Counting Cards (#152)

Denis H. put it very well when explained that there are two
challenges to
this quiz. The first was to implement a card counter. That’s the easy
bit.

Here’s the library Denis submitted for counting cards:

CARDS = %w{A K Q J T 9 8 7 6 5 4 3 2}
SUITS = %w{c s h d}

class Counter
def initialize(decks)
@count = 4 - 4decks
@shoe = []
decks.times do
CARDS.each do |c|
SUITS.each do |s|
@shoe << c.to_s + s.to_s
end
end
end
size = 52
decks
size.times do |i|
j = rand(size)
@shoe[i],@shoe[j] = @shoe[j],@shoe[i]
end
end

def deal
  card = @shoe.pop
  @count += 1 if "234567".include? card[0,1].to_s
  @count -= 1 if "TJQKA".include? card[0,1].to_s
  card
end

def count
  @count
end

def size
  @shoe.size
end

end

This code is very easy to follow. You construct a Counter from a number
of
decks and it will determine the starting count, load a shoe full of
cards, and
shuffle those cards (the code is just a longhand form of @shoe.sort_by {
rand
}).

The deal() method is the only other one that does any work. It pulls
cards from
the shoe, but before returning them it makes sure to update the count.
Our
counting system is easy, so it breaks down into the two simple
conditional
checks we see here.

That’s literally all it takes to setup some cards, deal, and track a
count.

The other challenge is how are we going to allow the user to interact
with this
code. I left the quiz wide open on this front, but the truth is that
you will
probably desire a GUI interface if you really want to practice.
Recognizing the
card faces will be import when you are actually sitting at a Blackjack
table.

Denis decided to use Rails as a GUI framework. He located some free
card images
and built a tiny web application to show them. All of the action takes
place in
a single controller and there are only two views. (The library we’ve
already
examined is the only model needed.)

When you first visit the application, it will display a simple form:

<%= javascript_include_tag :defaults %> Practice Card Counting <% form_tag :action => 'practice' do %> Number of Decks in Shoe: <%= text_field_tag :decks, '1' %>
Deal between <%= text_field_tag :min, '1', :size => 1%> and <%= text_field_tag :max, '3', :size => 1 %> cards per hand.
Deal cards every <%= text_field_tag :delay, '5', :size => 1%> seconds.
<%= submit_tag("Start") %> <% end %>

As you can see, this just collects a few parameters for the application.
You
can set a deck count, a range of cards that will be dealt at one time,
and a
delay between new deals.

Submitting this form will kick us into the controller, where the
majority of the
work is done:

require ‘card_counter’

class CardCounterController < ApplicationController

def practice
  session[:counter] = Counter.new params[:decks].to_i
  session[:min] = params[:min].to_i
  session[:max] = params[:max].to_i
  session[:delay] = params[:delay].to_i
end

def deal
  min = session[:min]
  max = session[:max]
  counter = session[:counter]
  max = counter.size if counter.size<max
  min = max if max < min
  count = min + rand(max-min+1)
  text = ""
  text = "Shoe complete" if count == 0
  count.times do
    card = session[:counter].deal
    text += "<img src='/images/#{card_index(card)}.png' " +
            "width='72' height='96'/>\n"
  end
  text += "<p id='count' style='visibility: hidden'>" +
          "Count is #{counter.count}</p>"
  render :text => text
end

# Convert card name ("6d", "Qs"...) to image index where
# 1=Ac,2=As,3=Ah,4=Ad,5=Kc and so on
def card_index(card)
  c = CARDS.index card[0,1].to_s
  s = SUITS.index card[1,1].to_s
  c * 4 + s + 1
end

end

The form we just saw dumps us into the practice() method which just
stores all
of the parameters in your session. Note that the full Counter object
(require()d at the top of this file) is constructed at this point and
also
placed in your session.

The deal() method is the only other action and it’s called to replace
some page
elements via Ajax. It reads your session parameters back, selects a
random
number of cards to display based on your range and what is left in the
shoe, and
renders a chunk of HTML text with the images for those cards as well as
a hidden
paragraph with the current count in it.

The card_index() method is just a helper that constructs image names
based on
the face and suit.

Just after practice() runs, Rails will render the only other view for
this
application:

<%= javascript_include_tag :defaults %> Practice Card Counting Pause
<%= periodically_call_remote(
:condition => "paused == false",
:update => "cards",
:frequency => session[:delay],
:url => { :action => "deal" }) %>

If you glance down at the body, you will see that there are really only
two
elements in this page: a link and an initially empty div.

The link controls a Javascript toggle function. When you click “Pause”
the
function shows the count, switches the link name to “Continue,” and
stops the
periodic Ajax calls. Clicking Continue changes the link name back to
Pause and
restarts the periodic calls. The next Ajax action will render a
(re-)hidden
count.

When you put all of these pieces together, you get an effective trainer
for card
counting with pictures. Do have a look at the other solutions though,
for
examples of how to handle the event loop in the console.

My thanks to all who were brave enough to risk having themselves labeled
a card
counter. With any luck, we will train a future generation of super
counters.

Tomorrow we will tackle a classic computer science optimization
problem…

On 17 Jan 2008, at 22:17, Ruby Q. wrote:

the code is just a longhand form of @shoe.sort_by { rand }).

That’s sweet. Time to go re-read Enumerable…

/dh

Ruby Q. <james grayproductions.net> writes:

  size.times do |i|
    j = rand(size)
    @shoe[i],@shoe[j] = @shoe[j],@shoe[i]
  end

(the code is just a longhand form of @shoe.sort_by { rand }).

Easy to think that, but this is the exact same definition of a “naive
algorithm”
demonstrated recently and very well summed up by Jeff Atwood:

http://www.codinghorror.com/blog/archives/001015.html

Gareth

On 18 Jan 2008, at 09:19, Gareth A. wrote:

demonstrated recently and very well summed up by Jeff Atwood:

http://www.codinghorror.com/blog/archives/001015.html

Gareth

That’s very interesting. The core of the bug is the the original
algorithm generates 5252 possible outcomes, instead of 52! outcomes.
The non-randomness occurs because 52
52 is not evenly dividable by 52!.

Also interesting that you can learn new things by reading C# code…

/dh

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