Minecraft Enchantments simulator

enchantments.rb

DEBUG = false
ROUNDS = 100000
DUMP_FILE = "stats_enchantment.marshal"
#                          #
#                          #
#  ##### DATA              #
#                          #
#                          #

# Combos:
@combos = []
@combos = [:fortune, :efficiency]
@combos = [:fortune, :efficiency]


# Items
@items = {}
@items[:tool] = [:sword,:bow,:pickaxe_shovel_axe]
@items[:armor] = [:helmet,:chestplate_leggins,:boots]


# Enchantability
@enchantabilites = {}
@enchantabilites[:wooden] = {:tool => 15}
@enchantabilites[:leather] = {:armor => 15}
@enchantabilites[:stone] = {:tool => 5}
@enchantabilites[:iron] = {:armor => 9, :tool => 14}
@enchantabilites[:chain] = {:armor => 12}
@enchantabilites[:diamond] = {:armor => 10, :tool => 10}
@enchantabilites[:gold] = {:armor => 25, :tool => 22}


# conflicting enchantments
@conflicts = []
@conflicts << [:protection,:fire_protection,:blast_protection,:projectile_protection]
@conflicts << [:sharpness,:smite,:bane_of_arthropods]
@conflicts << [:silk_touch,:fortune]


# possible enchantments: armor
@enchantments = {}
@enchantments[:protection] = [:helmet,:chestplate_leggins,:boots]
@enchantments[:fire_protection] = [:helmet,:chestplate_leggins,:boots]
@enchantments[:feather_fall] = [:boots]
@enchantments[:blast_protection] = [:helmet,:chestplate_leggins,:boots]
@enchantments[:projectile_protection] =[:helmet,:chestplate_leggins,:boots]
@enchantments[:respiration] = [:helmet]
@enchantments[:aqua_affinity] = [:helmet]
# possible enchantments: sword
@enchantments[:sharpness] = [:sword]
@enchantments[:smite] = [:sword]
@enchantments[:bane_of_arthropods] = [:sword]
@enchantments[:knockback] = [:sword]
@enchantments[:fire_aspect] = [:sword]
@enchantments[:looting] = [:sword]
# epossible enchantments: bow
@enchantments[:power] = [:bow]
@enchantments[:punch] = [:bow]
@enchantments[:flame] = [:bow]
@enchantments[:infinity] = [:bow]
# possible enchantments: tool
@enchantments[:efficiency] = [:pickaxe_shovel_axe]
@enchantments[:silk_touch] = [:pickaxe_shovel_axe]
@enchantments[:unbreaking] = [:pickaxe_shovel_axe]
@enchantments[:fortune] = [:pickaxe_shovel_axe]


# enchantmentlevels: armor
@enchantmentsLevels = {}
@enchantmentsLevels[:protection] = [[1,21],[17,37],[33,53],[49,69],[]]
@enchantmentsLevels[:fire_protection] = [[10,22],[18,30],[26,38],[34,46],[]]
@enchantmentsLevels[:feather_fall] = [[5,15],[11,21],[17,27],[23,33],[]]
@enchantmentsLevels[:blast_protection] = [[5,17],[13,25],[21,33],[29,41],[]]
@enchantmentsLevels[:projectile_protection] = [[3,18],[9,24],[15,30],[21,36],[]]
@enchantmentsLevels[:respiration] = [[10,40],[20,50],[30,60],[],[]]
@enchantmentsLevels[:aqua_affinity] = [[1,41],[],[],[],[]]
# enchantmentlevels: sword
@enchantmentsLevels[:sharpness] = [[1,21],[17,37],[33,53],[49,69],[65,85]]
@enchantmentsLevels[:smite] = [[5,25],[13,33],[21,41],[29,49],[37,57]]
@enchantmentsLevels[:bane_of_arthropods] = [[5,25],[13,33],[21,41],[29,49],[37,57]]
@enchantmentsLevels[:knockback] = [[5,55],[25,75],[],[],[]]
@enchantmentsLevels[:fire_aspect] = [[10,60],[30,80],[],[],[]]
@enchantmentsLevels[:looting] = [[20,70],[32,82],[44,94],[],[]]
# enchantmentlevels: bow
@enchantmentsLevels[:power] = [[1,16],[11,26],[21,36],[31,46],[41,56]]
@enchantmentsLevels[:punch] = [[12,37],[32,57],[],[],[]]
@enchantmentsLevels[:flame] = [[20,50],[],[],[],[]]
@enchantmentsLevels[:infinity] = [[20,50],[],[],[],[]]
# enchantmentlevels: tool
@enchantmentsLevels[:efficiency] = [[1,51],[16,66],[31,81],[46,96],[61,111]]
@enchantmentsLevels[:silk_touch] = [[25,75],[],[],[],[]]
@enchantmentsLevels[:unbreaking] = [[5,55],[15,65],[25,75],[],[]]
@enchantmentsLevels[:fortune] = [[20,70],[32,82],[44,94],[],[]]


