Gambling.Now!

What is it?

Pinochle (sometimes [tag]Pinocle[/tag] or [tag]Penuchle[/tag]), is a trick-taking game typically for two, three or four players and played with a 48 card deck. Derived from the card game Bezique, players score points by trick-taking and also by forming combinations of cards into melds. Each hand is played in three phases: bidding, melds, and tricks.

A Pinochle deck consists of two copies of each of the 9, 10, jack, queen, king, and ace cards of all four suits. Aces are always considered high. Pinochle follows the standard card ordering with the exception of the 10 being second highest. The complete ordering from highest to lowest is A, 10, K, Q, J, 9.

Variants of Pinochle can be played with three, five, six, eight or more players. These larger variations can combine two Pinochle decks called a “double deck”.

In some areas of the United States, such as Oklahoma and Texas, thumb wrestling is often referred to as “pinochle”. The two games, however, are not related.

The game is played with one Pinochle deck of 48 cards; one player is the dealer.

In Pinochle, after the shuffle, the dealer distributes the cards. All the cards are dealt in partnership Pinochle. In other variations a widow’ (or called the “kitty”, “talon”, or “stock”) of cards remain. Traditionally, this is done clockwise, three cards at a time, starting with the player to the left and ending with the dealer. The deal rotates clockwise, so the dealer’s left-hand opponent will deal next.

Some house rules allow a player with a hand of 6 nines or 5 nines and no meld to throw it in, making the deal null and void and demanding a redeal.^{[citation needed]} The player with this poor hand must declare this instead of bidding during an auction. Sometimes there is a limit of three deals for this reason, requiring the third deal to be played.

The Bid

In auction Pinochle, players bid for the points they predict their hand could earn. The highest bidder earns the right to declare the [tag]trump[/tag] suit. One of the players, usually the player to the left of the dealer, or the dealer themself, is obligated to open with a first bid. The minimum opening bid is usually an agreed upon value between players like 100 or 250. When a player has the turn to bid, the player may do either of the following:

1. make a new bid, or
2. pass.

Each bid must be greater than the previous one, and be a multiple of 10. When a player passes, they can no longer bid. The auction ends when subsequent players in rotation have passed after the last bid. The last bid becomes the contract. The player that made this final bid will then declare trump in the suit that is desired. In some house rules, trump cannot be declared in any suit not containing a run, marriage or dix meld.

In order to win the hand, the combined total of melding and trick points must be equal to or greater than the winning bid. Thus bidding involves anticipating the points that will be accumulated from melds and from the points acumulated from winning tricks. If the combined score is lower than the bid, then the bidding team or player has been set. This means that the total bid amount is subtracted from the total game score, often accompanied by losing the points scored in meld for that hand as well. This can result in a negative score.

[tag]Meld[/tag] – Not [tag]Melt[/tag]

Melding consists of displaying specific combinations of cards to all players. Typically this is done by placing the combination of cards face up on the playing surface until all players have had the opportunity to examine them. All players meld after the bid winner shows meld first. The types of melds include arounds, marriages, flushes and pinochles.

The rank melds containing four of the same face cards — ace, king, queen or jack — must include one card from each of the different suits . They are scored as follows:

• “100 Aces” or “Aces around” – 4 aces of different suits – 100 points
• “80 Kings” or “Kings around” – 4 kings of different suits – 80 points
• “60 Queens” or “Queens around” – 4 queens of different suits – 60 points
• “40 Jacks” or “Jacks around” – 4 jacks of different suits – 40 points

A player holding all eight aces, kings, queens or jacks is called a double around (or double aces, double kings, etc). This hand is worth 10 times the value of a single around. For instance, a kings double around is worth 800 points.

The marriages, flush and dix are the suit melds.

• “Trump Marriage” – king and queen of trump suit – 40 points
• “Marriage” – king and queen of a suit other than trump – 20 points
• “Flush”, “Family”, “Rope” or “Run” – A 10 K Q J of trump suit only – 150 points. Similar to what is done with Aces, Kings Around, etc. A double run, or two runs in trump in the same hand, is worth 1500 points.
• “[tag]Dix[/tag]” – nine of trump – 10 points

A marriage in each suit is worth 240 total points. As a shortcut, this is called a “roundtable”, “marriages around”, “[tag]Round House[/tag]“, or a “Round Robin”. This is nothing more than the sum of the marriages, plus kings around and queens around.

