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

[Xinef]

1. Anubis rush is slower than most rushes, but faster than some control decks, so I'd expect the perfect QI to be somewhat above 5.

I wrote a simple script (in a programming language called Scala) that calculated how many turns it takes (depending on your pillar to anubis ratio) to kill an opponent with 100 HP who does nothing, but waits for his demise

It's a bit heuristic, since I replaced probability with fractions (eg. instead of 1/2 probability of drawing a pillar, I assume I draw a half of a pillar and a half of an anubis). Obviously this means that the results aren't optimal, but still close enough to be useful.

So, here is the result:

Code: [Select]

Pillars per 100 cards: turns:
1 22
2 20
3 19
4 18
5 17
6 17
7 16
8 16
9 16
10 15
11 15
12 14
13 14
14 14
15 13
16 13
17 13
18 13
19 12
20 12
21 12
22 12
23 12
24 11
25 11
26 11
27 11
28 11
29 11
30 11
31 11
32 11
33 11
34 10
35 10
36 10
37 10
38 10
39 10
40 10
41 10
42 10
43 10
44 9
45 9
46 9
47 9
48 9
49 9
50 9
51 9
52 9
53 9
54 9
55 9
56 9
57 8
58 8
59 8
60 8
61 8
62 8
63 9
64 9
65 9
66 9
67 9
68 9
69 9
70 9
71 9
72 9
73 10
74 10
75 10
76 11
77 11
78 11
79 11
80 11
81 12
82 12
83 13
84 14
85 14
86 15
87 15
88 16
89 17
90 18
91 20
92 22
93 25
94 28
95 33
96 38
97 46
98 63
99 113And the script if anyone is interested:

Code: [Select]

var pillarRatio = 0.0d
println("Pillars per 100 cards: \t turns:")

for(i <- 1 to 100) {
pillarRatio += 0.01d
var anubisRatio = 1.0d - pillarRatio

var timeQuanta = 0.0d
var damage = 0.0d
var anubisInHand = 0.0d
var pillarInHand = 0.0d
var anubisCount = 0.0d
var pillarCount = 0.0d
var turnCount = 0

while(damage < 100.0d) {
// turn start - draw cards
turnCount += 1
if(turnCount == 1) {
// first turn, assume an average of 7.5 cards drawn
pillarInHand += 7.5d * pillarRatio
anubisInHand += 7.5d * anubisRatio
}
else {
// non-first turn
pillarInHand += pillarRatio
anubisInHand += anubisRatio
}

// main phase - play pillars and anubises if possible
pillarCount += pillarInHand
pillarInHand = 0.0d
while(timeQuanta >= 8.0d && anubisInHand >= 1.0d) {
timeQuanta -= 8.0d
anubisCount += 1.0d
anubisInHand -= 1.0d
}

// turn end - discard, deal damage, gain quanta
if(anubisInHand > 7.0d) {
anubisInHand = 7.0d
}
damage += 5 * anubisCount
timeQuanta += 1 + pillarCount
}
var ratio = (100.0d * pillarRatio + 0.5d).toInt
println("\t" + ratio + "\t\t" + turnCount)
}For example, with only 1 pillar per 100 cards, you can still win in only 22 turns, because you can play your first anubis on turn 9 (thanks to your Time mark) and second one on turn 17... on the other hand, with too many pillars and too few anubises you need much more Time on average to draw that anubis.

Anyway, it seems that the best ratio is somewhere around 0.6 pillars and 0.4 anubises, which means a deck consisting of 18 time pillars and 12 anubises can theoretically win on average in 8 turns.

The QI of this deck is ~5.33 (or ~5.05 if you count your mark as a pillar), which seems to make sense for a slow rush.


Of course, if we fight a real opponent, we might want an aether mark in case he has some CC. The results are similar, with much worse performance in case of very few pillars, and approximately 1 more turn needed to win in case of good pillar ratios.

