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Backgammon betting rules global sports betting market

Backgammon betting rules

While the dice may determine the outcome of a single game, the better player will accumulate the better record over a series of many games. With each roll of the dice, players must choose from numerous options for moving their checkers and anticipate possible counter-moves by the opponent. The optional use of a doubling cube allows players to raise the stakes during the game. Like chess , backgammon has been studied with great interest by computer scientists.

Owing to this research, backgammon software such as TD-Gammon has been developed that is capable of beating world-class human players. Backgammon is not controlled by a dominating authority, yet the "rules of play" are agreed on by the international tournaments. Backgammon playing pieces may be termed checkers, draughts, stones, men, counters, pawns, discs, pips, chips, or nips. The objective is for players to remove bear off all their checkers from the board before their opponent can do the same.

As the playing time for each individual game is short, it is often played in matches where victory is awarded to the first player to reach a certain number of points. Each side of the board has a track of 12 long triangles, called points. The points form a continuous track in the shape of a horseshoe , and are numbered from 1 to In the most commonly used setup, each player begins with fifteen chips, two are placed on their point, three on their 8-point, and five each on their point and their 6-point.

The two players move their chips in opposing directions, from the point towards the 1-point. Points 1 through 6 are called the home board or inner board, and points 7 through 12 are called the outer board. The 7-point is referred to as the bar point, and the point as the midpoint.

Usually the 5-point for each player is called the "golden point". To start the game, each player rolls one die, and the player with the higher number moves first using the numbers shown on both dice. Both dice must land completely flat on the right-hand side of the gameboard.

The players then take alternate turns, rolling two dice at the beginning of each turn. After rolling the dice, players must, if possible, move their checkers according to the number shown on each die. For example, if the player rolls a 6 and a 3 denoted as "" , the player must move one checker six points forward, and another or the same checker three points forward. The same checker may be moved twice, as long as the two moves can be made separately and legally: six and then three, or three and then six.

If a player rolls two of the same number, called doubles, that player must play each die twice. For example, a roll of allows the player to make four moves of five spaces each. On any roll, a player must move according to the numbers on both dice if it is at all possible to do so. If one or both numbers do not allow a legal move, the player forfeits that portion of the roll and the turn ends.

If moves can be made according to either one die or the other, but not both, the higher number must be used. If one die is unable to be moved, but such a move is made possible by the moving of the other die, that move is compulsory. In the course of a move, a checker may land on any point that is unoccupied or is occupied by one or more of the player's own checkers. It may also land on a point occupied by exactly one opposing checker, or "blot".

In this case, the blot has been "hit" and is placed in the middle of the board on the bar that divides the two sides of the playing surface. A checker may never land on a point occupied by two or more opposing checkers; thus, no point is ever occupied by checkers from both players simultaneously. Checkers placed on the bar must re-enter the game through the opponent's home board before any other move can be made.

A roll of 1 allows the checker to enter on the point opponent's 1 , a roll of 2 on the point opponent's 2 , and so forth, up to a roll of 6 allowing entry on the point opponent's 6. Checkers may not enter on a point occupied by two or more opposing checkers.

Checkers can enter on unoccupied points, or on points occupied by a single opposing checker; in the latter case, the single checker is hit and placed on the bar. More than one checker can be on the bar at a time. A player may not move any other checkers until all checkers on the bar belonging to that player have re-entered the board.

If the opponent's home board is completely "closed" i. When all of a player's checkers are in that player's home board, that player may start removing them; this is called "bearing off". A roll of 1 may be used to bear off a checker from the 1-point, a 2 from the 2-point, and so on.

If all of a player's checkers are on points lower than the number showing on a particular die, the player must use that die to bear off one checker from the highest occupied point. When bearing off, a player may also move a lower die roll before the higher even if that means the full value of the higher die is not fully utilized. For example, if a player has exactly one checker remaining on the 6-point, and rolls a 6 and a 1, the player may move the 6-point checker one place to the 5-point with the lower die roll of 1, and then bear that checker off the 5-point using the die roll of 6; this is sometimes useful tactically.

