Cost Management - Akachi

Card draw simulator

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gennis · 19

The art of deckbuilding is a meticulous accounting in Cost Minimization.

"Spell design is a business."

(Last updated date: 22/08/2023)

General Principle:

The core principle deals with following 3 costs when building a deck.


  • Time Cost

The mission of player(s) is to advance the act as early as possible before the agenda advances. When a card either advancs the act with insufficient pace or results a doom, it raises the time cost up after adding this card into your deck; i.e., the more OP the card, the less the time cost is.


  • Direct Cost

When a card reduces the resources spent or gains resources, it drops down the direct cost of the deck. In my opinion, playing a card with 3+ resources incurs expensive price, and it is fair but still a little bit high for paying 2 resources, especially when you put a lot of cost 2 cards in a deck.


  • Opportunity Cost (OT cost)

This cost is subject to drawing and playing core cards. There are severval types of OT cost:

  • Type I (OT) Cost

Drawing a card means paying OT cost that loses a chance to draw another core card in the deck, no matter where the draw chance comes from, even free draw. (n1)

  • Type II A (OT) Cost

When a card exhausts an action to Play it in investigation phase, it incurs type II A cost.

  • Type II B (OT) Cost

When a card exhausts an action to Activate it in investigation phase, it incurs type II B cost.

  • Type III (OT) Cost

When the deck size becomes more bulky, it dilutes the chance of drawing the core cards. Hence, type III cost would be reduced when the effective size of the deck is lower down. Only some cards that incur no type I & II costs are able to do so. I will discuss it in later section.


Preface:

Standard/Hard
This deck is originally designed to play in Standard multiplayer game though, I would sometimes analyse the cards in view of Hard mode as my friends may play different difficulties and I am lazy to build a new deck with the same investigator.

0 Experience / 30 Experience Deckbuilding
I would also share and discuss the deckbuilding under 0 experience here. Actually, when I search in the decklists, almost the builds are under 0 experience, and there is difficulty to find how a specific card with higher level that would be constructed in straightforward manner. Hence, I share the build with higher card levels so that players can search the end-game card I used more easily. Here is actually a 30 experience deck where 8 costs are discounted by duo Arcane Research over 4 scenarios.

See the 0 exp deck here.

Cost Quantification
In order to determine the fitness of a card in building the deck, I would like to quantify the costs in the same unit. In particular, a Draw, Play, or Activiate is stand for an unit of OT cost. Since Resource also exhausts an action in investigation phase, it offers a means to compare 1 OT cost and 1 direct cost, although it is rough a bit. When I consider the time cost, I would like to segregate the direct cost and focus on OT cost first. For each round, there is (3+1) actions (+1 comes from the draw during upkeep phase). Therefore, an unit of time cost is equal to 4 OT costs. (n2)


Agenda:


Deck Construction:

If the card is belong to CORE CARD in my deck, there would be a behind the name of the card.

Act Advancer

Rite of Seeking : To boost up the progress of act advance, mystic should never draw less than 2 clues per action. I would like to upgrade Rite of Seeking to Rite of Seeking (2) in advance with no experience spent due to duo Arcane Research. I only put one Rite of Seeking as I use Sign Magick (3) to trigger duo investigation to clean up the location by 1 action, or at least within 1 turn. The free investigation triggered by Sign Magick (3) must be activiated by different spell asset.

Clairvoyance : The advantage of Clairvoyance is that its side effect takes 1 horror rather than losing all remaining actions, especially when you have to investigate at first. Moreover, "+1" token is always removed by one and more are put into the chaos bag in Hard+ mode. This further raises up the value of Clairvoyance over Rite of Seeking. Nonetheless, the upgrade of Clairvoyance (3) exhausts 1 experience even with duo Arcane Research that is too scarce for experience.

Sign Magick (3) : It is the card I mostly like!

