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[SUMMARY] Counting Cards (#152)

 
 
Ruby Quiz
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      01-17-2008
Denis Hennessy 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 - 4*decks
@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:

<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8" />
<%= javascript_include_tag :defaults %>
<title>Practice Card Counting</title>
</head>
<body>
<% form_tag :action => 'practice' do %>
Number of Decks in Shoe: <%= text_field_tag :decks, '1' %><br/>
Deal between
<%= text_field_tag :min, '1', :size => 1%> and
<%= text_field_tag :max, '3', :size => 1 %>
cards per hand.<br/>
Deal cards every
<%= text_field_tag :delay, '5', :size => 1%> seconds.<br/>
<%= submit_tag("Start") %>
<% end %>
</body>
</html>

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:

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/2000/REC-xhtml1-20000126/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8" />
<%= javascript_include_tag :defaults %>
<title>Practice Card Counting</title>
<script type="text/javascript">
//<![CDATA[
paused = false;
function pause() {
paused = !paused;
if (paused) {
$('count').setStyle('visibility: visible');
$('pause').update('Continue')
} else {
$('pause').update('Pause')
}
}
//]]>
</script>
</head>
<body>
<a id='pause' href="#" onClick="pause()">Pause</a>
<div id="cards"></div>

<%= periodically_call_remote(
:condition => "paused == false",
:update => "cards",
:frequency => session[:delay],
:url => { :action => "deal" }) %>
</body>
</html>

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...

 
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Denis Hennessy
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      01-17-2008
On 17 Jan 2008, at 22:17, Ruby Quiz wrote:

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


That's sweet. Time to go re-read Enumerable...

/dh

 
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Gareth Adams
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      01-18-2008
Ruby Quiz <james <at> 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


 
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Denis Hennessy
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      01-18-2008
On 18 Jan 2008, at 09:19, Gareth Adams wrote:

> Ruby Quiz <james <at> 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


That's very interesting. The core of the bug is the the original
algorithm generates 52*52 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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