The pinochle is the unique combination that shares the name of the game.

• “Pinochle” – jack of diamonds and queen of spades – 40 points.
• “Double pinochle” – both jacks of diamonds and both queens of spades – 300 points.

Each card may be used in at most one meld of each type. Thus, a queen card can be used in one marriage with one king, regardless if the player has the other king of the same suit. However, a queen can be used to score a marriage and a pinochle if the player also has the correct jack.

After the melds are displayed, the points are counted and the teams total their individual meld scores to form a team score.

Playing tricks

The high bidder makes the first lead, which can be any card in their hand. (Some people play with a rule that the first card led must be a trump. ) Each player must follow suit if possible. If they can follow suit, and can play a card higher than any played so far, they must do so. If a player cannot follow suit, but has trump, they must play trump. Again, if they can play a card higher than any played so far, they must do so. If they cannot fulfill any of the previous conditions, then they can play any card in their hand. Finally, if two identical cards are played, the first one outranks the second. (One variation does not require playing a higher trump card if trump wasn’t led.)

After the first trick, the winner of each trick leads to the next.

Scoring tricks

Points are scored based on the tricks won in the hand. There are several ways to count up the points for play, but they always add up to 250 points. The last trick is always worth 10 points. The classic counting system of Pinochle is where aces are worth 11, tens are worth 10, kings are worth 4, queens are worth 3, jacks are worth 2, and nines are worth zero. This method takes longer to count the score at the end of each hand. A simpler method is to count aces and tens for 10 points, kings and queens for 5 points, and jacks and nines are worth zero.

An even simpler method that reduces strategy in trick-taking has aces, tens, and kings worth 10 (and known as “counters”), and everything else zero (“garbage”). Since all points are multiples of ten in the third method, some players drop the redundant zero. Aces, tens, and kings won in tricks are worth one point. The meld scoring can also avoid the zero in the tenth place. Melds like [tag]100 aces[/tag] are thus worth 10. The terms “100 aces”, “80 kings” and so on are still used, even though the point values are one-tenth.

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At least the games with regulated international professional competition have been referred to as “sports” or “sporting” events, not simply “games”, since 1893 at the latest.^[3] Quite a variety of particular games (i.e. sets of rules and equipment) are the subject of present-day competition, including many of those already mentioned, with competition being especially broad in nine-ball, snooker, three-cushion and eight-ball…

Snooker, though technically a pocket billiards variant and closely related in its equipment and origin to the game of English billiards, is a professional sport organized at the international level, and its rules bear little resemblance to those of pool games.

A “Billiards” category encompassing pool, snooker and carom was featured in the 2005 World Games, held in Duisburg, Germany, and the 2006 Asian Games also saw the introduction of a “Cue sports” category. Efforts have also been underway for many years to have cue sports become Olympic competitions.^{[citation needed]}

Equipment

Billiard balls

Main article: Billiard balls

Pool balls

Billiard balls vary from game to game, in size, design and number. Carom billiards balls are larger than pool balls, and come as a set of two [tag]cue balls[/tag] (one colored or marked) and an object ball (or two object balls in the case of the game four-ball also known as [tag]yotsudama[/tag]). American-style pool balls, used in any pool game and found throughout the world, come in sets of two suits of object balls, seven solids and seven stripes, an 8 ball and a cue ball; the balls are racked differently for different games (some of which do not use the entire ball set). Blackball (English-style eight-ball) sets are similar, but have unmarked groups of red (or blue) and yellow balls instead of solids and stripes, and are smaller than the American-style; they are used principally in Britain, Ireland, and some Commonwealth countries, though not exclusively, since they are unsuited for playing nine-ball. [tag]Snooker[/tag] balls are also smaller than American-style pool balls, and come in sets of 22 (fifteen reds, 6 “colours”, and a cue ball). Other games also have custom ball sets, such as Russian pyramid and [tag]bumper pool[/tag].

