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Gaps

Gaps

Gaps is a solitaire card game where the arrangement of cards from Deuce (a Two card) to King is the object. The game is also called Spaces or Vacancies. The game starts with all cards dealt on the tableau into four rows of thirteen. The aces removed and discarded from further play. The gaps that they leave behind are filled by cards that are the same suit and a rank higher than the card on the left of the gap. (For example, 4♣ can be placed beside 3♣.) However, any gap at the right of a King is considered dead and no card can fill it. Any gap on the left hand side of the row should be placed by a deuce and the row should be built up by suit beside the deuce (i. e. 2-3-4-5, etc.). It is the discretion of the player on which suit would occupy which row. When there are no more possible moves, the cards that are not in order are gathered, making sure to leave any suit sequence (e.g., 2-3-4-5) behind. Once the cards are reshuffled, they are redealt, making sure there is a gap in each row at the immediate right of each suit sequence or at the extreme left of the row if no suit sequence is formed in that row. This reshuffling and redealing of cards can only be done two or three times, depending on the rule set one follows. The game is won when all 48 cards are arranged in numerical order and in suits, with the gaps of each row beside the Kings at the extreme right hand of the row. But the game is mostly by chance and the probability of winning is low. ---- There are two variants of this game. One variant is called [http://games.yahoo.com/games/downloads/sa.html Addiction Solitare], a game developed by [http://www.gamehouse.com GameHouse] for Yahoo! Games. This game is played exactly as Gaps except that there are three reshuffles rather than the standard two and the aces can be used in each reshuffle and redeal to create any gaps. The game is so-called probably because of the addiction that can be brought out by the low chance of winning the game. Another variant is called Spaces and Aces, invented by Robert Harbin. The aces in this game are placed at one side of each row. Any gap that is immediately at the right of the ace must be placed with a deuce of the same suit as the ace and the suit sequence would be built up from there. Any other gaps are filled by cards that are the same suit and at least a rank higher than cards at the left of the gaps. There are no redeals in this variant. Category:Solitaire card games

Solitaire

:This article is about the solitaire family of card games. See Solitaire (disambiguation) for other meanings. Solitaire or patience is a family of single-player card games of a generally similar character, but varying greatly in detail. The games are more commonly known as "Patience" in British English whilst "Solitaire" is the American English term. These games typically involve dealing cards from a shuffled deck into a prescribed arrangement on a tabletop, from which the player attempts to reorder the deck by suit and rank through a series of moves transferring cards from one place to another under prescribed restrictions. Some games allow for the reshuffling of the deck(s), and/or the placement of cards into new or 'empty' locations. Solitaire has its own terminology; see solitaire terminology. There are many different solitaire games, but the term "Solitaire" is often used to refer specifically to the most well-known form, called "Klondike". Klondike and some other solitaire games have been adapted into two-player competitive games. There are a vast array of variations on the solitaire/patience theme, using either one or more decks of cards, with rules of varying complexity and skill levels. Many of these have been converted to electronic form and are available as computer games. Basic forms of Klondike solitaire and FreeCell come with every current installation of Microsoft Windows, for example, and Windows XP also includes a version of Spider. 123 Free Solitaire and PySol are two examples of solitaire collections that can be downloaded from the internet at no charge. The term 'solitaire' is also used for single-player games of concentration and skill using a set layout of tiles, pegs or stones rather than cards. These games include:
- Peg solitaire
- Shanghai solitaire (Computerised Mahjong)

Examples of Solitaire card games

A


- Above and Below
- Accordion
- Aces Square
- Aces Up
- Ace-To-King
- Acme
- Adela Patience
- Agnes I (Sorel)
- Agnes II (Bernauer)
- Algerian Patience
- Alhambra
- All Fours
- All In A Row
- Alternate Patience
- Alternation
- Amazons
- Ant
- American Toad
- Aremis
- Argos
- Auld Lang Syne
- Aunt Mary

B


- Babette
- Baccarat Solitaire
- Backbone
- Baker's Dozen
- Baker's Dozen Two Decks
- Baker's Game
- Baroness
-
- Batsford
- Beleaguered Castle
- Betsy Ross
- Bisley
- Black Hole
- Blind Alleys
- Block Fourteen
- Blockade
- Blondes and Brunettes
- Board Patience
- Box Kite
- Bridesmaids
- Brigade
- Bristol
- British Blockade
- British Constitution
- British Square
- Buffalo Bill
- Busy Aces
- But The Same

C


- Caesar
- Calculation
- Calculation by Threes
- Canadian Patience
- Canfield
- Canfield Three Decks
- Canister
- Capricieuse
- Captive Queens
- Carlton
- Carpet
- Carre Napoleon
- Casket
- Castles in Spain
- Chameleon
- Chess Solitaire
- Chessboard
- Chinese Patience
- Cicely
- Citadel
- Class Day
- Climb The Hill
- Clock
- Clock Patience/Clock Solitaire
-
- Coleopter
- Colonel
- Colorado
- Colours
- Concentration
- Cone
- Congress
- Connections
- Contradance
- Corners
- Corona
- Counting
- Courtyard
- Cover Up
- Crescent
- Crescent Four Decks
- Cribbage Solitaire
- Cribbage Square Solitaire
- Crazy Quilt
-
- Cruel
- Curds and Whey
-
- Czarina

D


- Decade
- Deuces
- Diamond
- Diplomat
- Double Canfield
- Double Dot
- Double Golf
- Double Klondike
- Double Line
- Double or Quits
- Double Rail
- Doublets
- Duchess
- Duchess de Luynes
- Duke