  1. It offers additional arcane slot and hence I can play Alchemical Transmutation or Earthly Serenity to gain resouces or heal when investigation spell asset and fight spell asset are both played.
  2. One more spell can be employed without exhausting action as it is after an activiation of another spell, especially reinforcing the number of clues discovered or the damages dealt to the enemies. When you hold 2 Sign Magick (3), you can even activiate 5 spells in every turn! It highly speeds up the act advance! Note that Spirit-Speaker can switch the combination of spells.
  3. It saves the charges and thus reduces the demand to Spirit-Speaker and resources. Its effect can activiate an spell without paying charges. It means that you can cast 2 spells in cost of 1 charge!
  4. Although you have to spend charges for Brand of Cthugha and Earthly Serenity after being activiated by the effect of Sign Magick (3), you can still activiate, say Brand of Cthugha, first and then activiate Shrivelling by the effect of Sign Magick (3) when there are none of charge in both of the spell assets. This combo help you to deal damages, discover clues, or gain resources under lack of charges in your play area.
  5. It is fast to play it so saves an action.
  6. It is ritual card so its playing cost can be saved by Uncage the Soul.

Virtuous Defender

Shrivelling : It can deal 2 damages per fight and thus avoid an embarrassing situation that faces an enemy attack in enemy phase with 4+ health enemy. In view of this, Azure Flame is a good substitute of Shrivelling, especially in Hard+ mode. Similar to the reason presented in Rite of Seeking, there is only one Shrivelling to perform the combo triggered by Sign Magick (3).

Azure Flame : The reason to choose it is same as Shrivelling, but Shrivelling would be more suggested in Standard mode as horror is relatively easier to deal with than damage for mystic.

Brand of Cthugha (1) : During the game, you can wait Rite of Seeking (2) for getting clues in the location with high shroud value, so just exploit Clairvoyance to investigate other locations with no bonus in effect. However, 4+ enemies would not wait for you to draw Shrivelling (5). That's why I at least spend 1 experience to purchase Brand of Cthugha (1) that offers bonus and is able to deal 2 damages per fight.     You can just upgrade a spell card with 2-cost discount after each scenario. This precious upgrade with allowance would be applied for Shrivelling (5), Rite of Seeking (2), Alchemical Transmutation (2), and Earthly Serenity (4) first. I would not wait for the upgrade of Azure Flame (3) but spend 1 experience to purchase Brand of Cthugha (1) in replace of Azure Flame.     You can exploit Spirit-Speaker to earn 5 net resources by playing and then discarding Brand of Cthugha (1).

Ward of Protection: Some treachery cards is too catastrophic (e.g., Ancient Evils, Terror from Beyond, Rites Howled, ...) or lethal (e.g., Beyond the Veil, Lost in Venice), or cuts down the number of available actions every rounds (e.g., Slumber, The Shadow Behind You). Without a doubt, Ward of Protection can save your time cost or even your life ...

Counterspell (2): This powerful card turns the tables.

  1. It makes you to pass a skill test for sure except . Just pass the skill test by your stat.
  2. You can play it after the chaos token is revealed. Unlike Defiance (2), it has to be commited before the token to be drawen.
  3. It avoids the negative effect that were be triggered after the test for Shrivelling, Rite of Seeking, Alchemical Transmutation, or the scenario reference card.

Empty Vessel: It act as Counterspell (2) after defeating 2 enemies. (When it is played, it gains 1 charge immediately from Akachi's ability.) Moreover, Wish Eater heals 3 damages and 3 horrors at the same time. If you still have Counterspell (2) on hand, defer the swap to the Wish Eater so that Empty Vessel can accumulate more charges after defeating enemies. (The swap is but not Forced.)


Electricity Generator

Uncage the Soul: It's a very nice card.