Billiard balls have been made from many different materials since the start of the game, including clay, bakelite, celluloid, crystalite, ivory, plastic, steel and wood. The dominant material from 1627 until the early to mid 1900s was ivory. The search for a substitute for ivory use was not for environmental concerns but based on economic motivation and fear of danger for elephant hunters. It was in part spurred on by a New York billiard table manufacturer who announced a prize of $10,000 for a substitute material. The first viable substitute was celluloid, invented by John Wesley Hyatt in 1868, but the material was volatile, sometimes exploding during manufacture and was highly flammable.^[4][5] Today, billiard balls are often made with the thermoset resin Bakelite.

Tables

There are many sizes and styles of pool and billiard tables. Generally, tables are rectangles twice as long as they are wide. Most pool tables are known as 7-, 8-, or 9-footers, referring to the length of the table’s long side. Full-size snooker and English billiard tables are 12 feet (3.7 m) long on the longest side. Pool halls tend to have 9 foot (2.7 m) tables and cater to the serious pool player. Pubs will typically use 7 foot (2.1 m) tables which are often coin-operated. Formerly, 10 foot (3 m) tables were common, but such tables are now considered antique collectors items; a few, usually from the late 1800s, can be found in pool halls from time to time. Ten-foot tables remain the standard size for carom billiard games. The slates on modern carom tables are usually heated to stave off moisture and provide a consistent playing surface.

The length of the pool table will typically be a function of space, with many homeowners purchasing an 8 foot (2.4 m) table as a compromise. High quality tables are mostly 4.5 by 9 ft (2.7 m). (interior dimensions), with a bed made of three pieces of thick slate to prevent warping and changes due to humidity. Smaller bar tables are most commonly made with a single piece of slate. Pocket billiards tables normally have six pockets, three on each side (four corner pockets, and two side pockets).

Cloth

All types of tables are covered with billiard cloth (often called “felt”, but actually a woven wool or wool/nylon blend called baize). Cloth has been used to cover billiards tables since the 15th century. In fact, the predecessor company of the most famous maker of billiard cloth, Iwan Simonis, was formed in 1453.

Bar or tavern tables, which get a lot of play, use “slower”, more durable cloth. The cloth used in upscale billiard parlours and home billiard rooms is “faster” (i.e. provides less friction, allowing the balls to roll farther across the table bed), and competition-quality pool cloth is made from 100% worsted wool. Snooker cloth traditionally has a nap (consistent fiber directionality) and balls behave differently when rolling against versus along with the nap.

The cloth of the billiard table has traditionally been green, reflecting its origin (originally the grass of ancestral lawn games), and has been so colored since the 16th century.^[6] However, the color also serves a useful function, as non-color-blind human eyes have a higher sensitivity to green than to any other color.^[7]

Rack

Main article: Rack (billiards)

A [tag]rack[/tag] is the name given to a frame (usually wood or plastic) used to organize billiard balls at the beginning of a game. This is traditionally triangular in shape, but varies with the type of billiards played. There are two main types of racks; the more common triangular shape which is used for eight-ball and straight pool and the diamond shaped rack used for [tag]nine-ball[/tag].

Cues

Billiards games are mostly played with a stick known as a cue. A cue is usually either a one piece tapered stick or a two piece stick divided in the middle by a joint of metal or phenolic resin. High quality cues are generally two pieces and are made of a hardwood, generally maple for billiards and ash for snooker.

The “butt” end of the cue is of larger circumference and is intended to be gripped by a player’s hand. The “shaft” of the cue is of smaller circumference, usually tapering to an 0.4 to 0.55 inch (11-14 mm) terminus called a ferrule, where a leather tip is affixed to make final contact with balls. The leather tip, in conjunction with chalk, can be used to impart spin to the cue ball when not being hit in its center.

Cheap cues are generally one piece cues made of ramin or other low quality wood with inferior tips of various materials (usually plastic). A quality cue can be expensive and may be made of exotic woods and other expensive materials which are artfully inlaid in decorative patterns. Skilled players may use more than one cue during a game, including a separate cue for the opening break shot and another, shorter cue with a special tip for jump shots.

