Is 30 cards always the optimum deck size?

[blarp]

Alright so I've given it some thought. Are 30 card decks always optimal? I'm not talking about stallout possibilities but for normal decks.

I've played other card games and know the reasoning behind minimum sized decks, but does that logic actually carry over for EtG?

Lets say you have a deck with X upgraded phase dragons (14 cost), Y upgraded phase recluses (4 cost), Z upgraded aether nymph (8 cost) with the rest of the deck being aether towers. How many aether towers should be in your deck to minimize the time in which you can play both of these cards?

To make it a little more straightforward, which deck is most likely to deal 100 damage first, assuming each deck plays against a dummy and goes first:

1 phase dragon, 29 towers
2 phase dragon 28 towers
3 phase dragon 27 towers
4 phase dragon 26 towers
5 phase dragon 25 towers
6 phase dragon 24 towers
6 phase dragon 25 towers
6 phase dragons 26 towers
etc....

How about if you add phase recluses? Aether nymphs?


What's the fastest aether rush you can make using only phase dragons, phase recluses and aether towers? Will this always be a 30 card deck?


Best,
Blarp

P.S. if you hate aether feel free to use stone dragons and golems or something. whatever you'd like.

Would also be interesting to see how like a light dragon and earth dragon duo deck with only pends would math out. would that also be a 30 card deck? how many pillars of each would be optimal if any?

[whatifidogetcaught?]

Interesting theory. Let's start with this basic mono-gravy deck for shtuffs and giggles:

Spoiler for gravy:

Hover over cards for details, click for permalink

Deck import code : [Select]

744 744 744 744 744 744 744 744 744 744 744 744 744 744 744 745 745 745 745 745 745 747 747 747 747 747 747 74c 74c 74c 8pl

Against a (mostly) biteless opponent with 1000 runs, it gets a 6.444TTW.

What if we add say, two towers? In this instance, it gets 6.47TTW (one extra tower is 6.446TTW)

If we bump it up to three towers, we get a 6.499TTW.

Simply put, for this instance at least, 30 cards is better. Can we create one where more than 30 is better?

This would probably mean more creatures and less towers with 30 cards, in which more towers means faster draws.

[blarp]

Interesting. In your case it really doesnt change much does it. I wonder what the difference would be if you faced an oppoent with sofo, black holes, discord, and other similar quantum denial cards. Not all at once of course. Would it be any noticebale advantage? And would that be negated by the loss in effectiveness against other decks?

What about in cases where you only have a very few number of pillars in your deck (6-8)? And you'd have to remove a monster or spell card to trim it down to 30 rather than removing a pillar?

Just putting these thoughts out there.

[Elbirn]

Spoiler for 6 Dargons + 6 recluses + towers:

Hover over cards for details, click for permalink

Deck import code : [Select]

808 808 808 808 808 808 808 808 808 808 808 808 808 808 808 808 808 808 80f 80f 80f 80f 80f 80f 80g 80g 80g 80g 80g 80g 8pu

QI = 4.78
5 game test: 8, 7, 6, 7, 6 turns to win. AVG = 6.8

Spoiler for Plus 2 towers:

Hover over cards for details, click for permalink

Deck import code : [Select]

808 808 808 808 808 808 808 808 808 808 808 808 808 808 808 808 808 808 808 808 80f 80f 80f 80f 80f 80f 80g 80g 80g 80g 80g 80g 8pu

QI = 4.32
5 game test: 7, 6, 6, 6, 6 turns to win. AVG = 6.2

Basically, what I've tried to do is prove that moar quanta = can play cards faster. Everyone gets that. The problem however is that if you have too much quanta and not enough of anything else, well, you'll never get to spend your quanta. Example, if I made a 40 card deck with 6 recluse, 6 dargons, and the rest towers, it would probably suck. So it's all some manner of maff and calculating odds of drawing any given cards, and all sorts of nonsense that I don't have the time for.

But you do make a wonderful point, that 30 cards shouldn't be the basis for best size. Deck should be based on odds of drawing the proper cards, and having the quanta to afford everything in a timely fashion.

[dragonsdemesne]

Given the problem you've posed here, I think that it would always be a 30 card deck, but I'll freely admit that this is based on an off-the-cuff educated guess based on my knowledge of statistics.  Perhaps someone (probably not me, but who knows?) will try this out with xeno's simulator, as it is exactly suited for this type of task; no-brainer decks playing against goldfish opponents.  As long as you can reach an optimal quanta supply with only 30 cards then 30 will be the best choice.

http://elements.alanbeam.net/qi.php?deckCode=808+808+808+808+808+808+808+808+808+80f+80f+80f+80f+80f+80f+80g+80g+80g+80g+80g+80g+81q+81q+81q+81q+81q+81q+81q+81q+81q+8pu&showImage=1

This is the code and QI calculator for a 6 dragon 6 recluse 18 (upped) quanta deck, and the QI is 4.78, which being under 5, is probably the best scenario.  Assuming that a QI=5 is ideal for this deck (it may not be; this would require simulation/testing) then the ideal number of quanta is actually a deck that is smaller than 30 cards.  Putting 6 dragon 6 recluse 17 towers into a QI calculator gives QI=5.05.  If you were to use less towers (and again, assuming QI=5 is ideal here, which may or may not be true) then the deck would actually become slower, because you'd be quanta starved.  Take the extreme case of 6 dragon 6 recluse 1 tower as a 13 card deck and you'll see what I mean... you won't get very far with that :p

Basically, what I'm saying is that as long as you can get the ideal QI in a 30 card deck (or less, but are forced to use 30 cards to get that high) then 30 is the best deck size for a rush.

