What's The Probability Of Two Boys?

There is a link going around about the most recent Gathering For Gardner. The writer hooks the reader with an intro featuring Gary Foshee (a top-notch designer of "secret box" puzzles, though they're rarely boxes), who poses this question to the crowd of mathematicians, puzzlers, and magicians: "I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"

The article then describes the Gathering. (I'm on the invite list, but I've not yet been.) It eventually explains the answer, but these probability questions never make sense. So I wrote a program to illustrate the first oddity, which is that announcing you have two children and one is a boy makes the probability of the other one being a boy only 1/3. Basically, create 10,000 sets, and remove any that are two girls. Now count up the total number of pairs left and the total number of those that are two boys, and you end up with something around one-third.

num_bbs = 0
total_pairs = 0

(0...10000).each do |count|
  children = [Kernel.rand(2),Kernel.rand(2)]
  next if children[0] == 1 && children[1] == 1

  total_pairs = total_pairs + 1
  num_bbs = num_bbs + 1 if children[0] == 0 && children[1] == 0
end

puts "#{num_bbs} pairs of boys out of #{total_pairs} valid pairs = #{(num_bbs.to_f/total_pairs.to_f) * 100}"

It's weird, but it's true.

We Rule: Maximize Your Time

I've been playing We Rule on my iPhone. I have to say, I don't really get the point of it. It seems like the only way to progress is to plant and harvest crops and exchange services with other players. But there are tons of things like trees and banners and what not that don't seem to do anything. Should I place a water tower? Who knows?

But this is not a game review. When you plant items and harvest them, you get paid some amount of gold depending on the crop. Planting each crop takes some defined amount of money (usually), and each crop requires some defined amount of real-world time to mature.

So, naturally, I wondered: Which plants are the best investment?

A simple spreadsheet offers the answer*. I wrote down the profit of the crop and divided that by the number of minutes it would take to grow. I did the same thing for experience points, which allow you to level up. (This list reflects the crops I currently have access to. I'll update as I go.)

Crop	Profit	Profit/Minute	XP/Minute
Magic Asparagus	1250	.87	.24
Potatoes	200	.56	.22
Pumpkins	160	.89	.36
Strawberries	120	1.33	.56
Carrots	260	.36	.15
Squash	180	.6	.25
Beans	340	.24	.10
Onions	100	1.67	.67
Wheat	20	4	1.60
Corn	5	6.67	1.33

Your definition of a good investment may be different than mine. Clearly the best investment is to plant and harvest corn like a madman every 45 seconds. You have fun with that. Wheat is somewhat more tolerable, with a 5-minute harvest time, but I like to set up a bunch of crops and then go do something else until they're done. Or set up a bunch overnight to have ready the next morning.

Strawberries and onions are good investments, with onions beating out strawberries for both cash and experience points. Plus, they only take an hour: That's about right for mid-day play. In the crops that take all day, Magic Asparagus is your best best, with beans not even close. Beans also give you one of the worst XP/Minute ratios. Don't plant beans.

Derive your own fun theories from the list.

*Yes, this is a programming blog. Spreadsheets are programs, too, though they're rarely treated as such.

Rails Rules

I get now why people love Rails.

I had a personal project in mind: a web-based application for organizing all the notes you collect while working on an article. Like the index cards you used to use for school reports. I decided to try Ruby on Rails, a web application framework built on top of the Ruby language, mostly to see what all the fuss was about.

Rails is the framework of choice for a wide range of startups because it lets you get up and running quickly. It works by driving home a brutal truth: Your website is not that unique.

Some sizable percentage of what you need to do for a real-world website is what everyone needs to do for a real-world website: working with databases, adding CRUD functionality, rendering HTML, mapping handlers to URLs, and so forth. "All of this has happened before and all of it will happen again."

Rails acknowledges this and takes care of most of that functionality out of the box. A lot of what it does seems like magic, but really it just imposes naming conventions that will let it do the right thing most of the time. Put your User objects into a users table, and you rarely have to write SQL. Organize your URLs as /controller/action/id, and you don't have to map anything manually. Call a controller method create, and it will automatically be called to handle POST operations. And you don't even have to remember any of this: The scripts that come with Rails generate tons of the code for you, so adding a new business object into the database and HTML-based CRUD pages to manage said objects take two scripts. Two lines at a command prompt, and poof.

I gave it a whirl and came away impressed. In five hours of flying to the East Coast this weekend, I, who know very little about Rails and something about Ruby, had a functional site for creating, viewing, and editing each of the key object types my application needs. I even added a whole bunch of "it would be nice if it did this" types of features. All on the way to New Hampshire. I wrote minimal amounts of code to do it, too. I have an app that I can use — indeed, I've started using it for real-world stuff.

On the way back, I started worrying about the user interface, and that's where I began to flounder a bit. Rails is smooth sailing if you're using all of its tools, but if you want to use something such as jQuery for your front-end JavaScript/AJAX, things get tougher. Or perhaps it's that the book I used doesn't explain the depths well enough to let me figure it out. A friend of mine says it's easy, and I'm sure it is, but I haven't quite grokked everything I need to do yet.

But even with this hiccup, Rails is clearly a valuable tool that any web developer should consider.