The mechanical bridge

The mechanical bridge, sometimes called “the ladies aid”, “rake”, “bridge stick” or simply “bridge”, and known as a “rest” in the UK, is used to extend a player’s reach on a shot where the cue ball is too far away for normal hand bridging. It consists of a stick with a grooved metal or plastic head which the cue slides on. Many amateurs refuse to use the mechanical bridge based on the perception that to do so is unmanly. However, many aficionados and most professionals employ the bridge whenever the intended shot so requires. Some players, especially current or former snooker players, use a screw-on cue butt extension instead of or in addition to the mechanical bridge. Bridge head design is varied, and not all designs (especially those with cue shaft-enclosing rings, or wheels on the bottom of the head), are broadly tournament-approved. In Italy a longer, thicker cue is available for this kind of tricky shots.

Chalk

Chalk is applied to the tip of the cue stick, ideally before every shot, to increase the tip’s friction coefficient so that when it impacts the cue ball on a non-center hit, no miscue (unintentional slippage between the cue tip and the struck ball) occurs. Cue tip chalk is not actually the substance typically referred to as “chalk” (generally calcium carbonate, also known as calcite or carbonate of lime), but any of several proprietary compounds, with a silicate base. “Chalk” may also refer to a cone of fine, white hand chalk; like talc (talcum powder) it can be used to reduce friction between the cue and bridge hand during shooting, for a smoother stroke. Some brands of hand chalk actually are made of compressed talc. (Tip chalk is not used for this purpose because it is abrasive, hand-staining and difficult to apply.) Many players prefer a slick pool glove over hand chalk or talc because of the messiness of these powders; buildup of particles on the cloth will affect ball behavior and necessitate more-frequent cloth cleaning.Cue tip chalk (invented in its modern form by straight rail billiard pro William A. Spinks and chemist William Hoskins in 1897)^[8][9] is made by crushing silica and the abrasive substance corundum or aloxite^[9] (aluminum oxide),^[10][11] into a powder^[9] and using forced air to achieve the desired consistency. It is combined with dye (originally and most commonly green or blue-green, like traditional billiard cloth, but available today, like the cloth, in many colors) and a binder (glue).Finally, a 15 ton-per-square-inch hydraulic press^{[citation needed]} is used to compress the “chalk” into large cakes which are dried on a rack, and then cut into small cubes, dimpled on the top to receive the cue tip, and wrapped in paper sleeves. Each manufacturer’s brand has different qualities, which can significantly affect play. High humidity can also impair the effectiveness of chalk. Harder, drier compounds are generally considered superior by most players.

All [tag]cue sports[/tag] are generally regarded to have evolved into indoor games from outdoor stick-and-ball lawn games, and as such to be related to croquet and golf, and more distantly to the stickless bocce and bowling. The word “billiard” may have evolved from the French word [tag]billart[/tag], meaning “mace”, an implement similar to a golf club, which was the forerunner to the modern cue. The term “cue sports” can be used to encompass the ancestral mace games, and even the modern cueless variants, such as finger pool, for historical reasons….Accordingly, in addition to the three general subdivisions listed earlier, a now rare obstacle category was prevalent in early times. The obstacle games (see illustration to the right, featuring a croquet-like variant), appear to have been the earliest,^{[citation needed]} and include the obsolete bagatelle and pin pool among many other variations, some with elaborate structures (likely inspirational of miniature golf), and yet others on a sloped table (the ancestors of pinball), up to the relatively recent bumper pool (popular in the 1970s in home game rooms).

The object of obstacle games varies from avoiding obstructions and traps, to hitting or passing through or into them on purpose to score, to using them strategically to score in some other way, such as by rebounding off them to reach a hole in the table or trapping opponents’ balls.^{[citation needed]}

The early croquet-like games eventually led to the development of the carom or carambole billiards category — what most non-US and non-UK speakers mean by the word “billiards”. These games, which once completely dominated the cue sports world but have declined markedly in most areas over the last few generations, are games played with three or sometimes four balls, on a table without holes (or obstructions in most cases, five-pins being an exception), in which the goal is generally to strike one object (target) ball with a cue ball, then have the cue ball rebound off of one or more of the cushions and strike a second ball. Variations include three-cushion, straight rail, balkline variants, cushion caroms, Italian five-pins, and four-ball, among others.

