Faëria Analysis 3: Cost Normalization

TrowMiner
As a follow-up to my original Faëria Analysis 1, and the details about Faëria Production in Faëria Analysis 2, let’s see if we can come up with a reasonable approach to normalize the Costs of a Faëria card.
As you know, cards specify cost in term of three basic resources: Gold (G), Faëria (F), and Lands (L) (although we will analyze Faëria last). Another resource we should use below is the Action Points (AP), of which you receive 3 at the beginning of your Player Turn [Note].

Gold:

Gold is easy to convert into APs, as during your turn you can use 1AP to gain 1G. So, if you want, you can spend your Player Turn to convert 3APs into 3Gs. Of course, there are other ways to obtain Gs (e.g.: Trow Miner), and we get a free gold piece at the beginning of each Production phase, but we are looking for a general, basic conversion rate and those cards or situations have a marginal effect on this basic conversion in the grand scheme of things.

1G = 1 AP

Lands:

Lands appear simple to convert into APs. After all, to get a colored land in play (eg: a Mountain), you need to spend 1 AP to create a Prairie, and 1 AP to convert the Prairie into the chosen color. Thus, a conversion rate of 2:1 seems reasonable.

1L = 2 APs

However, we should recognize some peculiar characteristics of Lands.

ThyrianColossus
Lands are Re-Used, at least in regard to satisfying the requirement for some card to be played. In fact, if you have 2 Mountains in play, and you play a Creature that requires 2 Mountains on one of them, you can immediately play another card requiring 2 Mountains.
It is very difficult to account for this effect when analyzing cards in the vacuum, because without the context of the deck surrounding the card, and the game board the card would be played on, you can’t know if the Lands requirement is already met or not. Therefore we must recognize that our analysis in the vacuum suffers from this lack of context and will be an approximation in this sense.

Playing a (Colored) Creature Requires an Unoccupied Land. You may have 4 Forests in play, but if they are all occupied, you won’t be able to play your Thyrian Colossus. On the other hand, Events can be played independently from the availability of colored Lands (with the proper exceptions where their effects specifically target occupied/unoccupied Lands), Structures (even colored ones) are not required to be played on a Land of the matching color, and colorless Human Creatures can be played on any Land (at least they do at this point in time: actually no Human Creature has any Land requirement cost). So the requirement of having an available Land of the proper color does not apply to all cards in the set. Additionally, as this requirement applies to Creatures, we know that Creatures are by large mobile and can usually move out of the colored land where you would like to play a new Creature. Moving a creature does not carry any AP cost, so this does not seem to impact the basic conversion rate between required Lands and APs, although at times you may have to wait a turn in order to play a creature, because all your lands of the appropriate color are occupied [Note].

Sinistar1

Faëria:

Finally, we must talk about Faëria. At first, this seems to be an alternate resource that we should be able to convert through some formula into Gold or Action Points. However, Faëria is so peculiar that I don’t believe anyone has found a proper conversion yet, and I will recommend we treat it separately when analyzing cards.
This is due to Faëria’s limited and sporadic availability (it gets populated once every 3 Game Turns), the fact that the players have no control on its appearance, and the fact that Faëria spawns in specific locations on the board (the Vortexes).

Analysis on the first aspect revealed that we can approximate the production of Faëria as 1.333.. Faëria per Game Turn for the whole board [Note]. As Players alternate in taking Game Turns, this translates into 2.66.. Faëria per Player Turn for the whole board. How many vortexes you can farm for Faëria on any given turn is anybody’s guess, as it will depend on the board state. Once again, we cannot resolve this issue in general terms, and have to recognize we will make assumptions that carry a margin of error with them. I recommend making 2 assumptions/simplifications in this regard.

Assume you control 2 Vortexes of the 4 available on the board. The alternative scenarios (where you control 0, 1, or 4 vortexes) are not as common (admittedly, this is based purely on anecdotal evidence), and usually imply the game will quickly resolve (in your favor or not) due to the relative board positions rather than your ability of playing specific cards.

