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Half Blood Deck Composition http://elementscommunity.org/forum/index.php?topic=23323.msg296654#msg296654
« on: March 23, 2011, 05:13:35 PM »
Hi,
Since my little wiki modification got deleted i'll post here my knowledge on how the Half Blood decks are made.

General stuff

Half Bloods (HB) have a randomly composed deck of 2 elements choosen at random from the 12 possible elements.
There is a primary element the HB is focused on and a secondary element, these 2 elements determines the name of the Half Blood. The secondary element determines the marks of the HB. Note that the 2 random elements can be the same, this yield a total of 144 (12 x 12) possible HB (but a lot more possible decks, see below).
The HB name is composed by a prefix and a suffix, each prefix and suffix corresponding to an element. The prefix is choosen by the primary element and the suffix by the secondary element.

Here is the corresponding table :

Prefix
Dis
Mor
Mas
Ter
Vit
Pyr
Aqua
Lum
Ari
Chr
Shad
Aeth
Suffix
cord
tis
sa
ra
al
ofuze
rius
iel
es
onos
ow
eric
Element
:entropy
:death
:gravity
:earth
:life
:fire
:water
:light
:air
:time
:darkness
:aether
example:
Vitofuze is an HB with main element :life and secondary element :fire . You can direcly verify his secondary element by looking at the marks.
Chronos is an HB with only :time as element because his primary and secondary elements are the same.


Deck composition

I'll call the primary element Pe1 and the secondary element Se2.
Pe1 and Se2 are choosen at random from
:entropy
:death
:gravity
:earth
:life
:fire
:water
:light
:air
:time
:darkness
:aether
HB decks are composed of 64 cards:
    4 quantum pillars30 random cards from
Pe1 in the card pool10 random cards from Se2 in the card pool20 pillars from Pe1[/list]
Each card has then 30% chance to become an upgraded card. This means that the vast majority of the decks (94.4%) will have between 20%-40% upgraded cards (13-26 cards). For the rest, 3% of the decks will have less than 13 upgraded cards and 2.6% will have more than 26 upgraded cards.


The card pool is a subset of the available cards in the game.
Here is the card pool:
(it is splitted due to the size of the pool)
Hover over cards for details, click for permalink
Deck import code : [Select]
4sa 4t3 4t4 4t5 4tb 4tc 4vc 4vd 4ve 4vf 4vg 4vh 4vi 4vj 4vk 4vl 4vm 4vn 4vo 4vp 4vq 50u 52g 52h 52i 52j 52k 52l 52m 52n 52o 52p 52q 52r 52s 52t 52u 52v 542 55k 55l 55m 55n 55o 55p 55q 55r 55s 55t 55u 55v 560 561 562 576

Hover over cards for details, click for permalink
Deck import code : [Select]
58o 58p 58q 58r 58s 58t 58u 58v 590 591 592 593 594 595 596 5aa 5bs 5bt 5bu 5bv 5c0 5c1 5c2 5c3 5c4 5c5 5c6 5c7 5c8 5c9 5de 5f0 5f1 5f2 5f3 5f4 5f5 5f6 5f7 5f8 5f9 5fa 5fb 5fc 5gi

Hover over cards for details, click for permalink
Deck import code : [Select]
5i4 5i5 5i6 5i7 5i8 5i9 5ia 5ib 5ic 5id 5ie 5if 5ig 5ih 5ii 5jm 5l8 5l9 5la 5lb 5lc 5ld 5le 5lf 5lg 5lh 5lj 5lk 5ll 5lm 5mq 5oc 5od 5oe 5of 5og 5oh 5oi 5oj 5ok 5ol 5om 5on 5oo 5op 5pu

Hover over cards for details, click for permalink
Deck import code : [Select]
5rg 5rh 5ri 5rj 5rk 5rl 5rm 5rn 5ro 5rp 5rq 5rr 5rs 5rt 5ru 5t2 5uk 5ul 5um 5un 5uo 5up 5uq 5ur 5us 5ut 5uu 5uv 5v0 5v1 5v2 606 61o 61p 61q 61r 61s 61t 61u 61v 620 621 622 623 624 63a


things to notice:
HB can not have non element cards, despite their presence in the pool.
Pillards and pendulums are in the card pool, so they can be choosed as part of the 30 Pe1 and 10 Se2 cards.
Miracle is missing, and its the only non-special card missing for an element.(special cards are Nymphs, malignant cell, ashe, ...)

Number of possible decks
Huge numbers coming ;)
There are 2 tables, one for the 12 monoelement decks and another for the remaining duo decks. I've regrouped elements to spare space. In the first table the number under an element is all the possible decks for that mono element deck.
In the second table the elements on the left indicates the primary element and those on top the secondary element with the restriction that you are not allowed to form a mono deck.
For example, the first number in the second table is the possible decks for Pyreric (:fire :aether) and Aethofuze (:aether :fire) but not for Pyrofuze nor Aetheric.
I've considered upped cards being different than the unupped cards when counting the decks.


