hit_soft17.rb

# some blackjack tables in Vegas were standing on soft 17, so it made me wonder what were the probable outcomes of hitting soft 17. if you want to see the possible outcomes of a different starting scenario, change the initial contents of "processing"

class Deck
  def initialize counts = nil, total = nil
    unless counts.nil?
      @counts = counts
      @total = total
      return
    end
    @counts = {}
    2.upto(9).each {|value| @counts[value] = 4}
    @counts[10] = 16 # 4 each of T, J, Q, K
    @counts[11] = 4
    @total = 52 # instead of constantly summing the counts
  end

  # returns hash of values mapped to probabilities
  def next_card
    probabilities = @counts.map {|value, count| [value, count * 1.0 / @total]}
    Hash[probabilities].reject {|value, count| count == 0}
  end

  def pull value
    raise 'trying to pull a card not in the deck' if @counts[value] == 0
    counts = @counts.dup
    counts[value] -= 1
    Deck.new(counts, @total - 1)
  end
end

class Hand
  attr_accessor :probability, :deck, :softness

  def initialize probability, value, deck, softness
    while value > 21 && softness >= 1
      value -= 10
      softness -= 1
    end
    self.probability = probability
    self.value = value
    self.deck = deck
    self.softness = softness
  end

  def done?
    value == :bust || value > 17 || (value == 17 && softness == 0)
  end

  def value
    return :bust if @value > 21
    @value
  end

  private
    attr_writer :value
end

outcomes = {}
17.upto(21).each {|value| outcomes[value] = 0}
outcomes[:bust] = 0

processing = [Hand.new 1, 17, Deck.new.pull(11).pull(6), 1]

count = 0
until processing.empty?
  count += 1
  hand = processing.pop

  if hand.done?
    outcomes[hand.value] += hand.probability
    next
  end

  hand.deck.next_card.each do |value, probability|
    softness = hand.softness
    softness += 1 if value == 11
    processing.push Hand.new(hand.probability * probability, hand.value + value, hand.deck.pull(value), softness)
  end
end

outcomes.each do |value, probability|
  puts "#{value}: #{probability}"
end

puts "analyzed #{count} hands"