Code: [Select]

Pillars per 100 cards: turns:
1 52
2 39
3 33
4 29
5 26
6 24
7 23
8 21
9 21
10 19
11 19
12 18
13 18
14 17
15 16
16 16
17 15
18 15
19 15
20 14
21 14
22 14
23 14
24 13
25 13
26 13
27 13
28 12
29 12
30 12
31 12
32 12
33 12
34 11
35 11
36 11
37 11
38 11
39 11
40 11
41 11
42 11
43 11
44 10
45 10
46 10
47 10
48 10
49 10
50 10
51 10
52 10
53 10
54 9
55 9
56 9
57 9
58 9
59 9
60 9
61 9
62 9
63 9
64 9
65 9
66 9
67 9
68 9
69 9
70 9
71 9
72 9
73 10
74 10
75 10
76 11
77 11
78 11
79 11
80 11
81 12
82 12
83 13
84 14
85 14
86 15
87 15
88 16
89 17
90 18
91 20
92 22
93 25
94 28
95 33
96 38
97 46
98 63
99 113The perfect ratio is probably somewhere in the middle of 9's so I'd take 0.63.
So, with an aether mark you should take 19 time factories and 11 anubises, which gives a QI of ~4,63



The questions remaining are, if we should make any alterations because real opponents usually don't wait doing nothing.
And whether my heuristic is good enough and reliable.




2. Theoretically, you need to draw anubises more often than your opponent draws SoGs, so for example if you have 85 anubises and 15 pillars and your opponent has 80 SoGs and 20 pillars, you'll be able to deal more damage than your opponent heals. The problem is, you'll need to draw your first 7 pillars to be able to play one anubis per turn (obviously a Time mark), and one more to slowly play the anubises remaining in your hand.

By the time you draw that many pillars, your opponent will already have a huge advantage in HP, so I suspect a game much longer than 100 turns... and thus much larger decks are needed. Let's see if I can alter my script to simulate a similar situation...

And... here are the results:

Code: [Select]

Pillars per 100 cards: turns:
1 3795
2 1944
3 1331
4 1029
5 851
6 733
7 656
8 601
9 562
10 538
11 522
12 516
13 523
14 542
15 578
16 646
17 767
18 1032
19 1859
So, I'd take 120 time factories and 880 anubises, just to stay on the safe side, but probably a deck of 600 cards should suffice

[LaFlibuste]

This is most interesting. I haven't read the whole thing, though, and I wondered if an answer was found regarding quantum pillars and towers. It would also be nice if you could somehow include pendulums, too. And Novas? And for non-mono, non-rainbow deck (like, 2 or 3 colors), how do you do it? Count each color separetely?

If answers for these have already been found, it'd be nice if it could be included in the first post, or at least place a link redirecting to the post/page where this is answered. Sorry for being lazy

In any event, I may eventually try to find a solution for these. My first thoughts on this is:

1) 2-3 color decks count colors separately;

2) Pendulums count for 1/2 of a pillar towards each color;

3) Towers should possibly counted like normal pillars, because they "only" give a bonus on the first turn. If you must, count them for 1.1 pillar? 1.2?

4) Quantum pillars/Towers I am not sure about, but I would either guess that: a) Rainbow decks with quantum pillars/towers have a higher ideal QI (6, perhaps?) or b) Quantum pillars in a rainbow are valued a bit more than regular pillars in a mono, something like 1.5-2 (counting them as 3 normal pillars seems wrong to me on account of them being random and a bit less reliable) (also, obviously quantum pillars in a mono/duo/trio should be valued less; maybe 0.8?). For Quantum towers, apply the same logic as other towers: give them a 0.x bonus?

5) Novas in a rainbow, are they worth 1 pillar? 2? 4 (the amount of turns it takes a pillar to generate as much quanta)? And Supernovas are worth double that amount? They both generate a lot of quanta instantly, which is very useful to get a jump start, but it doesn't generate qanta turn after turn, like a normal pillar does. In an 8 turns game, a quantum pillar generates 27 quanta, whereas a nova still only generates 12...

6) Is it customary to count the mark as a pillar? IIRC, it hasn't been mentionned in the first post. And how do you count the mark in a rainbow? Ignore it? Count it for less then a pillar (0.3)?

[pervepic]

I just read this, seems a good stuff, didn't read that all though, but I can add few things from my experience, how I build decks. Now this concerns mainly upgraded decks.

1. Overall, for the upgraded decks, we should count that 1 Tower should produce 7 quanta but not much more (if we don't count marks then it would be 6 and if we want to play with unupped cards, then it would be near 5 as also SG suggested). Mark counts as a Tower. Rush decks should have more Towers, control decks could have less (giving 6 or even 8 quanta accordingly). Costless quanta producing critters are Towers. Critters that produce quanta and cost 1 are semi-towers. Pests count as neither Towers nor critters - the best way to count them is to leave them uncounted. If you have 6 critters that use 1 cost ability, add a tower; if they use 2-cost abilities, add 2. Etc. But that's not all.