:fire :aether
:life :light :air
:entropy :gravity :earth :water :time :darkness
:death
4.3103e+020
2.4906e+021
1.3310e+022
6.6249e+022
:fire :aether
:life :light :air
:entropy :gravity :earth :water :time :darkness
:death
:fire :aether
5.1319e+026
9.3664e+026
1.6517e+027
2.8248e+027
:life :light :air
2.1627e+027
3.9473e+027
6.9608e+027
1.1905e+028
:entropy :gravity :earth :water :time :darkness
8.5114e+027
1.5534e+028
2.7394e+028
4.6850e+028
:death
3.1483e+028
5.7460e+028
1.0133e+029
NA
Same tables with precise numbers:
:fire :aether
:life :light :air
:entropy :gravity :earth :water :time :darkness
:death
431032911706002504360
2490648302616457820760
13310238778498704698040
66248688465709462019790
:fire :aether
:life :light :air
:entropy :gravity :earth :water :time :darkness
:death
:fire :aether
513193416417735345638290560
936641186122024362359540160
1651711338967870918569511680
2824801778575733786871721680
:life :light :air
2162743683474741813761367360
3947273570085674098515204960
6960783499936027442542942080
11904521781140592387530827080
:entropy :gravity :earth :water :time :darkness
8511442883352209718673768320
15534431469369427097382419520
27394051193296624128717384960
46850053461262976492863254960
:death
31482666574217548448048995320
57459743673633505911340654020
101326859811568763112471690960
NA
How to compute the numbers:
For mono decks, you must choose 40 cards from the list corresponding to that element to form the deck. If there is n possible cards in the list, that means each one of the 40 cards can be one of the n cards or its upped counterpart.
All the different possible hands with those 40 cards are all the combination with repetition of 40 cards choosen among 2n cards (n normal cards and n upped cards).
The formula for a combination with repetition of size K from a set S with N objects is given by   (N+K-1)!/(K! * (N-1)!).
For the 40 cards in the mono deck, N=2n and K=40, this gives (40+2n-1)!/( 40! * (2n-1)! ).
For the Pe1 pillars, there are 20 cards (K) and n=1 (N=2) , the formula gives 21. Its easy to see that all the possibilities for the 20 pillars are the hands with 0 upgraded pillar, 1 upgraded pillar, 2 upgraded pillars, ...., 20 upgraded pillars.
For the quantum pillars, the number of all possibilities is 5.
Finally the number of decks for a mono element is given by 5 * 21 * (40+2n-1)!/( 40! * (2n-1)! ).

For duo decks its the same approach but instead of using the formula with 40 cards you must use it twice, one with 30 cards and one with 10 cards.
The number of decks for a duo element is given by 5 * 21 * (30+2np-1)!/( 30! * (2np-1)! ) * (10+2ns-1)!/( 10! * (2ns-1)! ).
Where np and ns are the numbers of the primary and secondary elements cards in the pool.


Ideas on How to improve HB?
Get rid of the pillars/pendulums in the card pool.
Add the 'best' cards in the card pool in double or triple so they are choosen more often.
Instead of giving 20 pillards and relying on the 3 marks, one can compute the QI (quantum index) based on the 10 and 30 cards to determine the number of pillars to add.
...
« Last Edit: July 13, 2012, 10:24:26 AM by Kuroaitou »

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Re: Half Blood Deck Composition http://elementscommunity.org/forum/index.php?topic=23323.msg318464#msg318464
« Reply #1 on: April 23, 2011, 08:53:49 PM »
You shoud remove mono :death from the second table...
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Re: Half Blood Deck Composition http://elementscommunity.org/forum/index.php?topic=23323.msg344347#msg344347
« Reply #2 on: June 01, 2011, 11:15:18 AM »
Excellent work !

Information has been added to this Wiki page (http://elementscommunity.org/wiki/pve/half-blood/) (I don't know how it got deleted).

As for the number of possible decks, I'd like to know if Half-Bloods can have more than 6 copies of the same cards. If it's true, the math has to be done again (with an even more complex formula). Otherwise, I'll add the tables to the article.
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Re: Half Blood Deck Composition http://elementscommunity.org/forum/index.php?topic=23323.msg345578#msg345578
« Reply #3 on: June 03, 2011, 09:52:37 PM »
You shoud remove mono :death from the second table...
Thanks, i've changed the tables.
Quote
Excellent work !

Information has been added to this Wiki page
Great, thx :)

Quote
As for the number of possible decks, I'd like to know if Half-Bloods can have more than 6 copies of the same cards. If it's true, the math has to be done again (with an even more complex formula)
Yes they can, hence the formula used should be correct. And its the other way around for the formula, if there was a 6 card limit check then the formula would have been complex. Also note that those decks numbers are just here for fun as they are hardly useful for anything.


 

blarg: