Let's build a kitty breeding calculator that shows all possible traits with the odds / probabilities. Let's start with kitty #1001 and #1111 as parents a and b:
require 'copycats'
a = 0x00004a52931ce4085c14bdce014a0318846a0c808c60294a6314a34a1295b9ce # kitty 1001
b = 0x000042d28390864842e7b9c900c6321086438c6098ca298c728867425cf6b1ac # kitty 1111
agenes_kai = Base32.encode( a ).reverse # note: reverse string for easy array access
p agenes_kai
#=> "fffcaa9a466776661442979e55771661ffga2f225887aaaa"
bgenes_kai = Base32.encode( b ).reverse
p bgenes_kai
#=> "dedegfa984368776b77277f975554441affgf22a75589ac9"Remember: For passing on the parents (a or b) gene
to become the baby's (new) primary gene the odds / probabilities are:
0.375 (37.5%) for the primary (p) gene of parent (a or b),
0.09375 (9.375%) for the hidden 1 (h1),
0.0234375 (2.34375%) for the hidden 2 (h2), and
0.0078125(0.78125%) for the hidden 3 (h3).
Let's add up all the odds for the body (officially known as fur).
Let's start with parent a (that is, kitty #1001):
ODDS_BABY_TRAITS = {}
ODDS_BABY_TRAITS[:body] ||= Hash.new(0)
####
# step 1) add odds for parent a
trait = TRAITS[:body][:kai][agenes_kai[0]]
ODDS_BABY_TRAITS[:body][trait] += 0.375 # primary (p) - add ragamuffin (37.5%)
pp ODDS_BABY_TRAITS
#=> {:body=>{"ragamuffin"=>0.375}}
trait = TRAITS[:body][:kai][agenes_kai[1]]
ODDS_BABY_TRAITS[:body][trait] += 0.09375 # hidden 1 (h1) - add ragamuffin (9.375%)
pp ODDS_BABY_TRAITS
#=> {:body=>{"ragamuffin"=>0.46875}}
trait = TRAITS[:body][:kai][agenes_kai[2]]
ODDS_BABY_TRAITS[:body][trait] += 0.0234375 # hidden 2 (h2) - add ragamuffin (2.34375%)
pp ODDS_BABY_TRAITS
#=> {:body=>{"ragamuffin"=>0.4921875}}
trait = TRAITS[:body][:kai][agenes_kai[3]]
ODDS_BABY_TRAITS[:body][trait] += 0.0078125 # hidden 3 (h3) - add himalayan (0.78125%)
pp ODDS_BABY_TRAITS
#=> {:body=>{"ragamuffin"=>0.4921875, "himalayan"=>0.0078125}}And let's add parent b (that is, kitty #1111):
####
# step 2) add odds for parent b
trait = TRAITS[:body][:kai][bgenes_kai[0]]
ODDS_BABY_TRAITS[:body][trait] += 0.375 # primary (p) - add munchkin (37.5%)
pp ODDS_BABY_TRAITS
#=> {:body=>{"ragamuffin"=>0.4921875, "himalayan"=>0.0078125, "munchkin"=>0.375}}
trait = TRAITS[:body][:kai][bgenes_kai[1]]
ODDS_BABY_TRAITS[:body][trait] += 0.09375 # hidden 1 (h1) - add sphynx (9.375%)
pp ODDS_BABY_TRAITS
#=> {:body=>{"ragamuffin"=>0.4921875, "himalayan"=>0.0078125, "munchkin"=>0.375, "sphynx"=>0.09375}}
trait = TRAITS[:body][:kai][bgenes_kai[2]]
ODDS_BABY_TRAITS[:body][trait] += 0.0234375 # hidden 2 (h2) - add munchkin (2.34375%)
pp ODDS_BABY_TRAITS
#=> {:body=>{"ragamuffin"=>0.4921875, "himalayan"=>0.0078125, "munchkin"=>0.3984375, "sphynx"=>0.09375}}
trait = TRAITS[:body][:kai][bgenes_kai[3]]
ODDS_BABY_TRAITS[:body][trait] += 0.0078125 # hidden 3 (h3) - add sphinx (0.78125%)
pp ODDS_BABY_TRAITS
#=> {:body=> {"ragamuffin"=>0.4921875, "himalayan"=>0.0078125, "munchkin"=>0.3984375, "sphynx"=>0.1015625}}Voila! The odds for fur (body) traits for a new (offspring) baby read:
{"ragamuffin"=>0.4921875, "himalayan"=>0.0078125, "munchkin"=>0.3984375, "sphynx"=>0.1015625}.