2. Quanta producers overall (Towers, Novas, Pests, Immos etc) should have at least 1/3 room in the whole deck (or you can most likely play either quanta producer or something cheap feeded by mark in the next turn). Here, in this calculation, Pests count as Towers. Marks don't count, because they are not in the deck. But sometimes there are exceptions - Poison rush can do well even with 9 Towers, because it uses few quanta.

3. In whatever deck (mono, duo, trio) and no matter how much quanta you are planning to use, the amount of quanta producers of the specific element shouldn't be smaller than 1/6 of the deck size. That's near to minimum.

Rainbows are a bit different story, but overall the amount of quanta producers should be the same there too.

For Novas and Supernovas it's good to use near the 1/3 costing stuff from overall quanta they give (2 and 4 accordingly). 1/2 is close to maximum. With the Cremation it is quite similar thing: one can really count on between 1/3 and 1/2 quanta it promises to give. 4 Towers in upgraded Rainbow are mathematically close to 1 Tower in Mono, but it really may take some time if you get those Towers. A Rainbow without Supernovas is just 4 times (actually quite a bit more in practice) slower in terms of producing quanta to one element. Shouldn't it have 4 times more Towers? No  . Because you will get killed before you draw defensive cards. And luckily you don't usually have to collect quanta for the single element only, Rainbow has 12 options. In case of the bigger Rainbows it can vary how many quanta you can use from each element, because you should have more time to collect quanta. For example, in a 30-card and 4-Towers Supernova deck you should use 5-6 cost critters, not much more expensive ones, but a 60-card Timebow with 22 Towers and without the Novas can easily use like 20 quanta per element and even more (still-still you should really not to put there more than 1/4 costing stuff a same size mono deck could put there and besides balanced Rainbows are better, because they are quicker, since they often use all elements). But in that case don't use Supernovas and use at least 1 Hourglass per 10 cards. And a lot of shields. And Sundials are still good cards. To put it very brutally: because of the slowness, in a fat Rainbow you should count as if each Tower gives you only 1 quantum per each element, in a small deck with only few Towers this number is something like 0,5. In the small deck which uses only Towers and not Supernovas, this number is something like 0,7-0,8. This means that in practice the difference in quanta production for the given element between mono Tower and Quantum Tower is at least 7 imo (quite a bit more than just a mathematical 4). Btw I guess that there is no reason to count a mark in the Rainbow as something less than a mono-Tower.

[Pineapple]

I wondered if an answer was found regarding quantum pillars and towers. It would also be nice if you could somehow include pendulums, too. And Novas? And for non-mono, non-rainbow deck (like, 2 or 3 colors), how do you do it? Count each color separetely?

Here's how I do it, remembering to take my QI with a grain of salt because QI is geared towards end-game efficiency and should therefore only be used a rule of thumb:

Each element's QI in a deck is calculated separately. Mark is counted as 2 pillars, under the reasoning that 1 pillar card will on average be drawn after going through half of the deck, in which around half the game has progressed, and would therefore generate half as much quanta for the full game than a mark generates.

Since each element is calculated separately, pendulums count as 1/2 a pillar for both elements (although the quanta of the pendulum's element produced by a stack of pendulums is almost always higher than the quanta produced in any point of the game, since half the time it's higher from that element being produced for one more turn and the other half the time the two elements have equal generation from the stack... QI is geared towards end-game efficiency).
Also, quantum pillars count as 3 pillars that generate 1/12 quanta for each element, or as 1/4 a pillar for each element.

In addition, quanta generating creatures count as pillars. You add to the pillars for Light by 1 for each RoL, add to the pillars for Earth by 1 for each gnome rider, add to the pillars by 1 for each devourer, etc.

Quanta generation that is not produced in a turn-by-turn fashion and is instead instant (nova, immolation, the +1 from towers and upped pendulums) I treat as negative cost. This is because, just as playing a creature reduces all the quanta you've generated in that game by a fixed cost, playing a nova increases all the quanta you've generated in the game by a fixed value (1 per element).

The flaws of treating instant quanta as negative cost is that classical QI can be used for rushes while the tangents up there build off how QI is based on using all the quanta generated in one game.