# enchantmentsWeights: armor
@enchantmentWeights = {}
@enchantmentWeights[:protection] = 10
@enchantmentWeights[:fire_protection] = 5
@enchantmentWeights[:feather_fall] = 5
@enchantmentWeights[:blast_protection] = 2
@enchantmentWeights[:projectile_protection] = 5
@enchantmentWeights[:respiration] = 2
@enchantmentWeights[:aqua_affinity] = 2
# enchantmentWeights: sword
@enchantmentWeights[:sharpness] = 10
@enchantmentWeights[:smite] = 5
@enchantmentWeights[:bane_of_arthropods] = 5
@enchantmentWeights[:knockback] = 5
@enchantmentWeights[:fire_aspect] = 2
@enchantmentWeights[:looting] = 2
# enchantmentWeights: bow
@enchantmentWeights[:power] = 10
@enchantmentWeights[:punch] = 2
@enchantmentWeights[:flame] = 2
@enchantmentWeights[:infinity] = 1
# enchantmentWeights: tool
@enchantmentWeights[:efficiency] = 10
@enchantmentWeights[:silk_touch] = 1
@enchantmentWeights[:unbreaking] = 5
@enchantmentWeights[:fortune] = 2



#                          #
#                          #
#  ##### CLASSES           #
#                          #
#                          #
class Stats
  def initialize
    @levels = []
  end
  
  def add(level, enchantments) 
    @levels[level - 1] = {} if @levels[level - 1].nil?
    names = enchantments.map{ |e| e[:name]}
    names.sort {|a,b| a.to_s <=> b.to_s}
  
    oldCount = @levels[level - 1][names];
    oldCount = 0 if oldCount.nil?
    @levels[level - 1][names] = oldCount + 1
  end
  
  def highestChanceOf(enchantmentNames, min)
    bestWeightedPercentage = 0
    bestLevel = 0
    percentAtBestLevel = 0
    bestOccurences = 0 
    
    heighestPercentage = 0
    heighestPercentageLevel = 0
   heighestPercentageOccurences = 0 
    
    puts "want #{enchantmentNames.inspect} #{min}" if DEBUG
    
    1.upto(50) do |level|
      occurences = @levels[level - 1]
      occurences = {} if occurences.nil?
      
      occurencesOfCountAtLevel = 0
      occurences.each do |eList,occ|
        matchingNames = false
        if (!enchantmentNames.empty?)
          if (enchantmentNames.all? {|name| eList.include? name})
            matchingNames = true
          end
        else
          matchingNames = true
        end
        
        if (matchingNames && (eList.length >= min))
          puts "#{level} matches #{eList.inspect} #{occ}" if DEBUG
          
          occurencesOfCountAtLevel = occurencesOfCountAtLevel + occ
        else
          puts "no match #{eList.inspect} #{occ}" if DEBUG
        end
      end
      
      next if occurencesOfCountAtLevel == 0
      
      percent = (100 * occurencesOfCountAtLevel.to_f) / (ROUNDS.to_f)
      neededEnchants = (100 / percent)
      
      # weight percentage by dividing it through the xp needed
      weightedPercentage = percent / xpForLevel(level)
      
      # weight percentage by diving it through the enchants needed
      weightedPercentage = weightedPercentage / neededEnchants
      
      puts "L #{level} percent #{percent} weighted #{weightedPercentage}" if DEBUG
      if (weightedPercentage > bestWeightedPercentage)
        bestWeightedPercentage = weightedPercentage
        percentAtBestLevel = percent
        bestLevel = level
        bestOccurences = occurencesOfCountAtLevel
      end
      
      if (percent > heighestPercentage) 
        heighestPercentage = percent
        heighestPercentageLevel = level
        heighestPercentageOccurences = occurencesOfCountAtLevel
      end
    end