E


- Eagle Wing
- Easthaven
- Egyptian Pyramid
- Eight Off
- Eighteens
- Eleanor's Solitaire
- Elevens
- Elizabeth
- Emperor
- Engineer
- Everest
- Exchange

F


- Faerie Queen
- Falling Star
- Fan
- Fanny
- Fascination Fan
- Fifteens
- Fifteen to Win
- Figures
- Finesse
- Five Companions
- Florentine Patience
- Flower Garden
- Flower Garden Two Decks
- Fly
- Following
- Following Two Decks
- Forget-Me-Not
- Fortress
- Fortune's Favor
- Forty and Eight
- Forty Thieves
- Forty Thieves Four Decks
- Forty Thieves Three Decks
- Forty-Nine
- Four By Four
- Four Pegs
- Four Seasons
- Four Seasons Two Decks
- Four Sums
- Fourteen Out
- Frame
- FreeCell
- FreeCell Four Decks
- FreeCell Reversed
- FreeCell Thirteens
- FreeCell Three Decks
- FreeCell Two Decks
- French Patience
- French Solitaire
- Frog

G


- Gaps
- Gargantua
- Gate
- General's Patience
- German Patience
- Giant
- Glencoe
- Goldfield
- Golf
- Golf A-K
- Golf A-K Two Decks
- Golf Pyramids
- Good Measure
- Good Measure Two Decks
- Grandfather
- Grandfather's Clock
- Grandmamma's Patience
- Grant's Reinforcement
- Great Wheel
- Griffon
- Gay Gordons
-

H


- Haden
- Half And Half
- Harp
- Heads And Tails
- Hemispheres
- Hit or Miss
- Horloge
- House in the Wood
- House of Commons
- House of Lords
- House on the Hill

I


- Icarus
- Idle Aces
- Imaginary Thirteen
- Imperial
- Indian
- Intelligence
- Interregnum
- Intrigue

J


- Jacqueline
- Japanese Solitaire
- Joker Forty Thieves
- Joker FreeCell
- Joker Golf A-K
- Joker Klondike
- Joker Pyramid
- Jubilee
- Juvenile

K


- Khedive
- King Albert
- King Edward
- King of Scotland
- Kingdom
- Kings
- King's Audience
- King's Cross
- Klondike
- Klondike by Threes
- Klondike Four Decks
- Klondike Reversed
- Klondike Three Decks
- Knaves
- Knaves' Dial
- Knight Catch All
- Knights Errant

L


- La Belle Lucie
- La Belle Lucie Player's Choice
- La Belle Lucie with a Draw
- Labyrinth
- Lady Betty
- Lady of the Manor
- Lady Palk
- Laggard Lady
- Lagoon
- Lanes
- Le Croix d'Honneur
- Legion
- Letter A
- Letter X
- Leoni's Own
- Les Quatre Coins
- Limited
- Line Up
- Little Billee
- Little Spider
- Little Windmill
- Louis
- Louisa
- Lucas

M


- Mantis
- Maria
- Marshal
- Martha
- Matrimony
-
- Maze
- Memory-Up (6x4 grid)
- Memory-Up (8x5 grid)
- Midshipman
- Milky Way
- Milligan Harp
- Minerve
- Mirror
- Miss Milligan
- Mississippi
- Monte Carlo
- Monte Carlo Thirteens
- Mount Olympus
- Move for the Goal
- Mrs. Mop
- Museum

N


- Napoleon
- Napoleon's Exile
- Napoleon's Square
- Nationale
- Nestor
- Nestor Two Decks
- New York
- New Zealand Patience
- Nines
- Ninety-One
- Nivernaise
- Number Fourteen
- Number Ten

O


- Octagon
- Octave
- Odd and Even
- Only-One-Left (4x4 square) Puzzle
- Only-One-Left (5x5 square) Puzzle
- Open Crescent
- Open Start
- Opus
- Osmosis

P


- Pairs
- Palace
- Parallels
- Passengers
- Patriarchs
- Peek
- Peg Star Solitaire
- Penguin
- Peony
- Perpetual Motion
- Perseverance
- Persian Patience
- Picture Patience
- Poker Solitaire
- Portuguese Solitaire
-
- Precedence
- Princess Patience
- Prisoners
- Privileged Four
- Pulsar
- Push Pin
- Push in the Corner
- Put-Them-In-Order (3x3 square) Puzzle
- Put-Them-In-Order (4x4 square) Puzzle
- Put-Them-In-Order (5x5 square) Puzzle
- Pyramid
- Pyramid (Easy Couple)
- Pyramid by Seven
- Pyramid Two Decks
- Pyramid's Stories

Q


- Quadrangle
- Quadruplets
- Quartets
- Queen of Italy
- Queens and Knaves

R


- Rachel
- Railway
- Rainbow
- Rank and File
-
- Rank by Rank
- Red and Black
- Regal Family
- Reversi
- Robert
- Rosette
- Rouge et Noir
- Rows of Four
- Royal Aids
- Royal Cotillion
- Royal Marriage
- Royal Parade
- Royal Ranks
- Royal Rendezvous
- Royal Square
- Rule of Seven
- Russian Solitaire