Let's sort by highest odds / probability first:
ODDS_BABY_TRAITS[:body] = ODDS_BABY_TRAITS[:body].to_a.sort { |l,r| r[1] <=> l[1] }
pp ODDS_BABY_TRAITS
#=> {:body=> [["ragamuffin", 0.4921875], ["munchkin", 0.3984375], ["sphynx", 0.1015625], ["himalayan", 0.0078125]]}Resulting in:
- ragamuffin =>
0.4921875(~49%) - munchkin =>
0.3984375(~40%) - sphynx =>
0.1015625(~10%) - himalayan =>
0.0078125(~1%)
Compare with an online CryptoKitties (offspring) breeding calculator service:
(Source: cattributes.org/#/1001/1111)
Bingo! The cattribute traits and odds / probabilities match up.
Now let's take on
all the other trait types, that is, pattern, eye color (coloreyes),
eye shape (eyes), base color (color1),
highlight color (color2), and so on
and let's code a kittycalc method
where you pass in the parents a and b
and get the odds.
def kittycalc( a, b )
agenes_kai = Base32.encode( a ).reverse # note: reverse string for easy array access
bgenes_kai = Base32.encode( b ).reverse
odds = {}
TRAITS.each_with_index do |(trait_key, trait_hash),i|
odds[trait_key] ||= Hash.new(0)
offset = i*4
[agenes_kai, bgenes_kai].each do |genes_kai|
p_kai = genes_kai[0+offset]
h1_kai = genes_kai[1+offset]
h2_kai = genes_kai[2+offset]
h3_kai = genes_kai[3+offset]
## kai to trait name mapping (e.g. '1' => 'savannah', etc.)
kai = trait_hash[:kai]
p = kai[p_kai]
h1 = kai[h1_kai]
h2 = kai[h2_kai]
h3 = kai[h3_kai]
## use code (e.g. PU00, PU01, etc.) if trait is unnamed
code = trait_hash[:code]
p = "#{code}%02d" % Kai::NUMBER[p_kai] if p.nil?
h1 = "#{code}%02d" % Kai::NUMBER[h1_kai] if h1.nil?
h2 = "#{code}%02d" % Kai::NUMBER[h2_kai] if h2.nil?
h3 = "#{code}%02d" % Kai::NUMBER[h3_kai] if h3.nil?
odds[trait_key][p] += 0.375 # add primary (p) odds
odds[trait_key][h1] += 0.09375 # add hidden 1 (h1) odds
odds[trait_key][h2] += 0.0234375 # add hidden 2 (h2) odds
odds[trait_key][h3] += 0.0078125 # add hidden 3 (h3) odds
end
## sort by highest odds / probabilities first
odds[trait_key] = odds[trait_key].to_a.sort { |l,r| r[1] <=> l[1] }
end
odds
endLet's try:
odds = kittycalc( a, b )
pp oddsresulting in:
{:body=>
[["ragamuffin", 0.4921875], ["munchkin", 0.3984375], ["sphynx", 0.1015625], ["himalayan", 0.0078125]],
:pattern=>
[["luckystripe", 0.5], ["totesbasic", 0.46875], ["calicool", 0.03125]],
:coloreyes=>
[["mintgreen", 0.46875], ["strawberry", 0.375], ["sizzurp", 0.125], ["topaz", 0.0234375], ["chestnut", 0.0078125]],
:eyes=>
[["crazy", 0.4921875], ["thicccbrowz", 0.375], ["simple", 0.1328125]],
:color1=>
