n-sided dice to m-sided dice

dice_converter.rb

# rand(n) is a random number 0-(n-1)


# e.g. [1,0,0] => 4
def bit_array_to_integer(bit_array)
  return bit_array.join.to_i(2)
end


def uniform_bit_from_n_sided_dice(n)
  roll = rand(n)+1
  if n.odd?
    # e.g. if n = 5, ignore 5 and roll again.
    # correct but inefficient.
    while roll == n
      roll = rand(n)+1
    end
  end
  return roll[0]
end

def rand_with_dice(target_sides: 8, source_sides: 6)

  # roll the source-sided dice once for each bit in 
  # the target distribution.
  bit_array = []
  num_bits_in_target = Math.log(target_sides, 2)
  
  for i in 0...num_bits_in_target do
      bit_array[i] = uniform_bit_from_n_sided_dice(source_sides)
  end
  
  # + 1 to shift from zero-based to one-based
  return bit_array_to_integer(bit_array) + 1
end


# double check the outcomes appear uniform
histogram = {}

for i in 1...100000
  
  # ... we should really parallelize this histogram generation...
  target_roll = rand_with_dice(target_sides: 7, source_sides: 5)
  if histogram[target_roll].nil?
    histogram[target_roll] = 1
  else
    histogram[target_roll] += 1
  end
end

puts histogram

Unfortunately doesn't work if the target_sides is not a power of 2