S


- S Patience
- Salic Law
- Scorpion
- Scarab
- Scotch Patience
- Senior Wrangler
- Sentinel
- Serpent Poker Solitaire
- Seven Sisters
- Seven Up
- Shamrocks
- Shanghai
- Shifting
- Shuttle
- Simple Simon
- Simplex
- Simplicity
- Single Rail
- Sir Tommy
- Sir Tommy Two Decks
- Six By Six
- Sixes and Sevens
- Sly Fox
- Solid Square
- Solitaire Showdown
-
- Somerset
- Spaces
-
- Spanish Patience
- Spider
- Spider One Suit
- Spider Three Decks
- Spider Two Suits
- Spiderette
- Squadron
- Square
- St. Helena
- Stalactites
- Stalactites and Stalagmites
- Step by Step
- Steps
- Step-Up
- Stonewall
- Storehouse
- Strategy
- Streets
- Streets and Alleys
- Suit by Suit
- Sultan
- Sum of Five
- Super Flower Garden
- Superior Canfield
- Sydney Solitaire

T


- Tabby Cat
-
- Tam O'Shanter
- Tantalus
- Tens
- The Dial
- The Dial II
- The Flea
- The Plot
- The Red and the Black
- The Spark
- Thirteen, Fifteen, Seventeen
- Thirteen Up
- Thirteens
- Thirty
- Thirty-Six
- Three Blind Mice
-
- Three Hills
- Three Pyramids
- Three Shuffles and a Draw
-
- Thumb and Pouch
- Tournament
- Tower of Hanoy
- Tower of Pisa
- Trafalgar Square
- Transformation
- Trapezoid
- Travellers
- Trefoil
- Triad
- Tri Peaks
-
- Triple Alliance
- Triple Line
- Tristan and Isolde
- Twenty
- Twin Queens
- Two Rings

U-Z


- Uncle Sam
- Up or Down
- Variegated Canfield
- Vertical
- Virginia Reel
- Waning Moon
- Wasp
-
- Waste the Same
- Westcliff
- Wheatsheaf
- Whitehead
- Will o' the Wisp
- Windmill
- Wish
- Xantia
- Yukon
- Yukon Three Decks
- Yukon Two Decks
- Zodiac (Unless marked by an asterisk, all games are from the 447 games of [http://www.solsuite.com Solsuite 2006].)

Reference Materials


- Lee, Sloane & Packard, Gabriel. 100 Best Solitaire Games: 100 Ways to Entertain Yourself with a Deck of Cards. ; New York, N. Y.: Cardoza Publishing, 2004. (ISBN 1-58042-115-6)
- Arnold, Peter. Card Games for One. London: Hamlyn, 2002 (ISBN 0-600-60727-5)
- Moorehead, Albert H. & Mott-Smith, Geoffrey. The Complete Book of Solitaire and Patience Games. New York: Bantam Books, 1977 (ISBN 0553262408)
- Crépeau, Pierre. The Complete Book of Solitaire (a translation of Le Grand Livre des Patiences). Willowdale, Ontario: Firefly Books, 2001. (ISBN 1552095975)

See also


- Solitaire terminology
- Patience sorting

External links


- [http://www.solitairecentral.com/ Solitaire Central] - Comprehensive directory of solitaire games
- [http://oneplay.com/games/solitaire/solitaire.jsp A multiplayer solitaire game as Java applet ]
- [http://www.usplayingcard.com/gamerules/solitairegames.html Solitaire game rules] provided by The United States Playing Card Company
- [http://www.solitairecentral.com/rules/ Rules of Some Solitaire Games from Solitaire Central]
- [http://www.bvssolitaire.com/rules/ Solitaire game rules] provided by BVS Development Corporation
- [http://midsummer.mech.surrey.ac.uk/~xpvoke/patience/ Peter's Patience] - A site which includes rules to solitaire games and scans of solitaire books dating to as far back as 1839.
- [http://cardgames.mozdev.org/ Firefox extension for 27 Solitaire games]
- [http://www.solitairelaboratory.com Solitaire Laboratory] Articles on FreeCell, Fourteen Out, and Pyramid
- [http://home.arcor.de/amigasolitaire/e/welcome.html Picture Solitaire] Free solitaire game with more than 1100 carddecks.
- [http://stb.st.funpic.de/solranking/ Windows solitaire world records]
- [http://www.midoritech.com/solitaire.html solitaire] for pc and mac Category:Solitaire card games ja:ソリティア

Probability

The word probability derives from the Latin probare (to prove, or to test). Informally, probable is one of several words applied to uncertain events or knowledge, being more or less interchangeable with likely, risky, hazardous, uncertain, and doubtful, depending on the context. Chance, odds, and bet are other words expressing similar notions. As with the theory of mechanics which assigns precise definitions to such everyday terms as work and force, so the theory of probability attempts to quantify the notion of probable.