[["shadowgrey", 0.375], ["greymatter", 0.375], ["orangesoda", 0.1171875], ["aquamarine", 0.1171875], ["salmon", 0.015625]],
:color2=>
[["royalpurple", 0.5625], ["swampgreen", 0.40625], ["chocolate", 0.0234375], ["lemonade", 0.0078125]],
:color3=>
[["granitegrey", 0.59375], ["kittencream", 0.40625]],
:wild=>
[["WE03", 0.4921875], ["WE00", 0.390625], ["WE05", 0.1171875]],
:mouth=>
[["happygokitty", 0.5859375], ["pouty", 0.3828125], ["soserious", 0.03125]],
:environment=>
[["EN01", 0.5234375], ["EN14", 0.46875], ["EN09", 0.0078125]],
:secret=>
[["SE04", 0.4921875], ["SE06", 0.3828125], ["SE07", 0.125]],
:prestige=>
[["PU09", 0.59375], ["PU08", 0.3828125], ["PU11", 0.0234375]]}Let's make the odds more readable with a print_kittycalc_odds helper:
def print_kittycalc_odds( odds )
odds.each do |trait_key, recs|
trait_hash = TRAITS[trait_key]
puts "#{trait_hash[:name]} (#{trait_hash[:code]}):"
recs.each do |rec|
puts " #{'%5.2f'% (rec[1]*100)}% | #{rec[0]}"
end
puts
end
endTry print_kittycalc_odds( odds ). Resulting in:
Fur (FU):
49.22% | ragamuffin
39.84% | munchkin
10.16% | sphynx
0.78% | himalayan
Pattern (PA):
50.00% | luckystripe
46.88% | totesbasic
3.12% | calicool
Eye Color (EC):
46.88% | mintgreen
37.50% | strawberry
12.50% | sizzurp
2.34% | topaz
0.78% | chestnut
Eye Shape (ES):
49.22% | crazy
37.50% | thicccbrowz
13.28% | simple
Base Color (BC):
37.50% | shadowgrey
37.50% | greymatter
11.72% | orangesoda
11.72% | aquamarine
1.56% | salmon
Highlight Color (HC):
56.25% | royalpurple
40.62% | swampgreen
2.34% | chocolate
0.78% | lemonade
Accent Color (AC):
59.38% | granitegrey
40.62% | kittencream
Wild Element (WE):
49.22% | WE03
39.06% | WE00
11.72% | WE05
Mouth (MO):
58.59% | happygokitty
38.28% | pouty
3.12% | soserious
Environment (EN):
52.34% | EN01
46.88% | EN14
0.78% | EN09
Secret Y Gene (SE):
49.22% | SE04
38.28% | SE06
12.50% | SE07
Purrstige (PU):
59.38% | PU09
38.28% | PU08
2.34% | PU11
Good question. Let's add the missing odds / probabilities for new mewtations traits
to kittycalc. Remember: There's a 25% chance of getting a mutation for tier I & II
and a 12.5% chance for tier III & IIII
but only given A & B contain the right gene mutation pairs.
Remember: After swapping the genes in
the mixgenes formula
the odds / probabilities for the parents
genes ending up as primary are:
0.75 (75%) for the primary (p) gene of parent (a or b),
0.1875 (18.75%) for the hidden 1 (h1),
0.046875 (4.6875%) for the hidden 2 (h2), and
0.015625(1.5625%) for the hidden 3 (h3).