  1. It saves 3 resources to play Sign Magick, Shrivelling, Rite of Seeking, Clairvoyance, or Azure Flame. The efficiency of saving resources would be further discussed in the section of Cost Analysis.
  2. Playing spell or ritual card by Uncage the Soul would not exhaust additional action; i.e., it only incurs type I cost but no type II cost. This advantage would be further discussed in the section of Cost Analysis.
  3. It has 2 in commit skill test. It can save your teammates from the skill tests triggered by treachery cards or activiated in locations in mid to late game.

Prophetic:

  1. Its resources can used to pay for arcanes, Counterspell, and Ward of Protection. You can have up to 4 resources to pay for replenishment of charges with duo Prophetic and Spirit-Speaker every round.
  2. Since duo Sign Magick (3) occupy both of the hand slots, it is used to act as Spirit Athame to boost up the stat in casting spells, especially to maximize the resources gained or the healing effect from Alchemical Transmutation and Earthly Serenity.
  3. Since it is 3-class asset, it is sometimes to achieve combo with synergy cards like Close the Circle or Call for Backup. Since synergy strategy may incur high OT and time costs (although gains high returns, too), I would not exploit the multiple classes of Prophetic owned here. It would be explained in more detail in the section of Cost Analysis.

Alchemical Transmutation: Even the 0-exp version, it offers a potential 11 net resources in maximum. See the section of Cost Analysis for more detail about this card.

Spirit-Speaker : It is the exclusive OP card used for replenishment of charges! Undoubtedly, charges is the lifeline of Akachi Onyele.


Strategy Book:

The core cards mentioned would be drawed in the most advanced order.

Mulligan Therapy

In all sense, there must be at least a fight spell in hand when the game is started and that is why I put 3 fight arcane cards here.

Do not just rely on guardian player. He/she has to spend actions to get and play the gears and the whole team has to draw 1 treachery cards every round! Guardian cannot save the whole team and always be the same location with all of the teamates. Mystic must share the battle loading.

If you have at least one fight spell in hand, an investigation spell is the next target. Push the act advance now!

Action Moment

Akachi can do a lot even she just have each of the fight and investigation spells in play. Move now! Clean the clues!

If you have no fight spell on hand or the play, use Arcane Initiate, Eldritch Initiation, and the skill cards to enhance the drawing of the fight spell.

Do not waste too much time (action) to set up your phalanx like Prophetic, Four of Cups, ... The cards other than core cards would exhausts your actions to get enough resources to pay their costs and play them.

Auxiliary Summoning

The list below follows the priority to be played.

Since the deck has no card like Moonlight Ritual or Forbidden Knowledge that clear the doom generated by Arcane Initiate, so you should either:

  1. intentionally take damage/horror to kill Arcane Initiate before the agenda advance when there is a doom on Arcane Initiate; or
  2. play Arcane Initiate before the round that agenda to be advanced. (When the doom threshold is 8 and there are 7 dooms on the current agenda (and the play), for example, playing Arcane Initiate would not advance current agenda as the checking of doom against threshold is executed in the Mythos phase. When next round starts, add 1 doom first and the agenda advances as there are 9 dooms in the play. Thus, the doom on Arcane Initiate does not make the agenda advance earlier in this situation. Note that the doom on the Arcane Initiate is removed when the agenda advances so do not count the "doom" on the Arcane Initiate for next agenda.)

Play Prophetic (3) asap to save resources and boost up stat.

Play Sign Magick (3) asap to exploit free spell actions. Remember that playing Sign Magick (3) costs no action as it's fast asset.

Play Empty Vessel after fight spells summoned to accumulate charges.

Play Alchemical Transmutation (2) to earn sufficient resources to play and recharge spells.

You should play Spirit-Speaker once you have chance to do so. Do not wait to play it when the charges are exhausted. Sometimes the enemy spawns and engages you when the charges in your fight spell are going depleted. Now when you play Spirit-Speaker and then replenish the fight spell, you are suffered from 2 times of AOO and have only one action remained to activate the fight spell.

It is the least urgent to play Holy Rosary and Four of Cups (1) to boost up stat, especially they are not cheap. Akachi has 5 and upgraded spells against the chaos bag.

