Monte Carlo

A numerical method originally utilised to build and test the atomic bomb during World War II.

A Monte Carlo simulation typically - and in a random manner - creates hundreds of thousands of simulated solutions, and then ranks these solutions in a statistical manner.

Monte Carlo Simulation was required during WWII due to the large number of variables involved in the design of Atomic Weapons, as well as the lack of what is called a closed form solution, in other words a precise mathematical formula that defines the desired answer.

Using Monte Carlo Simulation the most likely outcome can be arrived at within a specified statistical confidence interval.

In the civilian world, Monte Carlo Simulation is most commonly used in finance to determine the value of a position of instruments, particularly involving the so-called non-linear variety.

Instruments which exhibit these characteristics are more commonly known as derivatives.

The valuation of derivatives at times also involves large numbers of variables and, like atomic weapons design, does not lend itself easily to closed form solutions.

A classic Monte Carlo simulation is to approximate pi. Take a 2 unit square, its area is 4. Within this square, a circle of radius 1 can be inscribed. The area of this circle is pi. So, for the approximation...

1. Take two 10, 20, or 100 sided dice.
   One for X, one for Y.
   For future reference, the number of sides is called N
2. Draw a one quadrant of the 2 unit square.
3. Divide this quadrant up into the number of sides on the selected dice.
4. Roll the two dice and plot this spot on the paper
5. Calculate if its a hit or miss:
   If X² + Y² < N², it is a "hit".
   Otherwise its a "miss".
6. Repeat Z times.
   Higher values of Z result in increased precision
7. 4 * (number of hits)/Z is approximately pi.

Monte Carlo simulations are also used in climatology. One example of a SETI@Home like project that plans to use Monte Carlo simulations can be found at http://www.climate-dynamics.rl.ac.uk/. Because of the number of variables in climate dynamics, you select one set of variables, run it and see if its right. In this model, the data is started at 1950, and run for 50 years to see if it matches present conditions. If it does, it is then run for another 50 years to form an approximation of what 2050 will be like.

Monte Carlo is one of the four quarters (or cities) of Monaco. It is the home most notably of the Grand Casino. The casino is what has made Monte Carlo famous the world over. Many things have been named after this place including mathematical ideas, vehicles, and even other casinos.

Other attractions in Monte Carlo include:

• The Gardens and Terraces of the Casino. A vast array of flowers and plants are presented against a background of luscious green lawns. These displays are further embellished with pools and fountains
• The Monte-Carlo Opera and Monte-Carlo Ballet are both located in the Grand Casino
• The National Musuem - houses the world's finest collection of automatons and dolls of the 18th and 19th centuries.
• The Japanese Garden - home for a pond, waterfall, a stream, tea house and Zen garden.
• The Monte Carlo Country Club - home of some 40 tennis courts. The courts are used on the professional tennis circuit -- ATP.
• Hotel de Paris - a luxury hotel situated on the Golden Square of the Place du Casino.
• The Cafe de Paris restaurant is famous for being the best in the country. The Cafe also offers lower limit gaming than the Grand Casino.
• The Sun Casino and Salle de Palmiers both provide alternative gaming spots (and lower limits) to visitors.

Monte Carlo is home to numerous other hotels, restaurants, and night clubs. The night life in Monaco is centered around this quarter.

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Monte Carlo has also lent its name to the fabulous Monte Carlo Resort and Casino in Las Vegas located on the southern end of the Las Vegas Strip. The theme of the casino is definitely French-Mediterranean. The Monte Carlo offers 3,002 guest rooms featuring Italian marble and granite finishes and a 21,000 square-foot pool area with cascading waterfalls and a wave pool.

Gaming - Monte Carlo Casino houses over 2,100 slot and video poker machines ranging from 5 cents to $100 and ninety-five table games including: double-deck Blackjack, single zero Roulette, Craps, Pai Gow Poker, Keno, Caribbean Stud, and Baccarat.

Entertainment is provided by the legendary magician Lance Burton, who performs Tuesday through Saturday in the $27 million Lance Burton Theatre. For dining guests can choose from any of seven restaurants in the casino: Blackstone's Steakhouse, The Monte Carlo Buffet, The Cafe, Monte Carlo Pub and Brewery, Andre's French Restaurant, Dragon Noodle, and the Market City Cafe. The Pub and Brewery is the place to be at night with live music, DJ, and dancing starting at 9pm nightly.