[I8SumOrangesNItWasK]

I've been using the same deck for a while and I'm in the process of upgrading the cards slowly but surely. Every once in a while I'll thrown in or take out a card -- often pillars/towers -- but what I currently have seems to be working quite well, quanta-wise. My QI, however, is quite interesting...

by tiamats4esgares

Hover over cards for details, click for permalink

Deck import code : [Select]

4ta 52g 52g 52g 52g 52g 52g 52r 52r 52r 52r 52t 52t 52t 52t 560 5rk 5rk 5rk 6rq 710 710 710 71d 71d 7q0 7q0 7q0 7q0 7q0 7q0 7q8 8pl

The first card is a non-upgraded SoR.

My deck runs into many problems which makes it hard for me to calculuate the QI, but here's what I did:

-I count my deck as a trio-deck. However, since I don't have any pillars at all (and it works that way), I simply chose to ignore the elment entirely.
-I count Shards of Readiness as being equally divided among all 3 elements, included.
-Since I'm ignoring , I don't count the Chimera at all, nor do I count the Scarabs' "Devour" cost. It would be pretty hard to calculate even if I wanted to.
-I have 6 Mummies in my deck, all of which count towards . I usually end up with about 2 Pharoahs out by the end of the game (or, at least there's no point in having more). I counted using the ability of 3 Pharaohs though, because other cards that may not necessarily make it out are all conted for. I figure I go through about 2/3 of the deck each game, so about 2/3 of the Pharoahs are used. Makes sense.
-I typically use my first SoR on a Pharoah, and second on a Scarab. Because of this, I counted 2 of the Pharoahs' abilities twice, but 1 of them only once (assuming that possibly I'll only use for it half the time).
-I counted towers as not only "pillars", but as -1 quanta each.
-I counted Eternity's ability twice, since if I have one out and can use it, I'm probably going to use it on something. It may be situational, but mainly only to save . If isn't an issue, I usually use it.

Following all the above "rules", I ended up with very close to 6 QI in (5  26/27) and very close to 4 QI in (3  17/18). Putting the 2 together, I end up with close to 5 (4  42/45). That sounds good, and all, but it makes me wonder why my QI for is so much higher than my QI for . Do you suppose it could be because is more important at the beginning of the duel (I need to get Mummies out, need a steady Bone Wall, etc.) while is more important at the end (I need to keep generating scrabas, I don't need to put out more Bone Walls once they start devouring)? To me, this makes sense, because the less-important one can "wait" until later and you have more of a chance to draw the right cards while your waiting, while the more-important one you need right away or you can't do anything. Am I onto something here, or are both of my QI's just way off, but in opposite dirrections...and maybe they should be the same? o.O

P.S.: If you count mark as 2 pilars, then I can only be alloted about 1/3 points for Devour (due to the Chimera's massive 7 and the SoR's 8/3) in order to have a QI for 5 in . Even though it's situational, I typically do have plenty of throughout the game (RoL + Fractal + Hope comes to mind as a good example as to when I don't...). Interesting that it seems my QI would be realatively low if I were able to acctualy calculate Devour properly.

[I8SumOrangesNItWasK]

P.S.S.

LOL /fail

http://www.quantum-index.com/qi.php?deckCode=4ta+52g+52g+52g+52g+52g+52g+52r+52r+52r+52r+52t+52t+52t+52t+560+5rk+5rk+5rk+6rq+710+710+710+71d+71d+7q0+7q0+7q0+7q0+7q0+7q0+7q8+8pl&showImage=1

Proof that computers truly aren't smarter than humans.

This "tool" has various flaws in my deck alone, but most importantly doesn't take into account the innate ability of the mummy to turn into a -sucking machine.

[Xinef]

It is alright to have different QI for different elements in your deck. And you shouldn't care about the average QI of the elements you are using. Individual QI for each element separately are important.

It seems that the disproportion between your and is caused by the fact that your deck is a mix between a rush and a control deck. The mummies are a kind of death rush, so it's natural that higher QI works better. You want to play them as early as possible. On the other hand the time part of your deck is more about control. Having a lot of early would be ineffective, since you'd have no mummies to rewind, and Pharaohs+Scarabs need a few turns to pay off. In those early turns you can deal much more damage with a few mummies than with half as much pharaohs (considering you need more quanta and cards to create a pharaoh, it's hard to compare how many pharaohs or mummies you can create with the same amount of cards and quanta, so I assumed half as much).