Play Earthly Serenity (4) before anyone going to be defeated.


Cost Analysis:

Now, I introduce 2 benchmarks first.

Emergency Cache: Since this card provides a basic way to gain resources for any investigators, this card would act as a benchmark to evaluate the efficiency of gaining resources or the reduction of the direct cost. (Gaining resources would be also included in the term "reduction of direct cost" for convenience, hereafter.) Obviously, this card incurs type I cost and type II A cost; i.e., it incurs 2 OT costs to gain 3 resources. Therefore, any way that saves the direct cost less or equal to 1.5 per OT cost should not be added to the deck, unless the card also saves enough time cost in effect.

Here, I introduce a new unit to measure the efficiency of reduction of direct cost (ERDC): d/ot, which means the unit of direct cost could be saved by paying 1 OT cost.


Guts / Manual Dexterity / Overpower / Perception: Literally, it only incurs type I cost. No type II or direct cost is involved as it is free to commit it in skill test. Nevertheless, it draws 1 card when the test is successful. It means this card earns back the 1 OT cost paid. It is a "0 cost" card. In other words, adding this card into the deck would not involve in the calculation of probability of drawing up the core card(s). Adding a "0 cost" card is effectively reducing the "deck size". If there is 4 "0 cost" cards, for example, the pseudo probability of drawing up, say Shrivelling (3), can be deemed as 1/26 instead of 1/30. In fact, it reduces type III cost! It is effectively a negative cost card! (n3)

What is more, it raises up the probability of passing a skill test. It can save you or your teammates from the bad stat attacks, and of course, reduce the time cost.

It becomes a benchmark in consideration about whether a card should be added or not. If a card is not classified as core card as the powerful function presented in the section of Deck Construction or has sufficiently high ERDC, I am very cautious whether it should be added or, rather, add an explicitly negative cost skill card, which, at least, enhances the draw of the core cards in the deck without "cost".

Please note that this draw enhancing would be realized after committing these negative cost skill cards. Therefore, 2 points should be noted:

  1. When you believe that your core card(s) is not yet on your hand or play, commit the negative cost skill cards asap to enhance the draw, whatever the skill test is needed to boost up the stat or not.
  2. The composition of the characters of your teammates in multiplayer game is highly related with which negative cost skill cards should be added; e.g., when the team is constituted by mystic, seeker, rogue, and survivor, then Overpower should not be added as there are seldom test that is mostly triggered by guardian and Overpower will be stuck in your hand.

Alchemical Transmutation: When it is fully utilized, it incurs 6 OT costs (1 Draw, 1 Play, 4 ) in order to gain 11 net resources in maximum; i.e., its ERDC is equal to 1.83 d/ot literally. However, it requests 4 consecutive tokens taken are more or equal to -1 and it is hard to do so; i.e., this number is upward biased.(n4)

That's why I don't really love Alchemical Transmutation, but there is no better option to reduce sufficient amount of the direct cost of the deck. Actually, I add it due to the presence of Spirit-Speaker and Sign Magick (3). They recharge and activite the effect through when investigation or fight; i.e., increase the ERDC of all arcanes by reducing the average OT costs incurred during the game.

Nevertheless, it is amazing for Alchemical Transmutation (2). The upgrade does highly raise up the ERDC of Alchemical Transmutation. Literally, its ERDC is equal to 2.86 d/ot. Moreover, its higher ceiling of resources gained and reduced base difficulty of the skill test allow it to have more resistance from the bad stat attack in Hard+ mode. If we apply the calculation presented in footnote 4, the erosion of the total resources gained for Alchemical Transmutation (2) is less than Alchemical Transmutation by 14% when playing Hard mode instead of Standard mode. It still has good performance in Hard+ mode with the combo of Spirit-Speaker and Sign Magick (3).


