【HEX】 Optimal resource ratio for multi-shard deck ~SBS Method~

A few people were asking about multi-shard resource calculation on official HEX forum.  So here is what I got for you.

Pre-requisite

  • Know what resource cards are, and how to optimize overall resource card #’s.  (See here).

Objectives

After reading this article, you will learn following(s):

  • Learn a mathematical approach to decide how many resource card of each shard are optimal for your deck

Why do I need to understand this?

In comparison to Magic, HEX’s threshold system allows easier to build multicolor deck.  However, there is still challenge in balancing the optimal ratio of how many resources from each color/shard to include.

Here is an extreme example to illustrate its importance.  If you have 3 threshold Diamond and Ruby cards in your deck.  Based on the previously discussed method, you may have identified optimal total resource cards in your deck to be 25.  But for some reason, you did not understand threshold rule and decided to include 22 diamond resources and 3 ruby resources i.e. total 25.  With this setting, expect you can never cast the 3 ruby resource card as your chance of drawing 3 ruby resources from your 60 cards deck has such low probability.

So the question now becomes how many should we include?  My goal for this article is to provide a basic guidance to achieve at least initial step of deciding this, which must always be followed by play/draw testing for fine tuning/optimization.

Magic Approach

Similarity between the Magic and HEX allows us to utilize what has been established in the world of Magic after 20 years as the guide.  However, despite subtle at glance, there is significant enough difference between the Magic’s mana system and HEX’s resource system especially when it comes to multi-shard deck.  Afterall, that is the reason why HEX developed threshold system!

Not only that, the objective method for multi-color deck, land ratio calculation are scarce.  I was bit surprised by this.  It is not a easy calculation, but given so many years of the game existence, and so many players, I had expected almost step by step standard guideline in place.

The one I could find was http://tappedout.net/mtg-articles/2010/jan/18/mana-ratios-basics/.  Unfortunately, I don’t think this system will work for HEX.  Perhaps modifying someway may allow us to build some HEX potential system but instead, I am going to present alternative, what makes more sense to me approach.

SBS Method

I like to name catchy method, and perhaps I should name this HoushaSen’s method or Mugen’s Method but since that would never be carried on, instead I have decided to abbreviate what I am doing here and call its a method name.  So SBS stands for Shard by Shard method.

Here is our keep this in your pocket table.

AvgCardTable

This table is once again created by extremely helpful site: http://ark42.com/mtg/land.php?decksize=60&landmin=1&landmax=30&firstdraw=7&minstartland=0&minstartnonland=0&turnsmax=30&chart=0&round=1

*This time rather than the table representing minimum card draw probability, each cells represent average number of cards that is drawn.  This means it is a bit underestimate when compared to 70% minimum probability analysis used in other article.  Nonetheless, this may be easier table for most to understand, and the difference may not be significant as both are just statistical prediction.

How would this work?

  • Treat individual shard as own.  # of copies of the specific shard you want is represented by X-axis (columns).
  • Target # of draw i.e. average lands card by turn (each cell) here is in respect to threshold value rather than cards cost.

SBS 7 Steps

For each Shard in your deck,

Step 1: Pick the highest threshold card with the lowest cost in the selected Shard.

*Basically, in this step we are trying to pick the most demanding card in the selected shard in regard to its casting.  So one may decide to pick some other card here because the real goal you want to achieve is for card X which is only 2 threshold, and 3 threshold card is you care much less rather you just put it for fun.
Step 2: Look at the table above pick a turn goal (which row) based on your expectation of when you want to use the card.

This may be the toughest and the most variable part.  You will see in the example below, but you might have to play around with this number back and forth.
Step 3: Look at the row # (from step 2) and find the lowest column # that achieves average value equal to or higher than the threshold (from step 1).

Once each Shard calculation are complete using above method,

Step 4: Add all to calculate the total resources.  Call this Shard Total Resource (STR).

Step 5: Calculate optimal resource card number using this method.  Call this plain total resource (PTR)

Step 6: Compare STR and PTR.

  • If STR is significantly higher than the PTR, you have high chance of resource flood.  So go back to one of the shard and repeat Step 1-3 then Step 4.
  • If STR is significantly lower than the PTR, just add additional resource cards of your choice.

Step 7: Play test for fine tuning and optimization

The most important step!

Specific Example

Let’s say you created a wild blood deck, and decided to include Chlorophyllia and Uruunaz.

Let’s start with wild shard.  It does not matter if we start out with blood shard as two are treated independently with this analysis.

Wild Shard

Step 1: Pick the highest threshold card with the lowest cost in the selected Shard.  The threshold # here is what you are going to plug in the table.

In this case, 2 thresholds with cost of 3.

Step 2: Look at the table above pick a turn goal (which row) based on your expectation of when you want to use the card.

Since the cost of Chlorophyllia is only 3, and its the key to boost my resources I want this guy out as early as possible.  Let’s say turn 3.

Step 3: Look at the row (from step 2) and find the lowest column # that achieves average value equal to or higher than the threshold.

So now based on Step 2, I am looking at third row and my target cell value is 2 or more since I need 2 wild threshold (per step 1).  According to the table, it falls under column value 13. 

Result:  Minimum 13 wilds resources will allow me to cast Chlorophyllia around turn 3.

