http://mindyourdecisions.com/blog/2010/09/22/a-fun-card-puzzle/

card_trick.rb

require 'pp'

class Card
  attr_reader :face_up

  def initialize(face_up)
    @face_up = face_up
  end

  def flip
    @face_up ^= true
  end

  def inspect
    "<Card #{face_up ? 'Up' : 'Down'}>"
  end
end

def trick
  deck = (
    (1..42).map { Card.new(false) } +
    (1..10).map { Card.new(true) }
  ).sort_by { rand }

  new_deck = deck.pop(10)
  new_deck.each { |c| c.flip }

  deck_face_up_count = deck.count { |c| c.face_up }
  new_deck_face_up_count = new_deck.count { |c| c.face_up }

  [deck_face_up_count, new_deck_face_up_count]
end

counts = {}

100000.times do
  c1, c2 = trick
  if c1 != c2
    puts "Error! #{c1} != #{c2}"
  end
  counts[c1] ||= 0
  counts[c1] += 1
end

counts.sort.each do |num, count|
  puts "#{num} => #{count}"
end

Ahh, I see. You are right. I updated the script to show me a spread of the face-up card count. Here is the output from 100,000 runs of the trick:

2 => 1
3 => 9
4 => 163
5 => 1388
6 => 6964
7 => 20590
8 => 33551
9 => 28064
10 => 9270

Seems it's most likely that 8 cards are face-up in each pile at the end of the trick. Cool stuff!

Here is the theoretical distribution of probability:

0 => 6.3211 × 10^-11
1 => 2.65486 × 10^-8
2 => 2.44911 × 10^-6
3 => 0.0000870795
4 => 0.00148579
5 => 0.0135504
6 => 0.0696342
7 => 0.204639
8 => 0.335736
9 => 0.281853
10 => 0.0930114

You're right, 8 is the most common.