Amiibo Probability 掉寶保底
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https://zeldamods.org/wiki/Amiibo_drops/zh
Eng Explanation
https://github.com/MrCheeze/botw-tools/blob/master/all_drops.txt
Eng Drop Table
Scan
20% GreatHit
80% BigHit
Scan
20% GreatHit
80% BigHit
Scan
20% GreatHit
80% BigHit
Scan
20% GreatHit
80% BigHit
Scan
20% GreatHit
80% BigHit
Scan
100% GreatHit
Reset counter
Scan
20%, reload if bad bow
80%, save if ore
Scan
20%, reload if bad bow
80%, save if ore
Scan
20%, reload if bad bow
80%, save if ore
Scan
20%, reload if bad bow
80%, save if ore
Scan
20%, reload if bad bow
80%, save if ore
Scan
reload if bad bow
Get Twilight Bow
Example: How to get
Twilight Bow 黃昏之光弓
Scan
20%, reload if sword/cloth
80%, save if arrow
Scan
20%, reload if sword/cloth
80%, save if arrow
Scan
20%, reload if sword/cloth
80%, save if arrow
Scan
20%, reload if sword/cloth
80%, save if arrow
Scan
20%, reload if sword/cloth
80%, save if arrow
Scan
reload if sword/cloth
Get Biggoron's Sword
Example: How to get
Biggoron's Sword 大鼓隆之劍
def MarkovScan( ProvableBigHit, DesiredTreasure ):
PBH = ProvableBigHit/100 * 4/5 # secure a big hit
DT = DesiredTreasure/100 * 1/5 # obtain the desired item
IC = 1 - PBH - DT # inconclusive
M = matrix(QQ, [ # transition matrix of the markov chain
[ IC,PBH, 0, 0, 0, 0, DT ], # initially no big hit
[ 0, IC,PBH, 0, 0, 0, DT ], # accumulate one big hit
[ 0, 0, IC,PBH, 0, 0, DT ], # accumulate two big hit
[ 0, 0, 0, IC,PBH, 0, DT ], # accumulate three big hit
[ 0, 0, 0, 0, IC, PBH, DT ], # accumulate four big hit
[ 0, 0, 0, 0, 0,1-DT*5,DT*5 ], # accumulate five big
[ 1, 0, 0, 0, 0, 0, 0 ] # dummy state for treasure
])
# Solve for the invarnat state
# = eigenvector of "lambda=1"
# = solve xM = 1x
# = solve x(M - I) = 0
M_I = (M - matrix.identity(7)).left_kernel()
InvState = M_I.basis()[0]
InvState /= sum(InvState)
InvState = vector(RR, InvState)
# print(InvState) # for curious cats
# Recurrent time = 1 / long-term probability
# -1 because we added a dummy state
ExpSteps = 1 / InvState[6] - 1
return ExpSteps
ProvableBigHit is the probability that, from the BigHit drop table,�we get an item that only appears in the this drop table.
DesiredTreasure is the probability that, from the GreatHit drop table,�we get an item that we want.
For example, assume that�the BigHit drop table is {itemA: a%, itemB: b%} (where a + b = 100),�the GreatHit drop table is {itemB: c%, itemD: d%}, (where c + d = 100),�and that itemD is what we want,�then ProvableBigHit = a and DesiredTreasure = d.
For Twilight Bow, the BigHit-exclusive items are Amber 5.00%, Opal 30.00%, Topaz 8.00%, Sapphire 8.00%, Ruby 8.00%, Diamond 2.00%, Star Fragment 2.00%, Luminous Stone 5.00%; sum = 68 = ProvableBigHit.
The Twilight Bow has chance 10% in the GreatHit drop table,�so 10 = DesiredTreasure.
MarkovScan(68, 10) gives 17.6,�meaning that every 17.6 scans gives you one Twilight Bow.