With two parents and four genes (p, h1, h2, h3) for every trait that results in 4 x 4 = 16 mewtation pairs:
(p', h1', h2', h3') x (p", h1", h2", h3")
=
(p', p"), (p', h1"), (p', h2"), (p', h3")
(h1',p"), (h1',h1"), (h1',h2"), (h1',h3")
(h2',p"), (h2',h1"), (h2',h2"), (h3',h3")
(h3',p"), (h3',h1"), (h3',h2"), (h3',h3")
Let's calculate the odds / probabilities for each pair:
p_p = 0.75 * 0.75
p_h1 = 0.75 * 0.1875
p_h2 = 0.75 * 0.046875
p_h3 = 0.75 * 0.015625
total = p_p + p_h1 + p_h2 + p_h3
puts "p_p=#{p_p}, p_h1=#{p_h1}, p_h2=#{p_h2}, p_h3=#{p_h3}, total=#{total}"
#=> p_p=0.5625, p_h1=0.140625, p_h2=0.03515625, p_h3=0.01171875, total=0.75
h1_p = 0.1875 * 0.75
h1_h1 = 0.1875 * 0.1875
h1_h2 = 0.1875 * 0.046875
h1_h3 = 0.1875 * 0.015625
total = h1_p + h1_h1 + h1_h2 + h1_h3
puts "h1_p=#{h1_p}, h1_h1=#{h1_h1}, h1_h2=#{h1_h2}, h1_h3=#{h1_h3}, total=#{total}"
#=> h1_p=0.140625, h1_h1=0.03515625, h1_h2=0.0087890625, h1_h3=0.0029296875, total=0.1875
h2_p = 0.046875 * 0.75
h2_h1 = 0.046875 * 0.1875
h2_h2 = 0.046875 * 0.046875
h2_h3 = 0.046875 * 0.015625
total = h2_p + h2_h1 + h2_h2 + h2_h3
puts "h2_p=#{h2_p}, h2_h1=#{h2_h1}, h2_h2=#{h2_h2}, h2_h3=#{h2_h3}, total=#{total}"
#=> h2_p=0.03515625, h2_h1=0.0087890625, h2_h2=0.002197265625, h2_h3=0.000732421875, total=0.046875
h3_p = 0.015625 * 0.75
h3_h1 = 0.015625 * 0.1875
h3_h2 = 0.015625 * 0.046875
h3_h3 = 0.015625 * 0.015625
total = h3_p + h3_h1 + h3_h2 + h3_h3
puts "h3_p=#{h3_p}, h3_h1=#{h3_h1}, h3_h2=#{h3_h2}, h3_h3=#{h3_h3}, total=#{total}"
#=> h3_p=0.01171875, h3_h1=0.0029296875, h3_h2=0.000732421875, h3_h3=0.000244140625, total=0.015625
total = p_p + p_h1 + p_h2 + p_h3 +
h1_p + h1_h1 + h1_h2 + h1_h3 +
h2_p + h2_h1 + h2_h2 + h2_h3 +
h3_p + h3_h1 + h3_h2 + h3_h3
puts "total=#{total}"
#=> total=1.0Note: All sixteen pairs totals sums up to 1.0, that is, 100%.
Or with predefined odds in p, h1, h2, h3:
p = 0.75
h1 = 0.1875
h2 = 0.046875
h3 = 0.015625
p_p = p * p
p_h1 = p * h1
p_h2 = p * h2
p_h3 = p * h3
puts "p_p=#{p_p}, p_h1=#{p_h1}, p_h2=#{p_h2}, p_h3=#{p_h3}"
#=> p_p=0.5625, p_h1=0.140625, p_h2=0.03515625, p_h3=0.01171875
h1_p = h1 * p
h1_h1 = h1 * h1
h1_h2 = h1 * h2
h1_h3 = h1 * h3
puts "h1_p=#{h1_p}, h1_h1=#{h1_h1}, h1_h2=#{h1_h2}, h1_h3=#{h1_h3}"
#=> h1_p=0.140625, h1_h1=0.03515625, h1_h2=0.0087890625, h1_h3=0.0029296875
h2_p = h2 * p
h2_h1 = h2 * h1
h2_h2 = h2 * h2
h2_h3 = h2 * h3
puts "h2_p=#{h2_p}, h2_h1=#{h2_h1}, h2_h2=#{h2_h2}, h2_h3=#{h2_h3}"
#=> h2_p=0.03515625, h2_h1=0.0087890625, h2_h2=0.002197265625, h2_h3=0.000732421875
h3_p = h3 * p
h3_h1 = h3 * h1
h3_h2 = h3 * h2
h3_h3 = h3 * h3
puts "h3_p=#{h3_p}, h3_h1=#{h3_h1}, h3_h2=#{h3_h2}, h3_h3=#{h3_h3}"
#=> h3_p=0.01171875, h3_h1=0.0029296875, h3_h2=0.000732421875, h3_h3=0.000244140625
total = p_p + p_h1 + p_h2 + p_h3 +
h1_p + h1_h1 + h1_h2 + h1_h3 +
h2_p + h2_h1 + h2_h2 + h2_h3 +
h3_p + h3_h1 + h3_h2 + h3_h3
puts "total=#{total}"
#=> total=1.0So what? In english that tells us if the primary gene (p')
of parent a
and the primary gene (p") of parent b are a mewtation pair
than the odds / probabilities are:
puts p_p_i = 0.75 * 0.75 * 0.25 # i) mutation (25%)
#=> 0.140625
puts p_p_ii = 0.75 * 0.75 * 0.75 # ii) no mutation (75%)
#=> 0.421875
puts p_p_i + p_p_ii
#=> 0.5625That's the "famous" 14% (0.140625) of mutation probability - written down in many mutation articles -
for mutation level I & II (25%) if p' and p" hold the right gene pair.
