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Build Your Own CryptoKitties Breeding (Offspring) Calculator

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
end

Let's try:

odds = kittycalc( a, b )
pp odds

resulting 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
end

Try 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

What about mewtations?

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=1.0

Note: 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=1.0

So 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
#=> 0.5625

That'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
#=> 0.140625

Resulting 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
end

Let's try the kitty #1001 and #1111:

a = 0x00004a52931ce4085c14bdce014a0318846a0c808c60294a6314a34a1295b9ce  # kitty 1001
b = 0x000042d28390864842e7b9c900c6321086438c6098ca298c728867425cf6b1ac  # kitty 1111

odds = kittycalc_mewtations( a, b )
pp odds

resulting 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
end

Try 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
end

Note: 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
end

Ready to go. Stand back two hundred meter and let's try:

odds = kittycalc( a, b )
pp odds

resulting 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