Deckbuilding: Doing Numbers

In the past I already made some articles about deck building based on mathematics. One was about the setup (what is anachronistic currently) and other about the cost weight calculation in your deck, what can yet be useful.

For 2.0, we need to do new analysis since many of the “numbers” had changed for the game. Overall costs, gold income, limited cards & economy producers are quite different than before. The true is that, so far, we had not enough data to achieve solid conclusions. I assume that metagames are not 100% competitive at all, the limited card pool (383 cards for eight factions) and the “young” state of the game and the community did lead us yet to the “top decking” at all.

Anyway, despite that “perhaps”, this preliminary observations can give us a good point to start with.

Instead of thinking on “what should be the optimal for a deck?”, the logic behind my reasoning is: if this deck was successful, there should be anything optimal inside it. Therefore, I decided to analyze the numbers of three of the last best decks in Spain Metagame: my own Stark Fealty Deck (semifinalist and 5-0 swiss at Madrid’s regional), Yamoro’s Greyjoy Fealth (Madrid’s regional winner) and Marquina’s Baratheon/Stark (Barcelona’s Regional winner).

Numbers and Proportions

These are the card cost distribution for those decks (for setup). Therefore, events and unplayable attachments in setup are considered as No Playable (NP)

	0	1	2	3	4	5	6	7	NP
Stark Fealty	6	8	10	6	6	6	8	X	10
Grejoy Fealty	8	12	11	4	5	7	3	3	8
Baratheon/Stark	6	8	12	12	3	3	5	3	9

Some observations about this deck to keep in mind:

• The sum of their cost 0 to 2 cards are from 24 (the less) to 31 (the most). 
• The sum of the cost 4 or more cards are from 14 (the less) to 20 (the most).
• No playable at setup cards are from 8 to 10.

Numebers and Setup

As in 1.0 a plot ruled the setup (Fear of Winter), which for a long time restricted us in setup terms. Currently, two plots act the same way: Marched to the Wall and First Snow of Winter. The existence of those plots in the pool, dictated to us some “obligations” for our setups, what are: 

1. Never, ever, setup just one expensive character (5 or more)
2.  Avoid to setup only cheap characters (3 or less). Two of them at maximum

Although a 4 cards setup or more were and are optimal, and we should feel happy if we achieved to have one during our games, in 2.0 I think that should not be our aim. There is a huge breach now between good and expensive cards vs crappy (suboptimal) and cheap ones. So, since we need to keep it balanced, our main goal should be, in my opinion, a good setup of 3 cards. Maybe Greyjoy could aim to achieve a consistent 4 cards setup (or more), but it is not the norm.

So, what the card combinations for these setups? The following:

        0 - 1 - 7      1 - 1 - 6      

        0 - 2 - 6      1 - 2 - 5     

        0 - 3 - 5      1 - 3 - 4      

        0 - 4 - 4      2 - 2 - 4      

There are other possibilities what doesn’t use the full eight golds we have, these are only the optimal ones. As we can see, the most restrictive options included a card of cost 3, and there are this only possibilities: 0-3-5, 1-3-4 and 1-3-4. Therefore, I’m going to considerate the cost 3 as the worst number for setup and won’t be taken into consideration.

So, the good setups of three cards are made from a combination of: two cards of cost 2 or less (Cheap cards) and 1 card of cost 4 or more (Expensive cards). So we need a starting hand with two or more Cheap cards and an Expensive card that fits with them.

So now, using the hypergeometric distribution, let’s start the magic:

Cheap cards: from 24 cards of this type (spread more or less equally) is when we maximized the probability of drawing 3 or more in the starting hand (31%) leaving a 28% probability of drawing even more. Below that, there are 27% chances of drawing just 2 (what could be enough with the correct Expensive cards in hand).

Copies	24	25	26	27	28	29	30	31
0	0,02	0,02	0,01	0,01	0,01	0,01	0,01	0,00
1	0,12	0,11	0,09	0,08	0,07	0,06	0,05	0,04
2	0,27	0,25	0,23	0,22	0,20	0,18	0,16	0,14
3	0,31	0,31	0,31	0,31	0,31	0,30	0,29	0,28
4	0,20	0,21	0,23	0,25	0,26	0,28	0,29	0,30

Therefore, from 24 Cheap cards in our deck, there are on and just 14% chances of drawing one or none, what is low enough to trust in our mulligan if necessary. If you rise the number of this Cheap cards at your deck, as Greyjoy does, to 31, the risk of draw one or none of them drops to 4%.

With this data, and taking in consideration that this Cheap cards are the worst in the game currently, but there are necessary to keep your decks balanced, my conclusion and advice is to keep the number of Cheap cards between a 24 and 28.

Expensive Cards: once we had draw our 3/4 Cheap Cards, we need to have in our hand a good Expensive Card that fits with them. Taking in mind that these cards are the most powerful, but the hardest to put in play also, we cannot save too much room for them in our decks. Decks being analyzed have from 14 to 20 cards of this type.

Copies	14	15	16	17	18	19	20
0	0,14	0,12	0,10	0,08	0,07	0,06	0,05
1	0,34	0,32	0,29	0,27	0,24	0,22	0,20
2	0,32	0,33	0,34	0,34	0,34	0,33	0,32
3	0,15	0,18	0,20	0,22	0,24	0,25	0,27
4	0,04	0,05	0,06	0,08	0,09	0,11	0,12

Perhaps, 14 are a very limited quantity, giving us a 48% chances of drawing one or none for setup, what would give us very limited options. From 16 cards we can maximize or chances of what we’re looking from: to have two of them at our starting hand, to have different choices for setup what can fit with our Cheap cards. With 16 to 18 we can also minimize the chances of the other two suboptimal situations: to draw one (few options, more restrictive) or to draw three (too heavy and expensive starting hand).

Then, I think that the ideal number of this cards are from 16 to 18.

Non playable and limited cards: NP cards at these decks are from 8 to 10. But this topic allows us to talk also about limited cards.

Copies	8	9	10
0	0,35	0,30	0,26
1	0,42	0,42	0,41
2	0,19	0,22	0,25
3	0,04	0,05	0,07
4	0,00	0,01	0,01

When we only have from 8 to 10 cards of this type in our deck, we find the perfect statistical point where we maximized the chances of drawing just one at starting hand (42% to 41%). Facing the setup, we just want to see one limited card at starting hand and we would like to see one or none of NP cards (Tears of Lys, Milk of the Poppy, etc). In this sense, I would say that the optimal number of Limited cards is 9 (max chances of just one, minimum of none), meanwhile the ideal number of NP cards is 8 (max chances of just one & max chances of none).

Last thing to say: isn't always posible to fit your deck to a perfect or ideal proportions, even while the stadistic already said what is best for you. In fact, I used to play around 12 NP Cards, what is a bit far from what I concluded with this article. What I find the most useful are the numbers about Cheap and Expensive cards (and the observation about how bad are the cost 3 cards, especially talking about characters).

Hope you found it useful