Let's try another pair with p' and h1":
puts p_h1_i = 0.75 * 0.1875 * 0.25 # i) mutation (25%)
#=> 0.03515625
puts p_h1_ii = 0.75 * 0.1875 * 0.75 # ii) no mutation (75%)
#=> 0.10546875
puts p_h1_i + p_h1_ii
#=> 0.140625Resulting in a mutation probability of 3.5% (0.03515625)
for mutation level I & II (25%).
Let's code a new kittycalc_mewtations( a, b ) method
that checks all traits for mewtation pairs and returns the odds / probabilites:
def kittycalc_mewtations( a, b )
agenes_kai = Base32.encode( a ).reverse # note: reverse string for easy array access
bgenes_kai = Base32.encode( b ).reverse
odds = {}
#########
# 4x4 = 16 gene pairs
# 0 = primary (p) - 0.75
# 1 = hidden 1 (h1) - 0.1875
# 2 = hidden 2 (h2) - 0.046875
# 3 = hidden 3 (h3) - 0.015625
pairs = [[0,0],[0,1],[0,2],[0,3],
[1,0],[1,1],[1,2],[1,3],
[2,0],[2,1],[2,2],[2,3],
[3,0],[3,1],[3,2],[3,3]]
odds_genes = [0.75, 0.1875, 0.046875, 0.015625]
TRAITS.each_with_index do |(trait_key, trait_hash),i|
odds[trait_key] ||= []
offset = i*4
pairs.each do |pair|
a_kai = agenes_kai[pair[0]+offset]
b_kai = bgenes_kai[pair[1]+offset]
gene1 = Kai::NUMBER[a_kai] ## convert kai to integer number
gene2 = Kai::NUMBER[b_kai]
## note: mutation code copied from mixgenes formula
if gene1 > gene2
gene1, gene2 = gene2, gene1
end
if (gene2 - gene1) == 1 && gene1.even? ## bingo! mewtation pair
probability = 0.25
if gene1 > 23
probability /= 2
end
mutation = (gene1 / 2) + 16
odds_pair = odds_genes[pair[0]] * odds_genes[pair[1]] * probability
odds[trait_key] << [pair,
[Kai::ALPHABET[gene1], Kai::ALPHABET[gene2]],
Kai::ALPHABET[mutation],
odds_pair]
end
end
odds[trait_key] = odds[trait_key].sort { |l,r| r[3] <=> l[3] }
end
odds
endLet's try the kitty #1001 and #1111:
a = 0x00004a52931ce4085c14bdce014a0318846a0c808c60294a6314a34a1295b9ce # kitty 1001
b = 0x000042d28390864842e7b9c900c6321086438c6098ca298c728867425cf6b1ac # kitty 1111
odds = kittycalc_mewtations( a, b )
pp oddsresulting in:
{:body=>[],
:pattern=>
[[[0, 3], ["9", "a"], "m", 0.0029296875],
[[1, 3], ["9", "a"], "m", 0.000732421875],
[[2, 2], ["9", "a"], "m", 0.00054931640625],
[[3, 3], ["9", "a"], "m", 6.103515625e-05]],
:coloreyes=>
[[[0, 2], ["3", "4"], "i", 0.0087890625],
[[3, 0], ["7", "8"], "k", 0.0029296875]],
:eyes=>
[[[0, 0], ["7", "8"], "k", 0.140625]],
:color1=>
[[[0, 3], ["1", "2"], "h", 0.0029296875]],
:color2=>[],
:color3=>[],
:wild=>[],
:mouth=>
[[[0, 3], ["f", "g"], "p", 0.0029296875],
[[2, 1], ["f", "g"], "p", 0.002197265625],
[[1, 3], ["f", "g"], "p", 0.000732421875],
[[2, 2], ["f", "g"], "p", 0.00054931640625]],
:environment=>[],
:secret=>
[[[1, 0], ["7", "8"], "k", 0.03515625],
