Consistency Equations in Yu-Gi-Oh!

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Consistency Equations in Yu-Gi-Oh!

Post by Stardog on Sun Jan 04, 2015 1:51 am

Hypergeometric Distribution

This uses the nCr (n choose r)[“n choose r” = C(n,r) = n! / ( r! (n - r)! )] method.

-D: Deck Size
-H: Hand Size
-K: # of given card in your deck
-X: # of given card in your hand

(KCX)(D-KCH-X)
---------------
(DCH)


Combination Formula

-D: Deck Size
-H: Hand Size
Of "D", choose "H"; Deck (40), choose (5).

Smaller Example:
Of the 5 cards in hand, choose 2.
N=5
R=2

NCR


N!
-------
R! (N-R)!
=
5*4*3*2*1
-----------------: 10 Possible Outcomes
(2*1)*(3*2*1)

Lets try an example.

Fire Fist Bob

Deck Size: 40 Cards
Opening Hand: 5 Cards
# of Tenkis in a deck: 3
X=1; open 1 Tenki

(3C1)(37C4)
------------
(40C5)

Answer: .301
30.1% of the time Bob will open 1 copy of Tenki.


Cumulative Hypergeometrics

Accounts for possibility multiple copies of the same card; i.e Fire Fist Bob doesn't care if he opens 2 or 3 Tenkis if is goal is to activate Tenki on the first turn.

Add probability of getting 1 + probability of getting 2 + probability of getting 3 to get probability of 1≤x≤3

Answer: .301 when x=1
30.1% of the time Bob will open 1 copy of Tenki.
"(3C1)(37C4)
------------
(40C5)"

Answer: .035 when x=2
3.5% of the time Bob will open 2 copies of Tenki.
"(3C2)(37C3)
------------
(40C5)"

Answer: .001 when x=3
0.1% of the time Bob will open 3 copies of Tenki.
"(3C3)(37C2)
------------
(40C5)"

Answer= .337 when 1≤x≤3
33.7% of the time Bob will open 1-3 copies of Tenki.

Limitations
Does not account for card effects
-Pot of Duality
-Upstart Goblin
-Trade-In, Cards of Consonance, etc.

I hope this helps everyone test the consistency of their deck.
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Re: Consistency Equations in Yu-Gi-Oh!

Post by Flip Flapper on Sun Jan 04, 2015 10:00 am

my head started to hurt just by reading the first 3 rows.......

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Re: Consistency Equations in Yu-Gi-Oh!

Post by Kira Yoshikage on Mon Jan 05, 2015 4:18 am

Math......... My worst enemy....... Mad

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Re: Consistency Equations in Yu-Gi-Oh!

Post by Rumpthumper on Mon Jan 05, 2015 5:29 am

Someone knows how to count cards!Lol

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Re: Consistency Equations in Yu-Gi-Oh!

Post by α27theDemonKnight on Fri Aug 25, 2017 12:57 am

I chuckled a bit. This is brilliant.
Shame that maybe people like only [You must be registered and logged in to see this link.] or [You must be registered and logged in to see this link.] is actually gonna make practical use of this X'D

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Re: Consistency Equations in Yu-Gi-Oh!

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