Over time, a type of obstacle returned, originally as a hazard and later as a target, in the form of pockets, or holes partly cut into the table bed and partly into the cushions, leading to the rise of pocket billiards, especially “pool” games, popular around the world in forms such as [tag]eight-ball[/tag], [tag]nine-ball[/tag], [tag]straight pool[/tag] and one-pocket amongst numerous others. The terms “pool” and “pocket billiards” are now virtually interchangeable, especially in the [tag]US. English billiards[/tag] (what UK speakers almost invariably mean by the word “billiards”) is a hybrid carom/pocket game, and as such is likely fairly close to the ancestral original pocket billiards [tag]history[/tag] outgrowth from eighteenth- to early nineteenth-century carom games.

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This information does not purport to be the alpha and omega of online gaming laws. Please in accordance to your local laws:

United States

The United States Court of Appeals for the Fifth Circuit ruled^[2] in November 2002 that the [tag]Federal Wire Act[/tag] prohibits electronic transmission of information for sports betting across state lines but affirmed a lower court ruling^[3] that the Wire Act “‘in plain language’ does not prohibit Internet gambling on a game of chance.”

Some states have specific laws against online gambling of any kind. Also, owning an online gaming operation without proper licensing would be illegal, and no states are currently granting online gaming licenses.

In March 2003, Deputy Assistant Attorney General John G. Malcolm testified before the Senate Banking Committee regarding the special problems presented by online gambling. A major concern of the United States Department of Justice is online money laundering. The anonymous nature of the Internet and the use of encryption make it especially difficult to trace online money laundering transactions.

In April 2004 [tag]Google[/tag] and [tag]Yahoo![/tag], the two largest internet search engines, announced that they were removing online gambling advertising from their sites. The move followed a United States Department of Justice announcement that, in what some say is a contradiction of the Appeals Court ruling, the Wire Act relating to telephone betting applies to all forms of Internet gambling, and that any advertising of such gambling “may” be deemed as aiding and abetting. Critics of the Justice Department’s move say^{[citation needed]} that it has no legal basis for pressuring companies to remove advertisements and that the advertisements are protected by the First Amendment. As of April 2005, Yahoo! has provided advertising for “play money” online gaming.

In August 2004, Casino City, an online portal for internet gambling sites, sued the US Department of Justice. The complaint alleged, inter alia, that the websites business—promoting internet gambling—was legal, and requested a declaration from the court that its business was protected by the First Amendment. The U.S. District Court for the Middle District of Louisiana dismissed the case in February of 2005.

In its opinion, the District Court wrote,

It is well-established that the First Amendment does not protect the right to advertise illegal activity… The government’s interest is specifically directed towards the advertising of illegal activity, namely Internet gambling… Furthermore, the speech in which the plaintiff wishes to engage is misleading because it falsely portrays the image that Internet gambling is legal… Because plaintiff’s speech concerns misleading information and illegal activities, it does not fall within the speech that is protected by the First Amendment.^[5]

The US Court of Appeals, 5th Circuit, dismissed [tag]Casino City[/tag]‘s appeal in January, 2006.

In February 2005 the North Dakota House of Representatives passed a bill to legalize and regulate online poker and online poker cardroom operators in the State. Testifying before the State Senate, Nigel Payne, CEO of Paradise Poker, pledged to relocate to the state if the bill became law. However, the measure was defeated by the State Senate in March 2005. Rep. Jim Kasper, who sponsored the 2005 legislation, plans to introduce similar bills in the 2007 North Dakota legislative session.

In July 2006, David Carruthers, the CEO of BetonSports, a company publicly traded on the London Stock Exchange was detained in Texas while changing planes on his way from London to Costa Rica. He and ten other individuals had been previously charged in a sealed indictment with violations of US Federal laws relating to illegal gambling. While as noted above, a United States Appeals court has stated that the Wire Act does not apply to non-sports betting, the Supreme Court of the United States previously refused to hear an appeal of the conviction of Jay Cohen, where lower courts held that the Wire Act does make it illegal to own a sports betting operation that offers such betting to United States citizens.

The BetOnSports indictment alleged violations of at least 9 different Federal statutes, including 18 USC Sec. 1953 (Operation of an Illegal Gambling Business). Carruthers is currently under house arrest on a one million dollar bail bond.