[[2, 0], ["7", "8"], "k", 0.0087890625],
[[3, 3], ["7", "8"], "k", 6.103515625e-05]],
:prestige=>
[[[0, 0], ["9", "a"], "m", 0.140625],
[[1, 0], ["9", "a"], "m", 0.03515625],
[[2, 0], ["9", "a"], "m", 0.0087890625],
[[3, 0], ["9", "a"], "m", 0.0029296875],
[[0, 3], ["9", "a"], "m", 0.0029296875],
[[1, 3], ["9", "a"], "m", 0.000732421875],
[[2, 3], ["9", "a"], "m", 0.00018310546875],
[[3, 3], ["9", "a"], "m", 6.103515625e-05]]}Let's use a print_kittycalc_mewtations_odds helper for
making the mewtation pairs and odds more readable:
def print_kittycalc_mewtations_odds( odds )
gene_names = ['p','h1','h2','h3']
odds.each do |trait_key, recs|
trait_hash = TRAITS[trait_key]
next if recs.empty? ## skip trait types with no mewtations
puts "#{trait_hash[:name]} (#{trait_hash[:code]}) - #{recs.size} Mewtation Pair(s):"
recs.each do |rec|
a_kai = rec[1][0]
b_kai = rec[1][1]
m_kai = rec[2]
a = trait_hash[:kai][a_kai]
b = trait_hash[:kai][b_kai]
m = trait_hash[:kai][m_kai]
## use code (e.g. PU00, PU01, etc.) if trait is unnamed
code = trait_hash[:code]
a = "#{code}%02d" % Kai::NUMBER[a_kai] if a.nil?
b = "#{code}%02d" % Kai::NUMBER[b_kai] if b.nil?
m = "#{code}%02d" % Kai::NUMBER[m_kai] if m.nil?
print " #{'%5.2f'% (rec[3]*100)}% | "
print "%-18s" % "#{m}"
print " | "
print "%-5s" % "#{gene_names[rec[0][0]]}+#{gene_names[rec[0][1]]}"
print " | "
print "#{a}+#{b}"
print "\n"
end
puts
end
endTry print_kittycalc_mewtations_odds( odds ). Resulting in:
Pattern (PA) - 4 Mewtation Pair(s):
0.29% | tigerpunk | p+h3 | calicool+luckystripe
0.07% | tigerpunk | h1+h3 | calicool+luckystripe
0.05% | tigerpunk | h2+h2 | calicool+luckystripe
0.01% | tigerpunk | h3+h3 | calicool+luckystripe
Eye Color (EC) - 2 Mewtation Pair(s):
0.88% | limegreen | p+h2 | topaz+mintgreen
0.29% | bubblegum | h3+p | chestnut+strawberry
Eye Shape (ES) - 1 Mewtation Pair(s):
14.06% | raisedbrow | p+p | crazy+thicccbrowz
Base Color (BC) - 1 Mewtation Pair(s):
0.29% | cloudwhite | p+h3 | shadowgrey+salmon
Mouth (MO) - 4 Mewtation Pair(s):
0.29% | tongue | p+h3 | happygokitty+soserious
0.22% | tongue | h2+h1 | happygokitty+soserious
0.07% | tongue | h1+h3 | happygokitty+soserious
0.05% | tongue | h2+h2 | happygokitty+soserious
Add-up and compare the mutation probabilities with an online CryptoKitties (offspring) breeding calculator service:
- Pattern: tigerpunk (0.4%)
- Eye Color: limegreen (0.9%), bubblegum (0.3%)
- Eye Shape: raisedbrow (14%)
- Base Color: cloudwhite (0.3%)
- Mouth: tongue (0.6%)
(Source: kittycalc.co/?k1=1001&k2=1111)
Bingo! The mewtations cattribute traits and odds / probabilities match up.