    puts "highest %: #{heighestPercentage} @ L #{heighestPercentageLevel} (#{heighestPercentageOccurences}), chosen %: #{percentAtBestLevel} @ L #{bestLevel} (#{bestOccurences})" if DEBUG
    {:percentage => percentAtBestLevel, :level => bestLevel}
  end
  
end


#                          #
#                          #
#  ##### ALGORITHMS        #
#                          #
#                          #

def xpForLevel(level)
  
  xp = 0
  1.upto(level) do |l|
    if (level == 1)
      xp = xp + 7
    else
       if (l % 2 == 0)
          # even
          xp = xp + 7 + l / 2 * 3 + (l / 2 - 1) * 4
        else
          # odd
          xp = xp + 7 + (l - 1) / 2 * 3 + (l - 1) / 2 *4
        end
    end
  end
  
  xp
end

def prettify(enchantment)
  return prettyString(enchantment[:name]) + " " + enchantment[:level].to_s
end

def prettyString(s)
  s.to_s.downcase.gsub(/_/," ").gsub(/\b[a-z]/) { |a| a.upcase }
end

# two dice
def triangularRandom(limit) 
  (rand(limit).to_f/2 + rand(limit).to_f/2)
end

def getAllCombinations 
  # tools,armors
  allCombinations = []
  
  @items.keys.each do |type|
    # run through all enchantable items
    items = @items[type]
    items.each do |item|
      
      # valid materials
      materials = []
      if item == :bow
        materials << :wooden
      else
        materials = @enchantabilites.keys.select {|material| @enchantabilites[material].include?(type)}
      end
    
      materials.each do |material|
        allCombinations << {:material => material, :item => item}
      end
    end
  end
  
  allCombinations
end

def modifiedEnchantLevel(level,enchantability)
  puts "calculating modification for level #{level}, enchantability #{enchantability}" if DEBUG
  
  modifiedLevel = level.to_f + triangularRandom(enchantability+1) + 1
  modifier = triangularRandom(0)*0.5 + 0.75
  finalLevel = (modifiedLevel * modifier).round
  finalLevel
end

@cache = {}
def possibleEnchantments(item, modifiedlevel)
  #cachedResult = @cache[{:item => item, :modLevel => modifiedlevel}]
  #if !cachedResult.nil?
  #  cachedResult = Array.new(cachedResult)
  #end

  matchingEs = @enchantments.keys.select {|key| @enchantments[key].include?(item)}  
  
  withLevels = []
  matchingEs.each do |e|
    level = 5
    @enchantmentsLevels[e].reverse.each do |rangeMin,rangeMax|      
      if !rangeMin.nil?
        if (modifiedlevel >= rangeMin && modifiedlevel <= rangeMax)
          break
        end
      end
      level = level - 1
    end
    
    if (level != 0)
      enchantment = {}
      enchantment[:name] = e
      enchantment[:level] = level
      withLevels << enchantment
    end
  end

  #@cache[{:item => item, :modLevel => modifiedlevel}] = Array.new(withLevels)
  
  withLevels  
end

def chooseE(enchantments)
  pool = []
  enchantments.each do |e|
    @enchantmentWeights[e[:name]].times {pool << e}  
  end
  
  pool[rand(pool.size)]
end

def conflictsFor(enchantment_name)
  conflicts = @conflicts.select {|c| c.include?(enchantment_name)}
  conflicts = conflicts.flatten.uniq - [enchantment_name]
  conflicts
end

def enchant(item,enchantability,level) 
  chosenEnchantments = []

  # get modified level
  modifiedLevel = modifiedEnchantLevel(level, enchantability)  
  
  # get possible enchantments
  possibleEs = possibleEnchantments(item, modifiedLevel)

  while(!possibleEs.empty?) do
    # 1. pick an enchantment
    puts "possible Es: #{possibleEs.inspect}" if DEBUG
    chosenE = chooseE(possibleEs)
    puts "chosen #{chosenE.inspect}" if DEBUG
    chosenEnchantments << chosenE

    # 2. remove this and conflicting
    possibleEs.delete(chosenE)
    possibleEs = possibleEs.reject do |e|
      conflictsFor(chosenE[:name]).include?(e[:name])
    end
    puts "after removal of conflicting: #{possibleEs.inspect}" if DEBUG
    