In September 2006, [tag]SportingbetPLC[/tag] reported that its chairman, Peter Dicks, was detained in New York City on a Louisiana warrant while traveling in the United States on business unrelated to online gaming. Louisiana is one of the few states that has a specific law prohibiting gambling online. At the end of the month, New York dismissed the Louisiana warrant.^[12]

Also in September 2006, just before adjourning for the midterm elections, both the House of Representatives and Senate passed legislation (as an amendment to the unrelated Safe Port Act) that would make transactions from banks or similar institutions to online gambling sites illegal. This differs from a previous bill passed only by the House that expanded the scope of the Wire Act. The passed bill only addresses banking issues.^[13] The act was signed into law on October 13, 2006 by President George W. Bush, and there is a provision for a 270-day period to develop enforcement measures. At the bill-signing ceremony, Bush never mentioned the Internet gambling measure, which was supported by the National Football League and opposed by banking groups.

In response to this new legislation, a number of online gambling operators including PartyGaming, The bwin Group, Cassava Enterprises, and Sportingbet announced that real-money gambling operations would be suspended for U.S. customers. PartyGaming’s stock dropped by 60% following its announcement. Other operators such as [tag]PokerStars[/tag], Bodog, and WSEX.com announced their intention to continue serving customers in the U.S.

On April 26, 2007, Rep. Barney Frank (D-MA) introduced [tag]HR 2046[/tag], the Internet Gambling Regulation and Enforcement Act (IGREA). The [tag]IGREA[/tag] would modify the [tag]UIGEA[/tag] by providing a provision for licensing of Internet gambling facilities by the Director of the Financial Crimes Enforcement Network. On June 8, 2007, the House Financial Services Committee, chaired by Rep. Barney Frank, held a hearing entitled, “Can Internet Gambling Be Effectively Regulated to Protect Consumers and the Payments System?”. Expert witnesses at the hearing testified that Internet gambling can be effectively regulated for age verification, money laundering issues, facilitation of state and federal tax collection, and for issues relating to compulsive gambling.

On June 7, 2007, Rep. Robert Wexler (D-FL) introduced HR 2610, the Skill Game Protection Act. This act would legalize Internet poker, bridge, chess, and other games of skill. Also on June 7, Rep. Jim McDermott [D-WA] introduced H.R. 2607, the Internet Gambling Tax Act. The IGTA would legislate Internet gambling tax collection requirements.

Australia

On the 28th of June 2001 the Australian Government passed the Interactive Gambling Act 2001 (IGA). The government said that the IGA was important to protect Australians from the harmful effects of gambling.

The IGA targets the providers of interactive gambling services, not their potential or actual customers. The IGA makes it an offence to provide an interactive gambling service to a customer physically present in Australia, but it is not an offence for Australian residents to play poker or casino games online. In stark contrast to the USA, sports betting online is also completely legal in Australia, with many state government licensed sportsbooks in operation, such as Centrebet, Sportingbet & [tag]Betfair[/tag].

The offence applies to all interactive gambling service providers, whether based in Australia or offshore, whether Australian or foreign owned. The offense carries a maximum penalty of $220,000 per day for individuals and $1.1 million per day for bodies corporate. (More information regarding the Interactive Gambling Act 2001 can be found Here.

Complaints regarding Online gambling facilities serving Australian users can be made to the Australian Communication and Media Authority at its Homepage.

Other countries

Various forms of online gambling are legal and regulated in many countries, including most members of the European Union and several nations in and around the Caribbean Sea.

In India it is neither legal nor illegal the Law is silent on the issue, but in the state of [tag]Maharashtra[/tag] it is a banned offence under the “[tag]Bombay Wager Act[/tag]“.

