## Thursday, May 21, 2020

### How to Calculate Backgammon Probabilities

Backgammon is a game that employs the use of two standard dice.Ã‚   The dice used in this game are six-sided cubes, and the faces of a die have one, two, three, four, five or six pips. During a turn in backgammon a player may move his or her checkers or draughts according to the numbers shown on the dice. The numbers rolled can be split between two checkers, or they can be totaled and used for a single checker. For example, when a 4 and a 5 are rolled, a player has two options: he may move one checker four spaces and another one five spaces, or one checker can be moved a total of nine spaces. To formulate strategies in backgammon it is helpful to know some basic probabilities. Since a player can use one or two dice to move a particular checker, any calculation of probabilities will keep this in mind. For our backgammon probabilities, we will answer the question, Ã¢â‚¬Å"When we roll two dice, what is the probability of rolling the number n as either a sum of two dice, or on at least one of the two dice?Ã¢â‚¬  Calculation of the Probabilities For a single die that is not loaded, each side is equally likely to land face up. A single die forms a uniform sample space. There are a total of six outcomes, corresponding to each of the integers from 1 to 6. Thus each number has a probability of 1/6 of occurring. When we roll two dice, each die is independent of the other. If we keep track of the order of what number occurs on each of the dice, then there are a total of 6 x 6 36 equally likely outcomes. Thus 36 is the denominator for all of our probabilities and any particular outcome of two dice has a probability of 1/36. Rolling At Least One of a Number The probability of rolling two dice and getting at least one of a number from 1 to 6 is straightforward to calculate. If we wish to determine the probability of rolling at least one 2 with two dice, we need to know how many of the 36 possible outcomes include at least one 2. The ways of doing this are: (1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (6, 2), (2, 1), (2, 3), (2, 4), (2, 5), (2, 6) Thus there are 11 ways to roll at least one 2 with two dice, and the probability of rolling at least one 2 with two dice is 11/36. There is nothing special about 2 in the preceding discussion. For any given number n from 1 to 6: There are five ways to roll exactly one of that number on the first die.There are five ways to roll exactly one of that number on the second die.There is one way to roll that number on both dice. Therefore there are 11 ways to roll at least one n from 1 to 6 using two dice. The probability of this occurring is 11/36. Rolling a Particular Sum Any number from two to 12 can be obtained as the sum of two dice. The probabilities for two dice are slightly more difficult to calculate. Since there are different ways to reach these sums, they do not form a uniform sample space. For instance, there are three ways to roll a sum of four: (1, 3), (2, 2), (3, 1), but only two ways to roll a sum of 11: (5, 6), (6, 5). The probability of rolling a sum of a particular number is as follows: The probability of rolling a sum of two is 1/36.The probability of rolling a sum of three is 2/36.The probability of rolling a sum of four is 3/36.The probability of rolling a sum of five is 4/36.The probability of rolling a sum of six is 5/36.The probability of rolling a sum of seven is 6/36.The probability of rolling a sum of eight is 5/36.The probability of rolling a sum of nine is 4/36.The probability of rolling a sum of ten is 3/36.The probability of rolling a sum of eleven is 2/36.The probability of rolling a sum of twelve is 1/36. Backgammon Probabilities At long last we have everything we need to calculate probabilities for backgammon. Rolling at least one of a number is mutually exclusive from rolling this number as a sum of two dice. Thus we can use the addition rule to add the probabilities together for obtaining any number from 2 to 6. For example, the probability of rolling at least one 6 out of two dice is 11/36. Rolling a 6 as a sum of two dice is 5/36. The probability of rolling at least one 6 or rolling a six as a sum of two dice is 11/36 5/36 16/36. Other probabilities can be calculated in a similar manner.

## Wednesday, May 6, 2020

### Analysis Of At The Abbey Theater By Rory O Neill

At the Abbey Theater in Dublin, Rory O Neill, a LGBT activist and drag queen known as Panti, confessed that he was a homophobe like everyone else. Panti explained that to grow up in a society that is overwhelmingly homophobic and to escape unscathed would be miraculous.Ã¢â‚¬  As a black man, I am very aware of racism and how it operates whether institutionally, internally or personally mediated. As a gay man, something I am still trying to deconstruct, I have been oblivious, perhaps intentionally, to my internalized homophobia. This dissonance in self-awareness is partially due to the fact that I knew I was black from early childhood but did not realize I was gay until sixth grade and did not begin to even accept it until twelfth. Many people compare the struggles of being black to that of being gay. In my opinion, despite some similarities the struggles are completely different. One is rooted in the legacy of over 200 years of slavery and the other in the tradition in people trying to cure homosexuality. One is more of an external conflict, the other internal. When I am followed around in stores like J.Crew or Saks, I am outraged and speak up. Realizing that ignorant people need to be educated, I usually write a letter to the VP of the company or loudly claim that I am being racially harassed in front of other customers. And it works. The VP s call me back and apologize, the staff goes through a sensitivity training, and I usually get a gift card with a hefty sum. On

## Sunday, April 26, 2020

### Napoleon Biography Essays - House Of Bonaparte, Napoleon, Ajaccio

Napoleon Biography Napoleon was born on August 15, 1769 in Ajaccio, Corsica, and was given the name Napoleone Buonaperte. He was the second of eight children of Carlo and Letizia Buonaperte, both of the Corsican-ltalian gentry. Before Napoleone, no Buonaparte had ever been a professional soldier. His father Carlo, was a lawyer who had fought for Corsican independence, but after the French occupied the island in 1768, he served as a prosecutor and ajudge and entered the French aristocracy as a count. Through his father's influence, Napoleone was educated at the expense of King Louis XVI, at Brienne and the Ecole Militaire, in Paris. Napoleone graduated in 1785, at the age of 16, and joined the artillery as a second lieutenant. After the revolution began in France, he became a lieutenant colonel (1791) in the Corsican National Guard. However, when Corsica declared independence in 1793, Buonaperte, a Republican, and a French patriot, fled to France with his family. He was assigned, as captain, to an army besieging Toulon, a naval base that was aided by a British fleet, while in revolt against the republic. It was here that Napoleone Buonaperte officially changed his name to Napoleon Bonaparte, feeling that it looked "more French". It was here too that Napoleon replaced a wounded artillery general, and seized ground where his guns could drive the British fleet from the harbor, and Toulon fell. As a result of his accomplishments, Bonapatre was promoted to brigadier general at the age of 24. In 1795, he saved the revolutionary government by dispersing an insurgent mob in Paris. Then in 1796 he married