Historical remarks

The scientific study of probability is a modern development. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions of use in those problems only arose much later. The doctrine of probabilities dates to the correspondence of Pierre de Fermat and Blaise Pascal (1654). Christiaan Huygens (1657) gave the earliest known scientific treatment of the subject. Jakob Bernoulli's Ars Conjectandi (posthumous, 1713) and Abraham de Moivre's Doctrine of Chances (1718) treated the subject as a branch of mathematics. The theory of errors may be traced back to Roger Cotes's Opera Miscellanea (posthumous, 1722), but a memoir prepared by Thomas Simpson in 1755 (printed 1756) first applied the theory to the discussion of errors of observation. The reprint (1757) of this memoir lays down the axioms that positive and negative errors are equally probable, and that there are certain assignable limits within which all errors may be supposed to fall; continuous errors are discussed and a probability curve is given. Pierre-Simon Laplace (1774) made the first attempt to deduce a rule for the combination of observations from the principles of the theory of probabilities. He represented the law of probability of errors by a curve y = \phi(x), x being any error and y its probability, and laid down three properties of this curve: (1) It is symmetric as to the y-axis; (2) the x-axis is an asymptote, the probability of the error \infty being 0; (3) the area enclosed is 1, it being certain that an error exists. He deduced a formula for the mean of three observations. He also gave (1781) a formula for the law of facility of error (a term due to Lagrange, 1774), but one which led to unmanageable equations. Daniel Bernoulli (1778) introduced the principle of the maximum product of the probabilities of a system of concurrent errors. The method of least squares is due to Adrien-Marie Legendre (1805), who introduced it in his Nouvelles méthodes pour la détermination des orbites des comètes (New Methods for Determining the Orbits of Comets). In ignorance of Legendre's contribution, an Irish-American writer, Robert Adrain, editor of "The Analyst" (1808), first deduced the law of facility of error, :\phi(x) = ce^ c and h being constants depending on precision of observation. He gave two proofs, the second being essentially the same as John Herschel's (1850). Gauss gave the first proof which seems to have been known in Europe (the third after Adrain's) in 1809. Further proofs were given by Laplace (1810, 1812), Gauss (1823), James Ivory (1825, 1826), Hagen (1837), Friedrich Bessel (1838), Donkin (1844, 1856), and Morgan Crofton (1870). Other contributors were Ellis (1844), De Morgan (1864), Glaisher (1872), and Giovanni Schiaparelli (1875). Peters's (1856) formula for r, the probable error of a single observation, is well known. In the nineteenth century authors on the general theory included Laplace, Sylvestre Lacroix (1816), Littrow (1833), Adolphe Quetelet (1853), Richard Dedekind (1860), Helmert (1872), Hermann Laurent (1873), Liagre, Didion, and Karl Pearson. Augustus De Morgan and George Boole improved the exposition of the theory. On the geometric side (see integral geometry) contributors to The Educational Times were influential (Miller, Crofton, McColl, Wolstenholme, Watson, and Artemas Martin).

Concepts

There is essentially one set of mathematical rules for manipulating probability; these rules are listed under "Formalization of probability" below. (There are other rules for quantifying uncertainty, such as the Dempster-Shafer theory and possibility theory, but those are essentially different and not compatible with the laws of probability as they are usually understood.) However, there is ongoing debate over what, exactly, the rules apply to; this is the topic of probability interpretations. The general idea of probability is often divided into two related concepts:
- Aleatory probability, which represents the likelihood of future events whose occurrence is governed by some random physical phenomenon. This concept can be further divided into physical phenomena that are predictable, in principle, with sufficient information (see Determinism), and phenomena which are essentially unpredictable. Examples of the first kind include tossing dice or spinning a roulette wheel, and an example of the second kind is radioactive decay.
- Epistemic probability, which represents our uncertainty about propositions when one lacks complete knowledge of causative circumstances. Such propositions may be about past or future events, but need not be. Some examples of epistemic probability are to assign a probability to the proposition that a proposed law of physics is true, and to determine how "probable" it is that a suspect committed a crime, based on the evidence presented. It is an open question whether aleatory probability is reducible to epistemic probability based on our inability to precisely predict every force that might affect the roll of a die, or whether such uncertainties exist in the nature of reality itself, particularly in quantum phenomena governed by Heisenberg's uncertainty principle. Although the same mathematical rules apply regardless of which interpretation is chosen, the choice has major implications for the way in which probability is used to model the real world.

Formalization of probability

Like other theories, the theory of probability is a representation of probabilistic concepts in formal terms -- that is, in terms that can be considered separately from their meaning. These formal terms are manipulated by the rules of mathematics and logic, and any results are then interpreted or translated back into the problem domain. There have been at least two successful attempts to formalize probability, namely the Kolmogorov formulation and the Cox formulation. In Kolmogorov's formulation, sets are interpreted as events and probability itself as a measure on a class of sets. In Cox's formulation, probability is taken as a primitive (that is, not further analyzed) and the emphasis is on constructing a consistent assignment of probability values to propositions. In both cases, the laws of probability are the same, except for technical details: # a probability is a number between 0 and 1; # the probability of an event or proposition and its complement must add up to 1; and # the joint probability of two events or propositions is the product of the probability of one of them and the probability of the second, conditional on the first. The reader will find an exposition of the Kolmogorov formulation in the probability theory article, and in the Cox's theorem article for Cox's formulation. See also the article on probability axioms. For an algebraic alternative to Kolmogorov's approach, see algebra of random variables.