    # 3. divide mod-level in half, rounded down
    modifiedLevel = (modifiedLevel / 2.0).floor

    # 4. With probability (modified level + 1) / 50, keep going
    r = rand()
    p = (modifiedLevel + 1)/50.0
    break if r > p
    
    puts "could pick another one" if DEBUG
  end
  
  chosenEnchantments
end

def enchantAll
  allCombinations = getAllCombinations()

  puts "calculating #{allCombinations.size} material/item combinations, using #{ROUNDS} runs for each level,"
  total = allCombinations.size * 50 * ROUNDS
  finished = 0
  puts "totaling #{total} enchants:"
  lastStr = nil
  
  # per combination[level]: enchantmentNames => count
  allStats = {}
  
  allCombinations.each do |c|
    # create Stats for material/item combination
    allStats[c] = Stats.new
    
    type = @items.keys.find {|t| @items[t].include?(c[:item])}
    enchantability = @enchantabilites[c[:material]][type]
    
    puts "* enchanting #{50*ROUNDS} #{prettyString(c[:material])} #{prettyString(c[:item])}, enchantability: #{enchantability}"
    1.upto(50).each do |level|
      ROUNDS.times do
        enchantments = []
        # redo value falls out of range for everything
        while (enchantments.empty?)
          enchantments = enchant(c[:item], enchantability, level)
        end
        
        # debug: output enchantment
        pretty = enchantments.map {|e| prettify(e)}.sort if DEBUG
        puts "  * enchanted Level #{level} #{prettyString(c[:material])} #{prettyString(c[:item])}:  #{pretty.join(", ")}" if DEBUG

        # statistics/counting:
        allStats[c].add(level, enchantments)
        
        # result percentage
        finished = finished + 1
        promille = (1000 * finished.to_f) / total / 10
        percentageStr = ("%3.1f" % promille).to_s
        if (percentageStr != lastStr)
          puts "* #{percentageStr}% done"
          lastStr = percentageStr
          STDOUT.flush
        end
      end
    end
  end
  
  allStats
end

def showStats(stats)
  allCombinations = getAllCombinations()
  
  # output statistics:
  puts "calculated #{allCombinations.size} material/item combinations, using #{ROUNDS} runs for each level,"
  puts "totaling #{ROUNDS * 50 * allCombinations.size} enchants:"
  puts ""
  
  # tools,armors
  @items.keys.each do |type|
    # run through all enchantable items
    items = @items[type]
    items.each do |item|
      
      # valid materials
      materials = []
      if item == :bow
        materials << :wooden
      else
        materials = @enchantabilites.keys.select {|material| @enchantabilites[material].include?(type)}
      end
      materials.sort! {|a,b| a.to_s <=> b.to_s}
      
      puts " * #{prettyString(item)}:"
      puts ""
      puts "   highest chances of getting <count> or more enchantments: (% at / optimal level)"
      puts ""
      puts "".ljust(39) + materials.map{|m| m.to_s.center(20," ") }.join()
      puts "".ljust(39) + "".ljust(20*materials.size,"_")
      
      1.upto(4) do |count|
        # map materials to the stats of the combination (1 item, many materials)
        temp = materials.map{|m| stats[{:material => m,:item => item}]}
        
        temp = temp.map do |stat|
          chance = stat.highestChanceOf([], count)
          
          percentString = "%3.1f" % chance[:percentage] + "% / L "
          percentString = percentString.rjust(10)
          percentString +  ("%2d" % chance[:level]).rjust(2)
        end
        
        puts "#{count.to_s} (or more) |".rjust(39) + temp.map{|c| c.center(20, " ")}.join()
      end

      puts ""
      puts ""
      puts "   highest chances of getting specific enchantments: (% at / optimal level)"
      puts ""
      puts "".ljust(39) + materials.map{|m| m.to_s.center(20," ") }.join()
      puts "".ljust(39) + "".ljust(20*materials.size,"_")
      matchingEs = @enchantments.keys.select {|key| @enchantments[key].include?(item)}
      matchingEs.sort {|a,b| a.to_s <=> b.to_s}
      matchingEs.each do |e|
        temp = materials.map{|m| stats[{:material => m,:item => item}]}
        temp = temp.map do |stat|
          chance = stat.highestChanceOf([e],1)
      
          percentString = "%3.1f" % chance[:percentage] + "% / L "
          percentString = percentString.rjust(10)
          percentString +  ("%2d" % chance[:level]).rjust(2)
        end

        eString = "     " + prettyString(e.to_s)
        puts eString.ljust(37) + " |" + temp.map{|c| c.center(20, " ")}.join()
      end
      
