single card in your deck, unless it is a stall deck and/or an OTK deck.
2) later in the game, you will tend to have an excess of quanta because you have more pillars and therefore more quanta gain per turn so you won't use up all your quanta every turn in late game, whereas it is very easily possible early-game.

for those reasons, i would be more inclined to make a mark worth 2.5-3 pillars. Look at the standard upped speed poison deck, for instance. It will generally use 6 congeals and 6 chrysaora = 12 water quanta. This is powered by a mark. if a mark = 2 pillars, 12/2=6. If a mark = 2.5 pillars, 12/2.5=4.8, and if a mark = 3 pillars 12/3=4. From what I have seen, a mark sufficiently powers a speed poison deck's water usage, so i would be inclined to say 2.5 is about right (assuming the optimal QI is about 5).

Also, I know it would be hard to factor all this in, but the factors that would affect quantum usage are:
1) game time - how long your game goes for
2) frequency of the use of creature abilities
3) type of card

to expand:
1) the longer the game goes on for, the more time you have to generate quanta.
-A stall deck lets you last longer, allowing you to generate more quanta
-a higher HP opponent will take longer to kill, allowing you to generate more quanta in that time period (this would only be factored in if you were fighting FG's or halfbloods),
-here's a big one: the average damage that your deck deals. If you have a speed deck that deals heaps of damage really quickly, you will have less time to generate quanta, so it would greatly affect the time a match takes.
2) Lets face it, an average of 1 or 2 uses for an ability isn't really that accurate.
-the ability will be used more times if it is:
(a) cheaper -or-
(b) belonging to a lower cost creature.
I'm not so sure about the cheaper cost ability, because the QI is trying to prevent quanta issues like that, but (b) definitely makes a difference. A chrysaora that costs 1 water quantum will start using its ability long before say, a nymph because it gets out so much sooner, therefore the ability will be usable earlier.
-the type of ability: an ability such as chrysaora's poison will be used much more often than an ability such as an arctic squids freeze, because freeze requires a target. Then for spells requiring a target, it gets really confusing with certain specifications for the target (such as paradox) and those that can be used both defensively and offensively (mutate, rage potion), and that math is way too confusing and complicated, so i won't go into that.
-overlapping creature abilities. If you have 6 maxwell's demons out, chances are you won't use each one's ability too many times, creature abilities with targets would be used less the more creatures you had with that ability.
3) creature cards and permanents can be played effectively more often than spells. Spells such as steal, earthquake, parallel universe, etc. require certain conditions to be used effectively, whereas creatures will often be more effective when played sooner. Permanents are then between creatures and spells, because some are situational (you don't need more than 1 sundial at a time, same with dim shields, or too many hourglasses), whereas others such as SoG or feral bond can be played straight away.

Overall, to estimate the QI more accurately, you should take into account:
-how many turns (on average) your deck will take to kill a 100hp or 200hp opponent, and how that affects quanta usage
-what your deck consists of, and whether or not you will want to play those cards straight away or not
-how often you will use creature abilities and which will overlap
-take into account a mark (i suggest is counts as about 2.5 pillars)

[jmdt]

I made a spreadsheet using essences method for towers and i have to say that this is a very effective method for balancing quantum usage with deck functionality.

[bojengles77]

Just so you know, at the end there talking about the 7.315 or whatever QI, you said that means you have too many pillars, but what it actually means is that you have too few pillars. You went on to say you needed to add pillars and take away high cost cards, but you said in yellow that the deck had too many pillars.

[Selenbrant]

About probability I made some tables for different deck sizes drawing at least "x" cards of a certain card depending on cards drawed, deck size, copies of a card. I continuously edit further tabels, but with a request I would be able to edit tables that are needed.
http://elementscommunity.org/forum/index.php/topic,8295.msg102495#msg102495