Representation and interpretation of probability values

The probability of an event is generally represented as a real number between 0 and 1, inclusive. An impossible event has a probability of exactly 0, and a certain event has a probability of 1, but the converses are not always true: probability 0 events are not always impossible, nor probability 1 events certain. The rather subtle distinction between "certain" and "probability 1" is treated at greater length in the article on "almost surely". Most probabilities that occur in practice are numbers between 0 and 1, indicating the event's position on the continuum between impossibility and certainty. The closer an event's probability is to 1, the more likely it is to occur. For example, if two mutually exclusive events are assumed equally probable, such as a flipped coin landing heads-up or tails-up, we can express the probability of each event as "1 in 2", or, equivalently, "50%" or "1/2". Probabilities are equivalently expressed as odds, which is the ratio of the probability of one event to the probability of all other events. The odds of heads-up, for the tossed coin, are (1/2)/(1 - 1/2), which is equal to 1/1. This is expressed as "1 to 1 odds" and often written "1:1". Odds a:b for some event are equivalent to probability a/(a+b). For example, 1:1 odds are equivalent to probability 1/2, and 3:2 odds are equivalent to probability 3/5. There remains the question of exactly what can be assigned probability, and how the numbers so assigned can be used; this is the question of probability interpretations. There are some who claim that probability can be assigned to any kind of an uncertain logical proposition; this is the Bayesian interpretation. There are others who argue that probability is properly applied only to random events as outcomes of some specified random experiment, for example sampling from a population; this is the frequentist interpretation. There are several other interpretations which are variations on one or the other of those, or which have less acceptance at present.

Distributions

A probability distribution is a function that assigns probabilities to events or propositions. For any set of events or propositions there are many ways to assign probabilities, so the choice of one distribution or another is equivalent to making different assumptions about the events or propositions in question. There are several equivalent ways to specify a probability distribution. Perhaps the most common is to specify a probability density function. Then the probability of an event or proposition is obtained by integrating the density function. The distribution function may also be specified directly. In one dimension, the distribution function is called the cumulative distribution function. Probability distributions can also be specified via moments or the characteristic function, or in still other ways. A distribution is called a discrete distribution if it is defined on a countable, discrete set, such as a subset of the integers. A distribution is called a continuous distribution if it has a continuous distribution function, such as a polynomial or exponential function. Most distributions of practical importance are either discrete or continuous, but there are examples of distributions which are neither. Important discrete distributions include the discrete uniform distribution, the Poisson distribution, the binomial distribution, the negative binomial distribution and the Maxwell-Boltzmann distribution. Important continuous distributions include the normal distribution, the gamma distribution, the Student's t-distribution, and the exponential distribution.

Probability in mathematics

Probability axioms form the basis for mathematical probability theory. Calculation of probabilities can often be determined using combinatorics or by applying the axioms directly. Probability applications include even more than statistics, which is usually based on the idea of probability distributions and the central limit theorem. To give a mathematical meaning to probability, consider flipping a "fair" coin. Intuitively, the probability that heads will come up on any given coin toss is "obviously" 50%; but this statement alone lacks mathematical rigor - certainly, while we might expect that flipping such a coin 10 times will yield 5 heads and 5 tails, there is no guarantee that this will occur; it is possible for example to flip 10 heads in a row. What then does the number "50%" mean in this context? One approach is to use the law of large numbers. In this case, we assume that we can perform any number of coin flips, with each coin flip being independent - that is to say, the outcome of each coin flip is unaffected by previous coin flips. If we perform N trials (coin flips), and let NH be the number of times the coin lands heads, then we can, for any N, consider the ratio NH/N. As N gets larger and larger, we expect that in our example the ratio NH/N will get closer and closer to 1/2. This allows us to "define" the probability Pr(H) of flipping heads as the limit (mathematics), as N approaches infinity, of this sequence of ratios: :\Pr(H) = \lim_ In actual practice, of course, we cannot flip a coin an infinite number of times; so in general, this formula most accurately applies to situations in which we have already assigned an a priori probability to a particular outcome (in this case, our assumption that the coin was a "fair" coin). The law of large numbers then says that, given Pr(H), and any arbitrarily small number ε, there exists some number n such that for all N > n, :\left| \Pr(H) - \right| < \epsilon In other words, by saying that "the probability of heads is 1/2", we mean that, if we flip our coin often enough, eventually the number of heads over the number of total flips will become arbitrarily close to 1/2; and will then stay at least as close to 1/2 for as long as we keep performing additional coin flips. Note that a proper definition requires measure theory which provides means to cancel out those cases where the above limit does not provide the "right" result or is even undefined by showing that those cases have a measure of zero. The a priori aspect of this approach to probability is sometimes troubling when applied to real world situations. For example, in the play Rosencrantz and Guildenstern are Dead by Tom Stoppard, a character flips a coin which keeps coming up heads over and over again, a hundred times. He can't decide whether this is just a random event - after all, it is possible (although unlikely) that a fair coin would give this result - or whether his assumption that the coin is fair is at fault.

Remarks on probability calculations

The difficulty of probability calculations lie in determining the number of possible events, counting the occurrences of each event, counting the total number of possible events. Especially difficult is drawing meaningful conclusions from the probabilities calculated. An amusing probability riddle, the Monty Hall problem demonstrates the pitfalls nicely. To learn more about the basics of probability theory, see the article on probability axioms and the article on Bayes' theorem that explains the use of conditional probabilities in case where the occurrence of two events is related.