Uncage the Soul: As explained in the section of Deck Construction, we can compute its ERDC that is 3 d/ot. Why I just can put 2 cards only. The only card used for reducing direct cost I am fully satisfied.


Prophetic: It costs 3 resources to play it. Although it is a reasonable price for its effects, 3 dollars is an expensive price as explained in the section of General Principle. 3-dollar cost means that it takes time to accumulate enough wealth and compete the resources and actions with the core arcane assets. It looks fluent that plays Prophetic first and then uses the 2 resources to pay the cost of playing arcane assets and boost up the skill values when activation of those arcanes. Nonetheless, the morning sun never lasts a day during the game.

The actual situation I encountered is that I have to spend actions to get and play any of the fight arcane first (that is why I put 3 fight arcane cards here); otherwise, you or your teammates would suffer from the enemy attacks. Do not just rely on guardian player. He/she has to spend actions to get and play the gears and the whole team has to draw 1 treachery cards every round! Guardian cannot save the whole team and always be the same location with all of the teammates. Mystic must to share the battle loading. As a result, I always take actions to get and play fight spell, and kill the enemies first to prevent from damages. In the meantime, I have to collect clues in advance also; otherwise the agenda would be advanced before the act advance.

In my opinion, current number of doom threshold set in Arkham Horror squeezes the chance for playing Prophetic when I aim to advance the act before the agenda advance. But when current scenario is not too demanding, it's worth to play Prophetic with 3 dollars.


Voice of Ra: It offers potentially 3.5 d/ot in maximum. It performs well when there are many tokens in chaos bag. However, it cannot beat Emergency Cache in reducing direct cost generally. (n5)


Eldritch Initiation: It is used when there is no fight spell in hand or other core card(s) is demanding. When Sign Magick (3) is in play, it raises up the number of cards to draw.

When you are looking for specific core card(s), it doesn't matter for discarding other cards from the hand. Drawing 2 cards with discarding 1 card is better than drawing only 1 card. Even drawing 4 cards with discarding 4 cards from the hand is better than only drawing 1 card. Getting and then playing the core cards asap lower down the time cost of the game. In other words, I would count the gain by the number of cards drawn instead of the net change of the hand size; e.g. when drawing 3 cards with discarding 2 cards, Eldritch Initiation gains 1.5 cards per OT cost.


Arcane Initiate: It enhances the drawing of the core cards. Although some core cards are not spell, Arcane Initiate still increases the chance of getting these cards by thinning the deck.

As I mentioned above, you should either:

  1. intentionally take damage/horror to kill Arcane Initiate before the agenda advance when there is a doom on Arcane Initiate; or
  2. play Arcane Initiate before the round that agenda to be advanced.
  3. play another ally card that places no doom such that discard Arcane Initiate with the doom on it before the agenda advance. I add Familiar Spirit to do so when I use the combo of Close the Circle (1). However, this set of combo has insufficiently low time cost in my analysis.

If you do not follow these suggestions, playing Arcane Initiate adds an unit of time cost! It is a loss unless you can earn back the [(3+1) + 2] OT costs through Arcane Initiate; i.e., draw not less than 14 cards additionally through the effect of Arcane Initiate in a 4-player game, but there is only 12 spell cards in the deck.


Earthly Serenity (1): Although this card cannot reduce the time cost directly, there are many different situations that deal damages / horrors to you and/or your teammates. Death can be deemed as infinite time costs. Apart from Wish Eater, Earthly Serenity (4) is added to heal you and your teammates.

Instead of Healing Words or Clarity of Mind, Earthly Serenity (1) is used since it can potentially heal more faster and heal damage and horror by one arcane slot.

If you want to have a fair benchmark to determine the cost-effectiveness among various card effects, the location effect of Temporary HQ may give an idea. It is equivalent for the following 4 effects:

  1. healing 3 damages;
  2. healing 3 horrors;
  3. gaining 5 resources;
  4. drawing 3 cards.