All together now. Let's add up the odds from step one and the mewtations
in a new all-in-one kittycalc version 2.0:
def kittycalc( a, b )
agenes = Base32.encode( a ).reverse # note: reverse string for easy array access
bgenes = Base32.encode( b ).reverse
odds = kittycalc_step1( agenes, bgenes )
odds_mewtations = kittycalc_mewtations( agenes, bgenes )
## update odds with mewtations
odds_mewtations.each do |trait_key, recs|
next if recs.empty? ## skip trait types with no mewtations
recs.each do |rec|
agene = rec[1][0]
bgene = rec[1][1]
mewtation = rec[2]
odds_mewtation = rec[3]
odds[trait_key][mewtation] += odds_mewtation
odds[trait_key][agene] -= odds_mewtation / 2.0
odds[trait_key][bgene] -= odds_mewtation / 2.0
end
end
odds.each do |trait_key, hash|
recs = odds[trait_key].to_a
recs = recs.map do |rec|
## map kai char e.g '1' to trait name e.g. savannah'
name = TRAITS[trait_key][:kai][rec[0]]
## note: use code (e.g. PU00, PU01, etc.) if trait is unnamed
name = TRAITS[trait_key][:code] + Kai::CODE[rec[0]] if name.nil?
[name,rec[1]]
end
## sort by highest odds / probabilities first
recs = recs.sort { |l,r| r[1] <=> l[1] }
odds[trait_key] = recs
end
odds
endNote: If you add the odds for the new mewtation trait
e.g. odds[trait_key][mewtation] += odds_mewtation
you also need to subtract the odds for the two traits
making up the mewtation pair
e.g. odds[trait_key][agene] -= odds_mewtation / 2.0 and
odds[trait_key][bgene] -= odds_mewtation / 2.0
to keep the balance of 100% (1.0).
Let's add the missing kittycalc_step1 and kittycalc_mewtations code:
def kittycalc_step1( agenes, bgenes )
odds = {}
TRAITS.each_with_index do |(trait_key, trait_hash),i|
odds[trait_key] ||= Hash.new(0)
offset = i*4
[agenes, bgenes].each do |genes|
p = genes[0+offset]
h1 = genes[1+offset]
h2 = genes[2+offset]
h3 = genes[3+offset]
odds[trait_key][p] += 0.375 # add primary (p) odds
odds[trait_key][h1] += 0.09375 # add hidden 1 (h1) odds
odds[trait_key][h2] += 0.0234375 # add hidden 2 (h2) odds
odds[trait_key][h3] += 0.0078125 # add hidden 3 (h3) odds
end
end
odds
end
def kittycalc_mewtations( agenes, bgenes )
odds = {}
#########
# 4x4 = 16 gene pairs
# 0 = primary (p) - 0.75
# 1 = hidden 1 (h1) - 0.1875
# 2 = hidden 2 (h2) - 0.046875
# 3 = hidden 3 (h3) - 0.015625
pairs = [[0,0],[0,1],[0,2],[0,3],
[1,0],[1,1],[1,2],[1,3],
[2,0],[2,1],[2,2],[2,3],
[3,0],[3,1],[3,2],[3,3]]
odds_genes = [0.75, 0.1875, 0.046875, 0.015625]
TRAITS.each_with_index do |(trait_key, trait_hash),i|
odds[trait_key] ||= []
offset = i*4
pairs.each do |pair|
gene1 = Kai::NUMBER[ agenes[pair[0]+offset] ] ## convert kai to integer number
gene2 = Kai::NUMBER[ bgenes[pair[1]+offset] ]
## note: mutation code copied from mixgenes formula
if gene1 > gene2
gene1, gene2 = gene2, gene1
end
if (gene2 - gene1) == 1 && gene1.even? ## bingo! mewtation pair
probability = 0.25
if gene1 > 23
probability /= 2
end
mutation = (gene1 / 2) + 16
odds_pair = odds_genes[pair[0]] * odds_genes[pair[1]] * probability
odds[trait_key] << [pair,
[Kai::ALPHABET[gene1], Kai::ALPHABET[gene2]],
Kai::ALPHABET[mutation],
odds_pair]
end
end
## sort by highest odds / probabilities first
odds[trait_key] = odds[trait_key].sort { |l,r| r[3] <=> l[3] }
end
odds