Applications of probability theory to everyday life

A major effect of probability theory on everyday life is in risk assessment and in trade on commodity markets. Governments typically apply probability methods in environment regulation where it is called "pathway analysis", and are often measuring well-being using methods that are stochastic in nature, and choosing projects to undertake based on their perceived probable effect on the population as a whole, statistically. It is not correct to say that statistics are involved in the modelling itself, as typically the assessments of risk are one-time and thus require more fundamental probability models, e.g. "the probability of another 9/11". A law of small numbers tends to apply to all such choices and perception of the effect of such choices, which makes probability measures a political matter. A good example is the effect of the perceived probability of any widespread Middle East conflict on oil prices - which have ripple effects in the economy as a whole. An assessment by a commodity trade that a war is more likely vs. less likely sends prices up or down, and signals other traders of that opinion. Accordingly, the probabilities are not assessed independently nor necessarily very rationally. The theory of behavioral finance emerged to describe the effect of such groupthink on pricing, on policy, and on peace and conflict. It can reasonably be said that the discovery of rigorous methods to assess and combine probability assessments has had a profound effect on modern society. A good example is the application of game theory, itself based strictly on probability, to the Cold War and the mutual assured destruction doctrine. Accordingly, it may be of some importance to most citizens to understand how odds and probability assessments are made, and how they contribute to reputations and to decisions, especially in a democracy. Another significant application of probability theory in everyday life is reliability. Many consumer products, such as automobiles and consumer electronics, utilize reliability theory in the design of the product in order to reduce the probability of failure. The probability of failure is also closely associated with the product's warranty.

See also


- Bayesian probability
- Bernoulli process
- Cox's theorem
- Decision theory
- Fuzzy measure theory
- Game of chance
- Game theory
- Information theory
- Law of averages
- Law of large numbers
- Measure theory
- Normal distribution
- Random fields
- Random variable
- Statistics
  - List of statistical topics
- Stochastic process
- Wiener process
- Important publications in probability

External links


- [http://www.cut-the-knot.org/probability.shtml A Collection of articles on Probability, many of which are accompanied by Java simulations] at cut-the-knot
- Edwin Thompson Jaynes. Probability Theory: The Logic of Science. Preprint: Washington University, (1996). -- [http://omega.albany.edu:8008/JaynesBook.html HTML] and [http://bayes.wustl.edu/etj/prob/book.pdf PDF]
- [http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html An online probability textbook which uses computer programming as a teaching aid]
- "[http://www.npr.org/display_pages/features/feature_1697475.html The Not So Random Coin Toss], Mathematicians Say Slight but Real Bias Toward Heads". NPR.
- [http://www.benbest.com/science/theodds.html Figuring the Odds (Probability Puzzles)]
- [http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv1-43 Dictionary of the History of Ideas:] Certainty in Seventeenth-Century Thought
- [http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv1-44 Dictionary of the History of Ideas:] Certainty since the Seventeenth Century

Quotations


- Damon Runyon, "It may be that the race is not always to the swift, nor the battle to the strong - but that is the way to bet."
- Pierre-Simon Laplace "It is remarkable that a science which began with the consideration of games of chance should have become the most important object of human knowledge." Théorie Analytique des Probabilités, 1812.
- Richard von Mises "The unlimited extension of the validity of the exact sciences was a characteristic feature of the exaggerated rationalism of the eighteenth century" (in reference to Laplace). Probability, Statistics, and Truth, p 9. Dover edition, 1981 (republication of second English edition, 1957). Category:Applied mathematics Category:Decision theory Category:Probability theory ja:確率 simple:Probability th:ความน่าจะเป็น

Yahoo!

For other uses, see Yahoo. Yahoo! Inc. is an American computer services company with a mission to "be the most essential global Internet service for consumers and businesses". It operates an Internet portal, the Yahoo! Directory and a host of other services including the popular Yahoo! Mail. It was founded by Stanford graduate students David Filo and Jerry Yang in January 1994 and incorporated on March 2, 1995. The company is headquartered in Sunnyvale, California. According to Alexa Internet and Netcraft, both of which are Web trends companies, Yahoo! is the most visited website on the Internet today. The global network of Yahoo websites received 3 billion page views per day as of October 2004.

History

as of October 2004 as of October 2004 as of October 2004 Yahoo! started out as "Jerry's Guide to the World Wide Web" but eventually received a new moniker with the help of a dictionary. "Yet Another Hierarchical Officious Oracle" is a backronym for "yahoo", but Filo and Yang insist they selected the name because they liked the word's general definition, as in Gulliver's Travels by Jonathan Swift: "rude, unsophisticated, uncouth." Yahoo itself first resided on Yang's student workstation, "Akebono," while the software was lodged on Filo's computer, "Konishiki"—both named after legendary sumo wrestlers. The "yet another" phrasing goes back at least to the Unix utility yacc, whose name is an acronym for "yet another compiler compiler". Yahoo had its initial public offering on April 12, 1996, selling 2.6 million shares at $13 each. As Yahoo's popularity has increased, so has the range of features it offers, making it a kind of one-stop shop for all the popular activities of the Internet. These now include: Yahoo! Mail, a Web-based e-mail service, an instant messaging client, a very popular mailing list service (Yahoo! Groups), online gaming and chat, various news and information portals, online shopping and auction facilities. Many of these are based at least in part on previously independent services, which Yahoo has acquired - such as the popular GeoCities free Web-hosting service, Rocketmail, and various competing mailing list providers such as eGroups. Many of these take-overs were controversial and unpopular with users of the existing services, as Yahoo often changed the relevant terms of service. An example of this would be their claiming intellectual property rights for the content on their servers, which the original companies had not done. At the pinnacle of the Internet boom in the year 2000, the cable news station CNBC reported that Yahoo! Inc. and eBay were in discussions to initiate a 50/50 merger [http://wired-vig.wired.com/news/business/0,1367,34967,00.html]. Yahoo has partnerships with telecommunications and Internet providers - such as BT in the UK, Rogers in Canada and SBC ,Verizon [http://www22.verizon.com/forhomedsl/channels/dsl/services/default.asp?view=yahoo]and BellSouth in the US - to create content-rich broadband services to rival those offered by AOL. The company offers a branded credit card, Yahoo! Visa, through a partnership with First USA. Beginning in late 2002, Yahoo quietly began to bolster its search services by acquiring competing technologies. In December 2002, it acquired Inktomi, and in July 2003, it acquired Overture Services, Inc., and through it, search sites AltaVista and AlltheWeb. On February 18, 2004, Yahoo dropped Google-powered results and returned to using its own technology to provide search results. As of 2005 Yahoo!'s news message boards have gained something of a cult following. Attached to every story is a discussion board, yet rarely are the posts pertinent to the story. Often, the posts are deliberately outrageous, attempting to provoke angry responses which, in turn, lead to more offensive posts and so on. No news story, however sacrosanct, is spared.