A typical deck has too few quanta during the first few turns to play everything in your hand, than approximately enough during midgame to play one card each turn, then during endgame you have more quanta production than you can spend. If you intend to use a specific element mostly during midgame/endgame, you can have lower production of that element, since the early phase is not an issue. You can have enough production to have exactly enough quanta during endgame, rather than too much.

As for the and your mark, you should simply assume that your total production is equal to the average number of turns a battle lasts. You say you typically go through 2/3 of your deck, so your mark is worth at least 3/2 of a pillar, in fact more since that would be the case only if you draw 2/3 of your pillars in your starting hand, than none afterwards. Pillars drawn later in the game are worth less.

I think you can calculate how much your mark is worth using a following algorithm:

• Divide the number of pillars in your deck by the total number of cards. Eg. 15/32 in your case.
• Multiply the number by 7.5 (an average starting hand size) to get the average number of pillars in your starting hand. In your case it is ~3.515625
• Calculate how many cards you will draw after the first turn. Assuming you win or lose after drawing 2/3 of your deck, and assuming you draw 7.5 cards during your first turn, it means you draw a total of 32 * 2/3 = ~21.333333333 cards, out of which ~13.833333333 are drawn after the first turn.
• Calculate how many of these are pillars. You simply have to multiply the previous result by the number you got in 1. so you get
  13.833333333  * 15/32 = ~6.484375
• Divide by two, since an average pillar out of these will be present for half the battle.
  6.484375 / 2 = ~3.2421875
• Add this number to the result of the 2. and you get the average number of pillars you have during your whole game. In your case that gives ~6.7578125
• In 3. we found out that your average battle lasts ~13.833333333 turns, so that's the average number of quanta generated by your mark.
• Multiply the result of 6. by the number of turns of your average battle and divide by the number of pillars in your deck to get average quantum production of a single pillar. In your case:
  6.7578125 * 13.833333333 / 15 = 6.232204861
• This means that your mark is worth approximately 13.833333333 / 6.232204861 = ~2,219653179 times as much as a pillar

So in conclusion... yeah, your mark is worth pretty much 2 pillars

[jmdt]

I posted this elsewhere, but thought it would fit the discussion here:

After my first pass reading I do have a few comments.  a LONG time ago when I first started deck building, I used to build all my decks off of a spreadsheet.  I set it up to give stats such as QI, draw probability, etc.  I used to start with everything at 5, but as an engineer I'd always run say 10-20 tests versus the AI and watch how the deck launches versus how much quanta is available late in the game.  Ultimately the ideal QI is the position were over a medium sample size you A.) generally always have the quanta to play cards as you get them and B.) Generally don't have ton of quanta of that element built up by the time of win.  Unfortunately, a hard QI number generally does not take this into account.

The next thing you look at is the overall speed of the deck.  For a rush you want to play your hand faster so you need more pillars early to dump everything.  Generally you win in 5-8 turns so with a low QI, you do not have the time to generate excess levels of quanta unless something goes wrong.  Speaking of something going wrong, in the real world, a pure rush is generally not the preferred option as CC can take a heavy toll on the deck and you will have tons of quanta and nothing to play it on.  When I used to experiemt with rushes, one thing I studied was the effect of adding the 9 hp powerhouse Jade dragon to bolster the fact that the faster frogs are easy to kill.  I learned that with 2-3 dragons that the ttw was not too much lower, maybe 0.2-0.4, but the deck was able to deal with adversity 100x better as Jade played the role of the late game finisher versus heavy CC decks.  The ideal of using 1-3 big creatures with the rest of the deck is the idea of the 'quanta sink'.  With a quanta sink you do not necessicarily have the fastest possible deck, but the deck will launch fast and be able to keep quanta balanced over a short and long game.

Along the same principle, even for rush decks, The QI and hence number if pillars depends on the size of the critters you need to get out for USEM since all the cards cost 1-3, the deck gets a QI of 4 with 10 pillars.  I never actually run less than 10 pillars as the probibilities of drawing them gets too low.  For a deck such as the shrieker rush, you run like 17 pillars to power the bulky cards on there way out.  The same way 10 pillars leaves you with 1 or no pillar starts a small % of the time, 17 pillars will give 6 or 7 pillar starts.  I always like 12-14 pillars based on probabilities to have the most optimal draws, but again, this depends on the what other critters and toys you roll in the deck.