The government of the island nation of Antigua and Barbuda, which licenses Internet gambling entities, made a complaint to the World Trade Organization about the U.S. government’s actions to impede online gaming. The Caribbean country won the preliminary ruling but WTO’s appeals body somewhat narrowed that favorable ruling in April 2005. The appeals decision held that various state laws argued by Antigua and Barbuda to be contrary to WTO agreements were not sufficiently discussed during the course of the proceedings to be properly assessed by the panel. However, the appeals panel also ruled that the Wire Act and two other federal statutes prohibiting the provision of gambling services from Antigua to the United States violated the WTO’s General Agreement on Trade in Services, or “GATS”. Although the United States convinced the appeals panel that these laws were “necessary” to protect public health and morals, the asserted United States defense on these grounds was ultimately rejected because its laws relating to remote gambling on horse-racing were not applied equally to foreign and domestic online betting companies, and thus the United States could not establish that its laws were non-discriminatory.^[16]

On March 30, 2007 the WTO confirmed the U.S. “had done nothing to abide by an earlier verdict that labeled some U.S. Internet gambling restrictions as illegal.”^[17]

On June 19, 2007, Antigua filed a claim with the WTO for USD $3.4 billion in trade sanctions against the United States, along with a request for authorization to ignore U.S. patent and copyright laws. This followed by a day similar demands for compensation made by the European Union.^[18]

In probability theory, the [tag]Kelly criterion[/tag], or [tag]Kelly formula[/tag], is a formula used to maximize the long-term growth rate of repeated plays of a given gamble that has positive expected value. It was described by [tag]J. L. Kelly, Jr[/tag], in a 1956 issue of the [tag]Bell System Technical Journal^[/tag]. The formula specifies the percentage of the current bankroll to be bet at each iteration of the game. In addition to maximizing the growth rate in the long run, the formula has the added benefit of having zero risk of ruin; the formula will never allow a loss of 100% of the bankroll on any bet. An assumption of the formula is that currency and bets are infinitely divisible, which is not a concern for practical purposes if the bankroll is large enough to support the [tag]gambling system[/tag].

Statement

The most general statement of the Kelly criterion is that long-term growth rate is maximized by finding the fraction f* of the bankroll that maximizes the expectation of the logarithm of the results. For simple bets with two outcomes, one involving losing the entire amount bet, and the other involving winning the bet amount multiplied by the payoff odds, the following formula can be derived from the general statement:

where

• f* is the fraction of the current bankroll to wager;
• b is the odds received on the wager;
• p is the probability of winning;
• q is the probability of losing, which is 1 − p.

As an example, if a gamble has a 40% chance of winning (p = 0.40, q = 0.60), but the gambler receives 2-to-1 odds on a winning bet (b = 2), then the gambler should bet 10% of the bankroll at each opportunity (f* = 0.10), in order to maximize the long-run growth rate of the bankroll.

If the gambler has zero or negative edge, i.e. if b ≤ q/p, then the gambler should bet nothing.

For even-money bets (i.e. when b = 1), the formula can be simplified to:

Since q = 1-p, this simplifies further to

The Kelly criterion was originally developed by AT&T Bell Laboratories physicist John Larry Kelly, Jr, based on the work of his colleague Claude Shannon, which applied to noise issues arising over long distance telephone lines. Kelly showed how Shannon’s information theory could be applied to the problem of a gambler who has inside information about a horse race, trying to determine the optimum bet size. The gambler’s inside information need not be perfect (noise-free) in order for him to exploit his edge. Kelly’s formula was later applied by another colleague of Shannon’s, Edward O. Thorp, both in blackjack and in the stock market.^[2]

[edit] Disadvantages

Using the Kelly system in practice does have drawbacks. While it guarantees that you will never lose all your bankroll, it does not guarantee that you will not lose money. When a series of serial bets are made the chance of dropping to 1/n of your bankroll is 1/n. Thus you have a 50% chance of at some point losing 50% of your bankroll, a 10% chance of dropping to 10%, and so on.

The optimum bet for the greatest growth of bankroll is making the full bet suggested by the Kelly criterion, but this produces a volatile result. There is a 1/3 chance of halving the bankroll before it is doubled. A popular alternative is to bet only half the amount suggested which gives three-quarters of the investment return with much less volatility. Where money would accumulate at 10% compound interest with full bets, it still accumulates at 7.5% for half-bets.

Over-betting beyond that suggested by Kelly is counter-productive as the long run return will fall, dropping to zero (with the loss of all the bankroll) when the Kelly bet is doubled. Using half-Kelly bets also safeguards against being ruined by unknowingly overbetting, as it can be easy to over-estimate the true odds by a factor of two.