Controversy

In April 2005, Shi Tao, a journalist working for a Chinese newspaper, was sentenced to 10 years in prison by the Changsa Intermediate People's Court of Hunan Province, China (First trial case no 29), for "providing state secrets to foreign entities". He had passed details of a censorship order to the Asia Democracy Forum and the website [http://www.wmd.org/democracynews/may1102sup.html Democracy News]. Reporters Without Borders (RSF) investigated the case, specifically the ease with which Mr Tao had been caught. He had sent the message through an anonymous Yahoo! account. But police had gone straight to his offices and picked him up. RSF later obtained a translation of the [http://www.rsf.org/IMG/pdf/Verdict_Shi_Tao.pdf verdict] which stated that Mr Tao's account information, telephone number and address were "furnished by Yahoo! Holdings".

Important events

Please note that this list is merely partial.
- 1995: Ziff Davis Inc. launches the magazine Yahoo! Internet Life, initially as ZD Internet Life. The magazine was meant to accompany and complement the web site.
- January 19 2000: At the height of the Dot-com tech bubble, shares in Yahoo Japan became the first stocks in Japanese history to trade at over ¥100,000,000, reaching a price of 101.4 million yen ($962,140 at that time). [http://www.internetnews.com/ent-news/print.php/289851]
- February 7 2000: Yahoo.com was brought to a halt for a few hours as it was the victim of a distributed denial of service attack (DDoS). [http://news.bbc.co.uk/1/hi/sci/tech/635444.stm] [http://news.com.com/2100-1023-236621.html?legacy=cnet]. On the next day, its shares rose about $16, or 4.5 percent as the failure was blamed on hackers rather than on an internal glitch, unlike what happened to eBay earlier.
- June 3, 2002: SBC and Yahoo! Launch National Co-Branded Dial Service -- [http://www.sbc.com/gen/press-room?pid=4800&cdvn=news&newsarticleid=20046 Press Release]
- December 2002: Yahoo! Inc. starts acquisition of Inktomi Web search engine
- July, 2003: BT Openworld announces an alliance with Yahoo! -- [http://www.groupbt.com/News/Articles/ShowArticle.cfm?ArticleID=fa2aec1b-0336-4b33-8d7e-85900c10ea33 Press Release]
- July 2003, Acquires Overture Services, Inc.
- January 19 2004: Yahoo! Inc. announces the formation of [http://research.yahoo.com Yahoo! Research Labs], a research organization focusing on the invention of new technologies and solutions for Yahoo. Yahoo's Head and Principal Scientist, Dr. Gary William Flake, leads the new organization. Dr. Flake has since left the company and now works at Microsoft.
- February 19 2004: Yahoo dropped Google-powered results, returning to its own results after a long time.
- March 2004: Yahoo launches its own search engine technology.
- March 1 2004: Yahoo announces (as cited in the New York Times article listed in the "References" section) that it will practice paid inclusion for its search service. However, it also announced it would continue to rely mainly on a free web crawl for most of its search engine content.
- March 25 2004: Yahoo acquires the European shopping search engine [http://kelkoo.com/ Kelkoo].
- December 15 2004: Yahoo launches beta version of its video search engine.
- February 9 2005 Yahoo! Launch is changed to Yahoo! Music, which still provides free music.
- February 15 2005 Yahoo establishes its European Headquarters in Dublin, Ireland with the creation of 400 new jobs. [http://en.wikinews.org/wiki/Yahoo_chooses_Dublin_as_location_of_new_European_Headquarters]
- February 28 2005 Yahoo! launches a [http://developer.yahoo.net/ developer network] giving an API to most of its search verticals.
- March 2 2005 Yahoo! completes 10 years of corporate existence. Gives out free ice cream coupons at Baskin Robbins to its users to celebrate its "birthday."
- March 20, 2005 Yahoo! acquires photo sharing service Flickr [http://blog.flickr.com/flickrblog/2005/03/yahoo_actually_.html]
- April 7, 2005 Wikimedia Foundation announces Yahoo! support [http://wikimediafoundation.org/wiki/Press_releases/Wikimedia_announces_Yahoo_support]
- May 26, 2005 Yahoo! announces its new PhotoMail service
- June 14, 2005 Yahoo! acquires VoIP provider DialPad Communications.
- July 15, 2005 Yahoo! announces Yahoo! Research Lab - Berkeley (YRLB)
- July 25, 2005 Yahoo! acquires widget engine Konfabulator
- August 11, 2005 Yahoo! acquires 40% of Alibaba.com for $1 billion US, and Alibaba will take over operation of Yahoo! China. [http://www.wired.com/news/business/0,1367,68497,00.html?tw=wn_tophead_5]
- August 23, 2005: Verizon and Yahoo! Launch Integrated DSL Service -- [http://newscenter.verizon.com/proactive/newsroom/release.vtml?id=92803 Press Release]
- September 7, 2005. Yahoo! supplies information to People's Republic of China which then jails reporter Shi Tao, age 37, for 10 years. Yahoo! states that they were following Chinese law. [http://news.bbc.co.uk/1/hi/world/asia-pacific/4221538.stm]
- October 4, 2005 Yahoo! purchases online social event calender Upcoming.org. [http://www.waxy.org/archive/2005/10/04/yahoo_an.shtml]
- October 17, 2005 Yahoo! buys British company [http://www.whereonearth.com Whereonearth Ltd] which provides location technology.
- November 15, 2005 The sports section of [http://my.yahoo.com My Yahoo!] is hacked; titles such as "selfhood + conscience" and "aesthetic freedom" link to various pages at doublereflection.org .
- December 8/ (US time) 9, (Australian time) 2005 Yahoo! 7 announced for January 2006. [http://yahoo7.com.au Official Site]
- December 9, 2005 Yahoo! acquires [http://del.icio.us del.icio.us].