Assume you have already reached the Vortexes with a Creature. This is not a simple assumption to make. For instance, before you can collect Faëria from the closest vortex, you must: play two Prairies (2 APs) and play a Creature (which carries its own variable AP cost). However, in the long term, these costs become marginal. In other words, the 3 or 4 APs you may have to pay before you can collect your first Faëria, have a significant impact on the numbers for a few Game Turns, but eventually become irrelevant. For instance, the Prairies or colored Lands you played to reach the Vortex will likely still be around when you want to collect Faëria a few Game Turns later. So: assume you already have a Land next to a Vortex when comparing Faëria costs, and that you already placed a creature (that can gather Faëria!) on that Land. Be aware of the effect that this assumption has on your analysis – especially in the initial phases of an actual game.

All that being said, we still lack a logical way to convert Faëria into Action Points. Some specific cards may allow direct or indirect (through Gold) conversions, but they are too few (compared to the entire card pool) to have a statistical impact, and we’re better off treating those cards as exceptional.
Aside from these exceptional conditions, there are no ways for the Player to use Action Points, or Gold to gather Faëria, and we’re therefore constrained to treat Faëria separately.

1F = ? AP
I would love to find a viable conversion for Faëria, so if you have ideas and theories in this regard, please get in touch!

Converted Costs Spreadsheet:

We may not be able to reduce the Faëria cost out of any equation or analysis yet, but the conversions described above already allow us to reduce the cost of a card from 3 resources down to 2: Action Points and Faëria. I have applied the conversions to the card list I have been using, and have shared it in a Google Spreadsheet accessible to everyone [Note]. You will see it includes a column named GL Cost, which represents the sum of the Gold cost and Land requirement for the card expressed in terms of Action Points. Further analysis, now that this value has been determined, should follow soon.

So, there you have it: we might have a way to move forward in ranking our cards, albeit it will still require that we deal with 2 incommensurable types of costs. We didn’t get any chart this time, but I plan to make up for it at the first opportunity.


Notes:

Action Points on the 1st Turn:

As you know, the Player that plays first gets one less Action point than usual, for that turn only. This is an important detail to recognize when analyzing specific decks and board configurations, but has little impact to the type of analysis we are working on at this point. If you plot the average number of APs received by a Player over the Game and Player Turns (like we did for Faëria Production), you will see that the impact of this missing AP on the first turn falls off quickly: by Game Turn 3 (aka Player Turn 2 for Player 1), the average value is already up to 2.5, and it is attracted by the basic value of 3 APs per Game Turn we are assuming.
By the same token, there are cards that modify the number of APs at your disposal, but we don’t account for them at this stage (it would certainly be an important detail to consider when analyzing a specific card or combination of cards).

One Assumption on Faëria Production:

One assumption made during analysis of the Faëria Production that is worth noting, although it is pretty self-contained, is that we assumed all of the Faëria on the board would be collected by the Players. In fact, each vortex has a maximum capacity of 3 Faëria; if the Players don’t collect the Faëria available, the number of units generated in the next Morning would not be the assumed 4, essentially biasing all of the values in the analysis.

On Lands and Structures:

As noted above, available unoccupied colored Lands may be critical at certain points in the game so that you may cast a Creature (assuming all other costs are met). Thus, it is probably a good idea to Play Structures on Prairies rather than colored Lands.
Conversely, balance this rule of thumb against the risk of your opponent running cards targeting Prairies, such as Sinkhole.

On the Shared Spreadsheet:

As usual, I have shared this spreadsheet with everyone, but have retained the editability to protect it from corruption (accidental or otherwise). You should still be able to copy it for your own use, and you are most welcome to contact me if you need a copy generated or wish to collaborate on the data.
Please also note that there have been 2 recent (within the last 24 hours) patches to the game that are not yet accounted for in the spreadsheet.


Image Credits: Card Images via FaeriaDecks Cardlist, with ©Abrakam.

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