The above applies to a sequence of serial bets. It is better to diversify, as the gambler who for example bets on every horse at a race using the Kelly criterion makes on average a better long-run return than the gambler who only bets on one horse per race, and similarly for the diversified stock market investor.

In a 1738 article, [tag]Daniel Bernoulli[/tag] suggested that when you have a choice of bets or investments you should choose that with the highest [tag]geometric mean[/tag] of outcomes. This is mathematically equivalent to the Kelly criterion, although the Bernoulli article was not translated into English until 1954 (in an economics journal) and it is unlikely that Kelly was aware of it. For the investor who does not re-invest the profits, but only invests a set amount each time, this rule does not apply; instead the investor should choose the investment with the greatest arithmetic mean.

- The [tag]Kelly Gambling System[/tag]

Originally, [tag]martingale[/tag] eventually flip heads, the Martingale [tag]betting strategy[/tag] was seen as a referred to a class of betting strategies popular in 18th century France. The simplest of these strategies was designed for a game in which the gambler wins his stake if a coin comes up heads and loses it if the coin comes up tails. The strategy had the gambler double his bet after every loss, so that the first win would recover all previous losses plus win a profit equal to the original stake. Since a gambler with infinite wealth will with probability 1sure thing by those who practised it. Unfortunately, none of these practitioners in fact possessed infinite wealth, and the [tag]exponential[/tag] growth of the bets would eventually bankrupt those foolish enough to use the Martingale. Moreover, it has become more impossible to implement in modern casinos, due to the betting limit at the tables. Because the betting limits reduce the casino’s short term variance, the martingale system itself does not pose a threat to the casino, and many will encourage its use, knowing that they have the house advantage no matter how much is wagered nor when.

Example Implementation

Suppose that someone applies the martingale betting system at an American roulette table, with 0 and 00 values; on average, a bet on either red or black will win 18 times out of 38. If the player’s initial bankroll is $150 and the betting unit is $10, he can afford 4 losing bets in a row (of $10, $20, $40, and $80) before he runs out of money. If any of these 4 bets wins he wins $10 and wins back any past losses. The chance of losing 4 bets in a row (and therefore losing the complete $150) is (20/38)⁴ = 7.67%. The remaining 92.3% of the time, the player will win $10.

We will call this one round (playing until you have lost 4 times or until you win, whichever comes first). If you play repeated rounds with this strategy then your average earnings will be (0.923·$10) − (0.0767·$150) = −$2.275 per round. Therefore, you lose an average of $2.275 each round.

Effect of Variance

As with any betting system, it is possible to have variance from the expected negative return by temporarily avoiding the inevitable losing streak. Furthermore, a straight string of losses is the only sequence of outcomes that results in a loss of money, so even when a player has lost the majority of their bets, they can still be ahead over-all, since they always win 1 unit when a bet wins, regardless of how many previous losses.

Detailed analysis of one round

Let q be the probability of losing (e.g. for roulette it is 20/38). Let y be the amount of the commencing bet (e.g. $10 in the example above). Let x be the finite number of bets you can afford to lose.

The probability that you lose all x bets is q^x. When you lose all your bets, the amount of money you lose is

The probability that you do not lose all x bets is 1 − q^x. If you do not lose all x bets, you win y amount of money. So the expected profit per round is

Whenever q > 1 / 2, the expression 1 − (2q)^x < 0 for all x > 0. That means for any game where it is more likely to lose than to win (e.g. all chance gambling games), you are expected to lose money on average. Furthermore, the more times you are able to afford to bet, the more you will lose.

Simpler analysis

Since expectation is linear, the expected value of a series of bets is just the sum of the expected value of each bet. Since in such games of chance the bets are independent, the expectation of all bets are going to be the same, regardless of whether you had previously won or lost. In most casino games, the expected value of any individual bet is going to be negative, so the sum of lots of negative numbers is also always going to be negative.

tag]Betting System[/tag]: The [tag]martingale system[/tag]

I know you need to rationalize the effort, but could be considered [tag]spam[/tag]. Interesting product though [tag]culinaryprep[/tag].

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