Blood Shard

Step 1: Pick the highest threshold card with the lowest cost in the selected Shard.

Here my target is Uruunaz, which again has 3 Shards but the cost is 7.

Step 2: Look at the table above pick a turn goal (which row) based on your expectation of when you want to use the card.

Average Cards by Turn  
Turn # of Card Copies in Deck
1 2 3 4
1 0.1 0.2 0.4 0.5
2 0.1 0.3 0.4 0.5
3 0.2 0.3 0.5 0.6
4 0.2 0.3 0.5 0.7
5 0.2 0.4 0.6 0.7
6 0.2 0.4 0.6 0.8
7 0.2 0.4 0.7 0.9
8 0.2 0.5 0.7 0.9
9 0.3 0.5 0.8 1
10 0.3 0.5 0.8 1.1
11 0.3 0.6 0.9 1.1
12 0.3 0.6 0.9 1.2
13 0.3 0.6 1 1.3
14 0.3 0.7 1 1.3
15 0.4 0.7 1.1 1.4
16 0.4 0.7 1.1 1.5
17 0.4 0.8 1.2 1.5
18 0.4 0.8 1.2 1.6
19 0.4 0.8 1.3 1.7
20 0.4 0.9 1.3 1.7
21 0.5 0.9 1.4 1.8
22 0.5 0.9 1.4 1.9
23 0.5 1 1.5 1.9
24 0.5 1 1.5 2
25 0.5 1 1.6 2.1
26 0.5 1.1 1.6 2.1
27 0.6 1.1 1.7 2.2
28 0.6 1.1 1.7 2.3
29 0.6 1.2 1.8 2.3
30 0.6 1.2 1.8 2.4

Now since Uruunaz costs 7, it will take longer time for me to cast Uruunaz for sure when compared to Chlorophyllia.  In fact, its a unique card and relatively high cost card, so I have decided to include only 3 copies of Uruunaz.  This means I won’t hit average draw of 1 until turn 13.  If I accept 0.9 as in Wild Resource case, it is turn 11.

Step 3: Look at the row (from step 2) and find the lowest column # that achieves average value equal to or higher than the threshold.

AvgCardTable

So looking at row 11 (target turn #), and searching for a cell with minimum 3 (threshold), I get 11.

Result: Minimum 11 blood resources will allow me to cast Uruunaz around turn 11.

Step 4: Calculate STR

13 + 11 = 24 resources.

Step 5: Calculate PTR

Let’s say I get 23 resources based on the rest of my deck. 

Step 6: Compare STR and PTR

There is 1 extra resource I ended up adding based on STR compared to PTR. 

At this point I have two options.  One is to go back to Step 1  for either Blood or Wild Shard and see if I can accept later turn as target i.e. decrease required # of resource card from the shard.

Alternatively, since it is only 1 resource above PTR, I can just go to step 7 and see how this one extra resource will perform.

Obviously, if my rSTR result like 30 resources i.e. way over PTR,  I would have had way too many resources which equates to high chance of resource flood.  So in such case I must go back to earlier steps or perhaps even change the deck content itself.

If your total was lower than that of calculated total resource cards, you can just add few extra to choice of your Shards.

Step 7: Play test for fine tuning

Again, I hope the Deck Builder of HEX be good enough that we can actually do all the draw testing without actually playing the game.

Conclusion

Shard by Shard method in theory should work but I have never played TCG that uses exact resource system of the HEX.  So the time will only tell if this is a valid approach or not; however, this is the best I can come up with and as far as I can tell I could not find any other article that went to this systematic approach even on Magic.  Though I must say this won’t work on Magic as their resource system is even more complicated than that of HEX when comes to multicolor deck.

Tell me what you think about this.

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4 responses to this post.

  1. Posted by Luxiom on July 5, 2013 at 6:23 am

    Hi!

    Thanks for a great article! Quick question, I didn’t really catch how you calculated PTR in this context?

    Reply

  2. Posted by houshasen on July 6, 2013 at 9:34 am

    @Luxiom,

    The selection of the exact target is pretty difficult thing to do as it really depends on the deck, style of play. In my example, I just simply went off based on the couple assumptions. 1. My deck works the best when Uruunz in play i.e. its a keycard, and I may even say that’s the highest cost card I have in my deck i.e. the worst case scenario. So that’s how I chose target.

    However, this may not necessary be true in all cases. For example, if you include newly revelaed cad like comet strike (10 cost) just for fun, you may not necessary need the card every game. So despite having 10 cost card in your deck, you may just use your tagert as 4 costing card as that is more of a real goal.

    Personally, one thing you might have to be careful is taking average of all cost and call it your target approach. If you have good distrubtion/mana curve, then I think that approach be fine. But say you have half 1 cost and half 8 cost cards in your deck, your average becomes 4.5. But targetting for 5 cost does nothing as you won’t still be able to use half of your card since they are 8. Obviously, noone would make such extreme deck, but this simply proves the math of taking average as target can easily fail.

    So long answer, but target is something you have to decide. I’m not a pro player, and just like math, and theory. So there may be someone who have good logical way of telling what’s the good target but so far what I have read are mostly just based on your experience and instinct.

    Reply

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