My last general consideration for QI is the damage and stalling potential of the deck.  USEM has a total combined damage of 72.  Its a 'weenie rush'  it will either flood the field fast for damage or it does not have the big hitters to catch up late game (ignoring heal obviously).  A shrieker rush has a total damage potential of 126 so over time it can ramp oout a ton more damage.  Against healing and/or CC sometimes bulk damage becomes very important and must be taken into consideration.  With stalls, one must look at the immediacy of quanta need.  Yeah 6 phase shields cost a ton, but you don't have to play them all at the same time either.  With a mere 2 pillars, you can chain phase shields indefinitely.  With 1 pillar on the field, you can chain wings out almost the entire game.  So in cases of chaining cards or wanting to save cards instead of playing them immediately a much higher QI number can be effectively used.

That's my quick random unorganized thoughts on QI on a Saturday afternoon.  Hopefully that helps you a bit to understand QI in a variety of decks.

[Gunthar]

Even this topic is a bit older there are some stuff not included in this thread which have a quite big effect on the QI index.

A solar shield or a soul catcher are requiring some creatures attacking the shield owner or dying. This is quite difficult to calculate in because it is depend on the deck build and the opponents deck. Solar shield costs 3  while the soul catcher costs none. But a solar shield is a bit easier to deploy than a soul catcher because solar shield is  and it creates  quanta while the soul catcher needs some cards who kills creatures (plaque) or have a kill like effect like the Schrödinger Cat. Some tests showed to me that a soul catcher can be considered as about 1 quanta or like a pillar while a solar shield can be counted even as 1.5 to 2  quanta.

Another aspect are adrenalined quanta generating creatures like gnomeriders or the upped gemriders, dragonfly/damselfly, fireflies/elite fireflies and similars. The strange thing is that it does not count for the devourer. Adrenalined quanta generating creatures are producing much more quanta per round than with no quanta. A test shows up to 4 or 5 quanta per round. But you need a card that uses 4 or 3 (upped) quanta or a life nymph to accomplish that. The most interesting effect is that even in the round when the quanta generating creature is played and then adrenalized it will create the additional quanta. Furthermore the upped version of some quanta generating creatures are playable with no quanta at all. They can replace some of the pillars quite well. An 1/1 quanta creature can be destroyed easier than a 1/2 creature. Therefore a 1/1 can not be counted as a full pillar replacement.

[BluePriest]

Ya know, someone smart (aka not me) could probably discover what the perfect QI would be based on the amount of turns you are planning to win in.

[Gunthar]

Cards with a hasten effect (drawing additional cards) have a much bigger effect on the QI than it appears first. It is like adding the quanta cost for the hasten ability to every card (including pillars and penduli) in the deck. A mono deck is even being much harder hit by this due the quanta is also used for same element cards. An aether mono deck even is requiring more quanta than a comparable time deck due Mindgate is drawing a copy of opponent top card and Fractal is eating all available aether quanta. Sundial is a small hastening card which is useable only once for just 1  and most useful to stall opponent attacks if he have more or bigger creatures out. A somewhat strange thing is that some time/nontime duos are performing better with Hourglass cards than a mono time deck. Best candidates are decks which can produce additional quantas out of creatures or shields. In a life/time deck better use Mitosis instead of Hourglasses

[Xinef]

It is like adding the quanta cost for the hasten ability to every card (including pillars and penduli) in the deck.

Not really every card in the deck. The 7/8 starting cards, and one card on every consecutive turn are still free. Even a deck with 6 hourglasses, golden nymphs, or sundials/precognitions will rarely draw more than half of the cards through 'paid' means.

Another thing worth noting is that drawing cards faster than once per turn allows you to draw pillars/pendulums/other quanta sources at a faster rate. Thus, you will both spend more quanta, and gain more quanta, than a player without those cards would in a given number of turns.

A good example is an upgraded Time Tower. There is no real difference between spending one to draw it one turn earlier, or not spending one and getting it one turn later. At least from the QI point of view, since it might make a difference if opponent is using earthquake or you are under effect of Neurotoxin, or you are going to deck out etc.

Anyway, in a deck with a given amount of cards, pillars are in fact worth more (as in giving you more quanta throughout the whole battle) if you have means of accelerating the card drawing than if you don't. Thus, if a given algorithm of calculating QI does consider the amount of quanta spent on abilities, it should also consider the amount gained by these abilities, even if it is indirect such as through drawing an additional pillar.