      puts ""
      puts ""
      puts ""
    end
  end
  
end

stats = nil
if File.exist?(DUMP_FILE)
  File.open(DUMP_FILE,'r') do|file|
   stats = Marshal.load(file)
  end
else
  stats = enchantAll()  
  File.open(DUMP_FILE,'w') do|file|
   Marshal.dump(stats, file)
  end
end
  
showStats(stats)

gistfile1.txt

Marshalled Ruby Data for 100.000 runs: http://dl.dropbox.com/u/168982/stats_enchantment.marshal

results.txt

optimal level is chosen by 
1. dividing the percentage through the XP needed for the level
2. dividing the result through the numbers of enchants needed with this percentage to gain a 100% chance. (5 for 22% for example)

calculated 26 material/item combinations, using 100000 runs for each level,
totaling 130000000 enchants:

 * Helmet:

   highest chances of getting <count> or more enchantments: (% at / optimal level)

                                              chain              diamond               gold                iron              leather       
                                       ____________________________________________________________________________________________________
                          1 (or more) |   100.0% / L  1       100.0% / L  1       100.0% / L  1       100.0% / L  1       100.0% / L  1    
                          2 (or more) |     9.5% / L  1         8.5% / L  1        16.2% / L  1         7.9% / L  1        10.9% / L  1    
                          3 (or more) |     6.0% / L 26         5.6% / L 25         1.5% / L  1         6.1% / L 28         0.5% / L  1    
                          4 (or more) |     0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0    


   highest chances of getting specific enchantments: (% at / optimal level)

                                              chain              diamond               gold                iron              leather       
                                       ____________________________________________________________________________________________________
     Fire Protection                  |     5.8% / L  1        16.3% / L  6        16.0% / L  1        15.5% / L  6         9.8% / L  1    
     Blast Protection                 |     8.5% / L  1         8.6% / L  1         8.1% / L  1         8.4% / L  1         8.5% / L  1    
     Projectile Protection            |    24.4% / L  1        25.5% / L  1        21.3% / L  1        25.9% / L  1        23.4% / L  1    
     Respiration                      |     4.1% / L  1        11.9% / L  6        13.3% / L  1        13.1% / L  7         7.0% / L  1    
     Aqua Affinity                    |    16.6% / L  1        17.2% / L  1        16.6% / L  1        17.2% / L  1        16.0% / L  1    
     Protection                       |    50.3% / L  1        52.3% / L  1        42.2% / L  1        53.4% / L  1        46.8% / L  1    



 * Chestplate Leggins:

   highest chances of getting <count> or more enchantments: (% at / optimal level)

                                              chain              diamond               gold                iron              leather       
                                       ____________________________________________________________________________________________________
                          1 (or more) |   100.0% / L  1       100.0% / L  1       100.0% / L  1       100.0% / L  1       100.0% / L  1    
                          2 (or more) |     0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0    
                          3 (or more) |     0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0    
                          4 (or more) |     0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0    


   highest chances of getting specific enchantments: (% at / optimal level)

                                              chain              diamond               gold                iron              leather       
                                       ____________________________________________________________________________________________________
     Fire Protection                  |     6.6% / L  1        16.2% / L  5        18.2% / L  1        17.9% / L  6        11.0% / L  1    
     Blast Protection                 |     9.5% / L  1         9.6% / L  1         9.2% / L  1         9.4% / L  1         9.6% / L  1    
     Projectile Protection            |    27.6% / L  1        28.4% / L  1        24.1% / L  1        28.8% / L  1        26.0% / L  1    
     Protection                       |    56.3% / L  1        58.4% / L  1        48.5% / L  1        59.8% / L  1        53.4% / L  1    



 * Boots:

   highest chances of getting <count> or more enchantments: (% at / optimal level)

                                              chain              diamond               gold                iron              leather       
                                       ____________________________________________________________________________________________________
                          1 (or more) |   100.0% / L  1       100.0% / L  1       100.0% / L  1       100.0% / L  1       100.0% / L  1    
                          2 (or more) |     9.0% / L  1         7.9% / L  1        15.8% / L  1         7.0% / L  1        10.4% / L  1    
                          3 (or more) |     0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0    
                          4 (or more) |     0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0    


   highest chances of getting specific enchantments: (% at / optimal level)