As I deem the (reasonable maximum) cost of drawing a card as 1 OT cost, a fair benchmark now becomes: (1) healing 1 damage / horror per OT cost, and (2) 1.67 d/ot.

With recharge made by Spirit-Speaker, increasing the healing effect with boosting the stat by Holy Rosary, Four of Cups (1) and Prophetic (3), and saving OT cost(s) by the effect triggered by Sign Magick (3), Earthly Serenity (4) is able to give a satisfactory healing effect. That is why I don't really like it (as it doesn't save time cost directly) but still put and upgrade it in the deck. (n6)


Delve Too Deep: By drawing one more treachery card for each teammate, your team can earn 1 more experience for each time Delve Too Deep played. Obviously, it explicitly raises up the time cost of current scenario, but implicitly drops down the future time costs of all scenarios remained (unless your team get trauma due to the additional treachery cards drawn).

Delve Too Deep is mostly criticized for the increase of the probability of defeat. Generally, the difficulty of the scenario in the late campaign is greater than the early one. Delve Too Deep acts as a balance to raise the difficulty of the early game and decrease it for the late one. If you would lose your life in the early game due to drawing one more treachery card, then why you believe that you can pass later scenarios, especially the timing of playing Delve Too Deep is fully under control. If you believe that playing it is dangerous, just keep it in your hand and deem it as just wasting 1 OT cost (type I).

Akachi Onyele has high , is good at battle and counter against negative stat, and has some healing ability. She can suppress the negative effects brought by Delve Too Deep for the team. Remember to remove it before the final scenario as now Delve Too Deep cannot yield additional benefit for your team to win current campaign any more. Remove it earlier once any teammate believe that it can kill him/her in latter scenarios.


Occult Lexicon: TBC


Hallowed Mirror: TBC


Quantum Flux: TBC


Astral Travel: TBC


Close the Circle (1): TBC


The Red Clock (2E): TBC


Divination (1): TBC


Blur (1): TBC


Call for Backup (2): TBC


Segment of Onyx (1): TBC


The Hierophant • V (3): TBC


Decorated Skull: TBC


Forbidden Knowledge: TBC


David Renfield: TBC


Blood Pact: TBC


Spirit Athame (1): TBC


Defiance (2): TBC


Upgrade Path


Q&A

Q1: Why there are seldom to analyse time cost?

A1: I only focus on the cards OP enough that can pass the benchmark, otherwise I would prefer to add the "negative" cost cards instead. The cards with high time cost have no value to be discussed.

Q2: Why segregate direct cost and focus on OT cost?

A2: As I mentioned in the section of Preface, in order to simplify the idea, I only focus on OT cost minimization as the foundation to access which cards should be added to a deck.

Q3: If I want to integrate the direct cost analysis into your cost minimization analysis, what would be the steps?

A3: If you want to consider both of the direct cost and OT cost of a card, one of the way could be to convert the direct cost into OT cost (in exchange rate of 1.5 or 1.67, depending on which benchmark adopted) and evaluate the cost-effectiveness of each card with this new total OT cost.


Epilogue:


Footnotes

n1: Even the draw is what exactly you want, say Shrivelling, this is still deemed as paying an unit of type I cost, too. For fair and consistent comparison, gauge of type I cost would not specify which core card actually is.

n2: There is a variety of methods of gaining resources and click a resource by taking an action is an impotent way to do so. Thus, we cannot simply equalize the OT cost and the direct cost. Instead, we have to compare the OT cost paid for a common way of gaining resouces as the benchmark. For time cost, delaying a round is not only wasting, or at least not fully utilizing, your (1+3) actions, but also dealing with treachery cards or enemies in mythos phase. Quantification does not mean the qualification analysis could be missed. It is a little bit special for type III cost quantification. The relevant description and calculation is introduced in footnote 3.