Your question would have a lot more meaning and discussion if you added one more card to it, since in this case I think the ideal is almost certainly the 6/6/18 split I mentioned above.  If you were to ask instead "say you have a deck with X upgraded phase dragons, Y upgraded phase recluses, *and Z upgraded aether nymphs*, with the rest of the deck being aether towers, what is the fastest rush deck, assuming you play against a dummy", then the question would get a whole lot more interesting.

edit: my point still stands, but some examples were posted while I was creating this post, which should hopefully further illustrate what I was trying to explain.

[Pella]

It seems to me that 30 cards is the optimum size for rush decks, although I have nothing scientific to support that claim. On the other hand, bigger stall decks tend to work better than smaller stall decks, again using only anecdotal evidence. In other words, it depends on the purpose of your deck.

I'm confident that we could build a deck with 40, 50, or even 60 cards that would be viable. For example, a 60-card mono deck with 24 pillars, balanced QI, and few to no combos probably would work very well. Add more elements, and it's trickier, but probably still possible.

I know what I'm going to do when I get home tonight.

[neuroleptics]

No. the keyword there was 'always'. Not so if you're using a stall deck. Not so, if you have good draw power.

[Drake_XIV]

But we are assuming it to mean optimization in terms of speed/damage, since 30 cards is specified and one does not simply have a 30 card stall.

[ARTHANASIOS]

No. It is not always the best deck size. Each card type holds a percentage of the whole deck and you may add/remove an amount of cards to keep that percentage as low or as high you wish or need.
You can take a look at the Card Type's Percentage in a Deck in my RNG and Luck article in ETG wiki.

Here is another example:

We have the following 30-card mono-life rushing deck.

Hover over cards for details, click for permalink

Deck import code : [Select]

5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bt 5bt 5bt 5bu 5bu 5bu 5c0 5c0 5c0 5c7 5c7 5c8 5c8 5c8 5c9 5c9 5de 5de 5de 5de 5de 5de 5de 8pn

Why don't we run the following 60-card version which is much more difficult to be defeated via deckout but it has exactly the same percentage of every single card in it, so the same chance to draw every single card?

Hover over cards for details, click for permalink

Deck import code : [Select]

5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bt 5bt 5bt 5bt 5bt 5bt 5bu 5bu 5bu 5bu 5bu 5bu 5c0 5c0 5c0 5c0 5c0 5c0 5c7 5c7 5c7 5c7 5c8 5c8 5c8 5c8 5c8 5c8 5c9 5c9 5c9 5c9 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 8pn

[Marsu]

^
This example is flawed though. It's simple statistics, you will have way more really bad draws with the 60 card version.

I still agree though that 30 isn't always best.

[whatifidogetcaught?]

lol. used Artha's examples for the Game Simulator.

Spoiler for Hidden:

Hover over cards for details, click for permalink

Deck import code : [Select]

5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bt 5bt 5bt 5bu 5bu 5bu 5c0 5c0 5c0 5c7 5c7 5c8 5c8 5c8 5c9 5c9 5de 5de 5de 5de 5de 5de 5de 8pn

The 30 card deck above had an average of 8.1247 TTW against Level 1. (1000 runs)

Spoiler for Hidden:

Hover over cards for details, click for permalink

Deck import code : [Select]

5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bs 5bt 5bt 5bt 5bt 5bt 5bt 5bu 5bu 5bu 5bu 5bu 5bu 5c0 5c0 5c0 5c0 5c0 5c0 5c7 5c7 5c7 5c7 5c8 5c8 5c8 5c8 5c8 5c8 5c9 5c9 5c9 5c9 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 5de 8pn

The 60 card deck above had an average of 8.3168 TTW against Level 1. (1000 runs)

That's less than a 0.2 TTW increase. Interesting.

[ARTHANASIOS]

^
This example is flawed though. It's simple statistics, you will have way more really bad draws with the 60 card version.

I still agree though that 30 isn't always best.

Nope. You won't have more bad draws; the chance of drawing each card type is the same. However, there is indeed a reason the 60-card version can be proven slightly different than the 30-card counterpart, but it is not luck. It is speed. In a 30-card deck, you draw 1/30th of your deck per draw, while in a 60-card deck you draw 1/60th of your deck per draw. Because of that, you draw twice as fast in a 30-card deck, so you deckout twice as fast. Its a double-edged sword...