endReady to go. Stand back two hundred meter and let's try:
odds = kittycalc( a, b )
pp oddsresulting in:
{:body=>
[["ragamuffin", 0.4921875],
["munchkin", 0.3984375],
["sphynx", 0.1015625],
["himalayan", 0.0078125]],
:pattern=>
[["luckystripe", 0.49786376953125],
["totesbasic", 0.375],
["totesbasic", 0.09375],
["calicool", 0.02911376953125],
["tigerpunk", 0.0042724609375]],
:coloreyes=>
[["mintgreen", 0.46435546875],
["strawberry", 0.37353515625],
["sizzurp", 0.125],
["topaz", 0.01904296875],
["limegreen", 0.0087890625],
["chestnut", 0.00634765625],
["bubblegum", 0.0029296875]],
:eyes=>
[["crazy", 0.421875],
["thicccbrowz", 0.3046875],
["raisedbrow", 0.140625],
["simple", 0.1328125]],
:color1=>
[["greymatter", 0.375],
["shadowgrey", 0.37353515625],
["aquamarine", 0.1171875],
["orangesoda", 0.1171875],
["salmon", 0.01416015625],
["cloudwhite", 0.0029296875]],
:color2=>
[["royalpurple", 0.5625],
["swampgreen", 0.40625],
["chocolate", 0.0234375],
["lemonade", 0.0078125]],
:color3=>
[["granitegrey", 0.59375],
["kittencream", 0.40625]],
:mouth=>
[["happygokitty", 0.582733154296875],
["pouty", 0.3828125],
["soserious", 0.028045654296875],
["tongue", 0.00640869140625]]}Note: The "real" output if you follow along coding on
your very own computer includes the "unnamed" traits
wild, environment, secrect and prestige too.
{:wild=>
[["WE03", 0.4921875],
["WE00", 0.390625],
["WE05", 0.1171875]],
:environment=>
[["EN01", 0.5234375],
["EN14", 0.46875],
["EN09", 0.0078125]],
:secret=>
[["SE04", 0.4921875],
["SE06", 0.360809326171875],
["SE07", 0.102996826171875],
["SE19", 0.04400634765625]],
:prestige=>
[["PU09", 0.498046875],
["PU08", 0.287109375],
["PU20", 0.19140625],
["PU11", 0.0234375]]}Let's keep it shorter and snip out the "unnamed" traits.
Let's reuse the print_kittycalc_odds helper
to make the odds more readable.
Try print_kittycalc_odds( odds ). Resulting in:
Fur (FU):
49.22% | ragamuffin
39.84% | munchkin
10.16% | sphynx
0.78% | himalayan
Pattern (PA):
49.79% | luckystripe
37.50% | totesbasic
9.38% | totesbasic
2.91% | calicool
0.43% | tigerpunk
Eye Color (EC):
46.44% | mintgreen
37.35% | strawberry
12.50% | sizzurp
1.90% | topaz
0.88% | limegreen
0.63% | chestnut
0.29% | bubblegum
Eye Shape (ES):
42.19% | crazy
30.47% | thicccbrowz
14.06% | raisedbrow
13.28% | simple
Base Color (BC):
37.50% | greymatter
37.35% | shadowgrey
11.72% | aquamarine
11.72% | orangesoda
1.42% | salmon
0.29% | cloudwhite
Highlight Color (HC):
56.25% | royalpurple
40.62% | swampgreen
2.34% | chocolate
0.78% | lemonade
Accent Color (AC):
59.38% | granitegrey
40.62% | kittencream
Mouth (MO):
58.27% | happygokitty
38.28% | pouty
2.80% | soserious
0.64% | tongue
Now if you compare the new numbers with a CryptoKitties (offspring) breeding calculator service - than the numbers match up. Bingo!
To double check let's sum up all odds for the cattribute traits
to see if the match up to 100% (1.0) each.
def check_odds( odds )
odds.each do |trait_key,recs|
total = recs.reduce(0) {|sum,rec| sum+=rec[1]; sum}
puts "#{trait_key}: #{total}"
end
end
check_odds( odds )Resulting in:
body: 1.0
pattern: 1.0
coloreyes: 1.0
eyes: 1.0
color1: 1.0
color2: 1.0
color3: 1.0
wild: 1.0
mouth: 1.0
environment: 1.0
secret: 1.0
prestige: 1.0