n3: It is not introduced how to compute the amount of type III cost to be reduced for a card as the complexity. If you just add 1 such negative cost skill card, the OT cost saved is equal to (1 / effective deck size after the card added) x (number of core cards). The first card inherently lowers down 0.28 OT cost of my deck. However, the denominator keeps changing when further negative cost skill card replaces other card in the deck. This formula also ignores the interaction between the reduced effective deck size and the draw enhancing mechanism in the deck, especially the number of draws enhanced by Arcane Initiate and Eldritch Initiation are not fixed. The marginal OT cost saved could be an advanced probability exercise to calculate the unbiased estimator of the draw enhancing mechanism and then compute the interaction term between this expected value and the reduced effective size of the deck. But, it's just a game. Why so series?

n4: To calculate the unbiased estimator of ERDC of Alchemical Transmutation, it depends on the initial setting of chaos bag of the scenario played. Here give an example of the first scenario of the Dunwich Legacy. For Standard mode, the ERDC is equal to [ (10/15 x 3 + 2/15 x 2 + 1/15 x 1) x 4 - 1] / (6 - 0.28 x 2) = 1.53 d/ot. It is a very rough calculation with assumption of the stat of are -1 and the benefit of reduction of type 3 cost is based on saving 2 cards in deck size whose approximated value is adopted the formula presented in footnote 3. That is why I believe that it is the commonplace for reduction of direct cost and upgrade it via duo Arcane Research in early campaign. With respect to Alchemical Transmutation (2), its ERDC is [ (10/15 x 4 + 2/15 x 3 + 1/15 x 2 + 1/15 x 1) x 5] / (7 - 0.28 x 3) = 2.65 d/ot and [ (7/16 x 4 + 4/16 x 3 + 2/16 x 2 + 1/16 x 1) x 5] / (7 - 0.28 x 3) = 2.18 d/ot in Standard and Hard modes, respectively.

n5: Again, take the first scenario of the Dunwich Legacy as an example. In Hard mode, the ERDC is equal to { 7 x (4/16 x 3/15 x 2/14) + 5 x [3C2 x (4/16 x 3/15 x 12/14)] + 3 x [3C1 x (4/16 x 12/15 x 11/14)] + 1 x (12/16 x 11/15 x 10/14) } / 2 = 1.25 d/ot. It becomes 1.21 d/ot and 1.30 d/ot in Expert and Standard modes, respectively. Obviously, Voice of Ra does not perform well when there are insufficient tokens in chaos bag, since its ERDC does not pass the 1.5 d/ot benchmark test.

n6: Again, take the first scenario of the Dunwich Legacy as an example and the assumption applied in footnote 4. The expected amounts of healing per activation are shown below:

Difficulty        Earthly Serenity (1)     Earthly Serenity (4)
Standard 2.73 per activation 3.67 per activation
Hard 2.25 per activation 3.13 per activation
Expert 1.65 per activation 2.41 per activation


By employing the numbers in the table above, the cost-effectiveness of healing now becomes:

Difficulty        Earthly Serenity (1)     Earthly Serenity (4)
Standard 1.30 per OT cost 1.79 per OT cost
Hard 1.18 per OT cost 1.65 per OT cost
Expert 0.99 per OT cost 1.42 per OT cost

(Nonetheless, the cost-effectiveness is still biased here, because the charges used and remained must be an integer in actual game and hence the cost-effectiveness has to be calculated with probabilistic floor and ceiling functions subjected to optimization problem instead of decimal numbers of expected healing amount.)

The table above illustrates that even in the hardest situation, the 1-exp version of Earthly Serenity (1) passes (although very marginally) the benchmark and perform 50% better than the 0-exp healing cards Healing Words and Clarity of Mind (cost-effectiveness: 0.67 per OT cost).

In fact, when consider the combo interaction between Spirit-Speaker, Holy Rosary, Four of Cups (1), Prophetic (3), and Sign Magick (3), the cost-effectiveness of Earthly Serenity (4) can be raised up to healing 2.90 damages / horrors per OT cost with 0.125 (expected) direct cost per recharge.

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