This analogy is so great and so powerful that I want to find a place to use it and give you a bonus double reward for actually having an analogy and for it making sense!

As Mr. Skeptical I would ask... but how does the market come to that agreement?

Essentially, because it's set that way from the get-go.  It says so, right there in the name.  Once people accept that, it self-perpetuates. 

It's announced at the beginning, "1 BitUSD = 1 USD" and everybody buys into the market based on that assumption, and all market participants have the incentive to keep it that way.  It will be the same way with BitBTC, BitEUR, BitJPY, BitOzAg or any other currency/commodity that you can come up with.  You could come up with Bit_MSFT_QtrRev to represent the value of Microsoft's quarterly revenue. 

People do this kind of thing all the time in Futures markets and legal and illegal betting on anything you want.  When Kate Middleton becomes pregnant again, there can be a value set to Bit_FutureRoyalIsMale for people to bet on whether the heir to the throne will be male or female.  People want to bet on all kinds of things.  All you have to do is create a market for it, and people will use that market to place bets.

So somebody may come along and say "Well then what is the point of the entire BitUSD market?  Why not just keep my USD where they are?"  The answer is that there may be many reasons for holding BitUSD instead of holding USD.  Why do you put your paycheck in a bank account?  Why not carry all of your net worth around with you all of the time, in cash?  Because having that money in a bank account gives certain benefits... security, transferability, insurance.  While cash has its own benefits; anonymity, proximate-immediacy*, etc.  Of course, you can change BankUSD into CashUSD at any time, or vice-versa.**

BitUSD holdings will have certain benefits to them, just as BankUSD or CashUSD holdings have their own benefits.  Anonymity, security, and transferability will be some of those benefits.

*A word that I just made up meaning that if you are in close proximity to me, I can transfer cash to you immediately, irrevocably, and provably.  There's no password needed, no external verification, no network delays.

**(Not really "at any time" of course -- banks aren't open 24/7, and ATM's have limits, and deposits usually take a while to clear.... but close enough that it's fair to say, for most purposes, "you can change your BankUSD into CashUSD at any time" is approximately true.)

Bachelor's degree in mathematics from top-10 US university.  Also extensive study in Economics and CS.  A lot of that stuff has been forgotten (graduated in 2003), but I can always re-learn anything.

Not really a programmer now, although I have been one in the past.  Mostly PHP.  Proficient in Photoshop, Illustrator, etc.  Advanced amateur photographer.

Good at thinking about difficult ideas, modeling them, and explaining them.

Very good written and spoken English.  I know all the rules, and I'm a great editor (both to correct pure grammar mistakes, and to resolve unclear/improper wording); but I'm not against breaking the rules when it makes sense stylistically.  I know/speak/read a good bit of German, and a little bit of Spanish.  This sounds strange to say, but I have very good language-comprehension skills, no matter what the language.  Even if I am unfamiliar with the grammar and vocabulary (or even the written characters), I can usually understand foreign-language documents fairly well, given enough time and a good dictionary; and I am well above-average at both understanding non-native English speakers when they use poor English (written or spoken), and producing English that can be understood by non-native English speakers (same).  In short, I believe that I am very good at interfacing and communicating with other humans.

Please see my "horse race" analogy in the Analogy Bounty thread:

https://bitsharestalk.org/index.php?topic=2368.msg38118#msg38118

I believe that this accurately represents my ability to take difficult concepts and explain them in plain English, even if that plain English gets a little wordy sometimes . 

In my day-to-day job, I work on databases, simplifying office work and converting inter-related sets of Excel spreadsheets to relational DB's, while training co-workers on how to use the new DB's.  (DBMS = FileMaker Pro, which if you haven't tried it, is EXCELLENT for rapid application development and prototyping, although the prototype can end up fulfilling the client's needs 95% of the time if you're looking at an application that only needs to support a handful of users.)

I could see myself playing a role similar to that of Tom in Office Space.  "Look, I already told you!  I deal with the Goddamn customers so the engineers don't have to!"

It is like betting on a horse race, which I think most people understand, but just in case, I will first explain briefly how a standard peri-mutuel betting system operates at most horse tracks. 

In a normal horse race scenario, you bet on which horse you think will win.  The winnings that you receive are based on the "odds" which are calculated constantly, determined by how much money has been bet on each horse, from all of the bettors placing bets on that race.  So, for example, say there is a 3-horse race, and all the winnings will be paid out to bettors (in real life, there would be more horses, and the event organizer would take a cut).  $100 have been bet on Horse A to win, $20 have been bet on Horse B to win, $10 have been bet on Horse C to win.  So $130 has been wagered in total.  Most people think that Horse A will win, so there must be some reason for this, and it is probably likely that Horse A will win.  So the payout if Horse A wins, is $130/100 = $1.3 per $1 wagered.  So if you bet $1 on Horse A, and Horse A wins, you will receive $1.30 in winnings.  If you bet on Horse B, and Horse B wins, you will receive $130/20 = $6.50 if you wagered $1.  So you win much more money, but Horse B winning was much less likely.  So the reward is always proportional to the risk, and the risk is determined by the knowledge of the market as a whole -- all of the people betting on that race.

Now, let's change things a bit.  In a real horse race, all betting is closed when the race starts.  So you can't watch half of the race, and go up and bet on the horse who's in the lead at that time.  However, in this race, you can make bets during the race, and you can even change your bets during the race.  So you're watching the race, and you see Horse B now has the lead, so you can change your bet from Horse A to Horse B.  However, EVERYBODY will do this!  The entire market will gradually change their bets to Horse B as the race progresses, and as Horse B is seen to be in the lead.  By the time the race is over, everybody will have changed their bets to Horse B.  Therefore everybody's payout will be the same, $130/130 = $1.00 exactly. 

Now, you may say: What is the point of this?  The whole fun of betting is to win something!  Just getting your money back is boring!  But if you were at a horse race, and you were given the option to change your bet in the middle of the race, wouldn't you take advantage of it?  Wouldn't you at least NOT LOSE your money, even if it means it's not possible to win?

Ok, now what does this mean for BitUSD?  It is a perpetual horse race, where you can change your bets at any given moment.  The market converges on everybody "betting" that 1 BitUSD = 1 USD.

Now say that someone had a lot of BitUSD that they want to get rid of quickly.  So maybe they put in an order for 1 BitUSD = 0.99 USD.  There will be long a line of people waiting to buy the BitUSD's for the price of only 0.99 USD, because that will mean instant profit!  And it also works the other way around.  If someone has a lot of USD that they want to use to buy BitUSD, and they're in a hurry to do it, they'll come up and say "All right, gimme a bunch of BitUSD, and I'll pay 1.01 USD for each of them!"  And again, there will be a long line of people happy to sell them BitUSD at 1.01 each, because hey, profit of 1 cent each! 

As long as the market "agrees" that the price of 1 BitUSD = 1 USD, all of this will happen automatically.  It is just like the market "agreeing" that Horse B is going to win the race, right before Horse B crosses the finish line.