                                              chain              diamond               gold                iron              leather       
                                       ____________________________________________________________________________________________________
     Fire Protection                  |     5.5% / L  1        15.8% / L  6        15.4% / L  1        15.3% / L  6         9.3% / L  1    
     Blast Protection                 |     7.7% / L  1         7.6% / L  1         7.9% / L  1         7.4% / L  1         7.7% / L  1    
     Projectile Protection            |    22.8% / L  1        23.5% / L  1        20.3% / L  1        24.1% / L  1        21.9% / L  1    
     Feather Fall                     |    25.8% / L  1        24.7% / L  1        31.4% / L  1        23.6% / L  1        27.4% / L  1    
     Protection                       |    47.1% / L  1        49.1% / L  1        40.8% / L  1        50.1% / L  1        44.0% / L  1    



 * Sword:

   highest chances of getting <count> or more enchantments: (% at / optimal level)

                                             diamond               gold                iron               stone               wooden       
                                       ____________________________________________________________________________________________________
                          1 (or more) |   100.0% / L  1       100.0% / L  1       100.0% / L  1       100.0% / L  1       100.0% / L  1    
                          2 (or more) |     7.6% / L  1        14.5% / L  1        10.2% / L  1         5.8% / L  2        10.7% / L  1    
                          3 (or more) |    17.1% / L 50         1.1% / L  1        18.2% / L 50        15.3% / L 49        18.5% / L 50    
                          4 (or more) |     2.6% / L 50         3.3% / L 49         2.8% / L 49         2.2% / L 49         3.0% / L 50    


   highest chances of getting specific enchantments: (% at / optimal level)

                                             diamond               gold                iron               stone               wooden       
                                       ____________________________________________________________________________________________________
     Bane Of Arthropods               |    17.0% / L  1        18.8% / L  1        18.1% / L  1        10.1% / L  1        18.5% / L  1    
     Knockback                        |    22.3% / L  1        26.3% / L  1        24.3% / L  1        19.7% / L  2        24.7% / L  1    
     Fire Aspect                      |     9.5% / L  6         8.9% / L  1         5.0% / L  1        11.0% / L  9         5.5% / L  1    
     Looting                          |    12.4% / L 19        10.4% / L 12        11.9% / L 17        12.4% / L 21        11.6% / L 16    
     Sharpness                        |    49.6% / L  1        41.5% / L  1        45.1% / L  1        70.7% / L  1        44.2% / L  1    
     Smite                            |    17.1% / L  1        18.8% / L  1        18.2% / L  1        10.0% / L  1        18.3% / L  1    



 * Bow:

   highest chances of getting <count> or more enchantments: (% at / optimal level)

                                              wooden       
                                       ____________________
                          1 (or more) |   100.0% / L  1    
                          2 (or more) |     4.3% / L  1    
                          3 (or more) |     8.8% / L 32    
                          4 (or more) |     1.1% / L 35    


   highest chances of getting specific enchantments: (% at / optimal level)

                                              wooden       
                                       ____________________
     Flame                            |    20.1% / L 16    
     Infinity                         |    11.9% / L 18    
     Power                            |    96.1% / L  1    
     Punch                            |     8.2% / L  1    



 * Pickaxe Shovel Axe:

   highest chances of getting <count> or more enchantments: (% at / optimal level)

                                             diamond               gold                iron               stone               wooden       
                                       ____________________________________________________________________________________________________
                          1 (or more) |   100.0% / L  1       100.0% / L  1       100.0% / L  1       100.0% / L  1       100.0% / L  1    
                          2 (or more) |     7.7% / L  1        14.4% / L  1        10.3% / L  1         5.6% / L  2        10.7% / L  1    
                          3 (or more) |    16.9% / L 50        18.5% / L 47        18.1% / L 50        15.6% / L 50        18.3% / L 50    
                          4 (or more) |     0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0         0.0% / L  0    


   highest chances of getting specific enchantments: (% at / optimal level)

                                             diamond               gold                iron               stone               wooden       
                                       ____________________________________________________________________________________________________
     Silk Touch                       |     9.2% / L 25         9.0% / L 20         9.0% / L 23         9.4% / L 27         9.5% / L 24    
     Fortune                          |    17.0% / L 18        14.7% / L 12        16.2% / L 16        17.2% / L 20        16.5% / L 16    
     Unbreaking                       |    33.5% / L  1        40.9% / L  1        37.1% / L  1        18.7% / L  1        38.0% / L  1    
     Efficiency                       |    74.3% / L  1        71.7% / L  1        73.2% / L  1        84.6% / L  1        72.7% / L  1