Yahoo! Research Labs

Yahoo! has 3 research labs:
- Berkeley, California in association with the School of Information Management and Systems at the University of California, Berkeley.
- Pasadena, California (moving to Burbank, California in November 2005).
- Sunnyvale, California.

See also


- List of search engines
- Yahoo! trolling phenomena
- GAMEY

External links


- [http://www.yahoo.com/ Official website]
- [http://docs.yahoo.com/info/pr/milestones.html Corporate milestones]
- [http://docs.yahoo.com/info/misc/history.html The History of Yahoo! - How It All Started...]

Yahoo!-owned sites and services

This is a partial, alphabetized list. For a complete listing of the services see [http://docs.yahoo.com/docs/family/more/ List of Yahoo! services].
- del.icio.us – popular social bookmarking site, http://del.icio.us/
- Flickr – popular photo sharing site, http://flickr.com/
- GeoCities – free homepage hosting, http://geocities.yahoo.com/
- Yahoo! 360º – http://360.yahoo.com/
- Yahoo Assistant
- Yahoo! 7 joint entity with Seven Network Australia, http://yahoo7.com.au
- Yahoo! Developer Network – resources for software developers using Yahoo! technologies and Web services, http://developer.yahoo.net/
- Yahoo! Directory – hierarchical directory of web-sites, http://dir.yahoo.com/
- Yahoo! Finance – stock exchange rates and other financial information, http://finance.yahoo.com/
- Yahoo! Games – playing games (i. e. on-line against other users), http://games.yahoo.com/
- Yahoo! Groups – mailing lists, http://groups.yahoo.com/
- Yahoo! HotJobs – http://hotjobs.yahoo.com/
- Yahoo! Mail – web-based email, http://mail.yahoo.com/
- Yahoo! Maps – http://maps.yahoo.com/
- Yahoo! Messenger – http://messenger.yahoo.com/
- Yahoo! Mobile – http://mobile.yahoo.com/
- Yahoo! Music – Music videos and internet radio (LAUNCHcast). http://music.yahoo.com/
- Yahoo! Personals – http://personals.yahoo.com/
- Yahoo! Photos – http://photos.yahoo.com/
- Yahoo! Real Estate – http://realestate.yahoo.com/
- Yahoo! Search – websearch, http://search.yahoo.com/
- Yahoo! Search Marketing (Overture) – http://searchmarketing.yahoo.com/
- Yahoo! Shopping – shopping search & compare, http://shopping.yahoo.com/
- Yahoo! Sports – scores, stats, and fantasy games, http://sports.yahoo.com/
- Yahoo! Travel travel guides, booking and reservation, http://travel.yahoo.com/
- Yahoo! Widgets – a cross-platform desktop widget runtime environment, formerly called Konfabulator
- Yahooligans!Children's version of the web portal. – http://www.yahooligans.com/
- Kelkoo – Shopping search engine in 10 European Countries – http://www.kelkoo.com/

Information about Yahoo!


- [http://yahoo.weblogsinc.com/ yahoo.weblogsinc.com] - The Unofficial Yahoo! Weblog
- [http://www.interviewat.com/yahoo Job interviews at Yahoo!] - employees and job seekers share information on Yahoo! interview process
- [http://www.rustybrick.com/rustysearch-results.php The Search Engine Relevancy Challenge Results] – A search engine that compares search relevancy by letting users rank results from several major search engines including Yahoo!
- [http://www.mg.co.za/articlePage.aspx?articleid=250230&area=/breaking_news/breaking_news__international_news/ Mail & Guardian online (South Africa)] – Watchdog says Yahoo! gave data on jailed journalist to Chinese government.
- [http://security.yahoo.com Yahoo! Security Center] - Guide to Online Security

Opposition to Yahoo!


- [http://www.super70s.com/Super70s/About/Yahoo-MSN.asp Why Yahoo's search results cannot be trusted] - Opposition to Yahoo!'s pay-for-placement search results
- [http://www.yahoo-watch.org Yahoo Watch]
- [http://www.booyahoo.com BooYahoo!] Category:Companies based in California Category:Companies traded on NASDAQ Category:Internet companies of the United States Category:Internet search engines Category:Websites
-
ko:야후! ja:Yahoo! nb:Yahoo! simple:Yahoo! th:ยาฮู!

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