As before, if there is a way to use all moves showing on the dice by moving checkers within the home board or by bearing them off, the player must do so. If a player's checker is hit while in the process of bearing off, that player may not bear off any others until it has been re-entered into the game and moved into the player's home board, according to the normal movement rules.

The first player to bear off all fifteen of their own checkers wins the game. If the opponent has not yet borne off any checkers when the game ends, the winner scores a gammon , which counts for double stakes.

If the opponent has not yet borne off any checkers and has some on the bar or in the winner's home board, the winner scores a backgammon , which counts for triple stakes. To speed up match play and to provide an added dimension for strategy, a doubling cube is usually used.

The doubling cube is not a die to be rolled, but rather a marker, with the numbers 2, 4, 8, 16, 32, and 64 inscribed on its sides to denote the current stake. At the start of each game, the doubling cube is placed on the midpoint of the bar with the number 64 showing; the cube is then said to be "centered, on 1". When the cube is centered, either player may start their turn by proposing that the game be played for twice the current stakes.

Their opponent must either accept "take" the doubled stakes or resign "drop" the game immediately. Whenever a player accepts doubled stakes, the cube is placed on their side of the board with the corresponding power of two facing upward, to indicate that the right to re-double belongs exclusively to that player. For instance, if the cube showed the number 2 and a player wanted to redouble the stakes to put it at 4, the opponent choosing to drop the redouble would lose two, or twice the original stake.

There is no limit on the number of redoubles. Although 64 is the highest number depicted on the doubling cube, the stakes may rise to , , and so on. In money games, a player is often permitted to "beaver" when offered the cube, doubling the value of the game again, while retaining possession of the cube. A variant of the doubling cube "beaver" is the "raccoon". Players who doubled their opponent, seeing the opponent beaver the cube, may in turn then double the stakes once again "raccoon" as part of that cube phase before any dice are rolled.

The opponent retains the doubling cube. An example of a "raccoon" is the following: White doubles Black to 2 points, Black accepts then beavers the cube to 4 points; White, confident of a win, raccoons the cube to 8 points, while Black retains the cube.

Such a move adds greatly to the risk of having to face the doubling cube coming back at 8 times its original value when first doubling the opponent offered at 2 points, counter offered at 16 points should the luck of the dice change. Some players may opt to invoke the "Murphy rule" or the "automatic double rule". If both opponents roll the same opening number, the doubling cube is incremented on each occasion yet remains in the middle of the board, available to either player.

The Murphy rule may be invoked with a maximum number of automatic doubles allowed and that limit is agreed to prior to a game or match commencing. When a player decides to double the opponent, the value is then a double of whatever face value is shown e. The Murphy rule is not an official rule in backgammon and is rarely, if ever, seen in use at officially sanctioned tournaments. The "Jacoby rule", named after Oswald Jacoby , allows gammons and backgammons to count for their respective double and triple values only if the cube has already been offered and accepted.

This encourages a player with a large lead to double, possibly ending the game, rather than to play it to conclusion hoping for a gammon or backgammon. The Jacoby rule is widely used in money play but is not used in match play. The "Crawford rule", named after John R. Crawford , is designed to make match play more equitable for the player in the lead. If a player is one point away from winning a match, that player's opponent will always want to double as early as possible in order to catch up.

Whether the game is worth one point or two, the trailing player must win to continue the match. To balance the situation, the Crawford rule requires that when a player first reaches a score one point short of winning, neither player may use the doubling cube for the following game, called the "Crawford game". After the Crawford game, normal use of the doubling cube resumes.

The Crawford rule is routinely used in tournament match play. If the Crawford rule is in effect, then another option is the "Holland rule", named after Tim Holland , which stipulates that after the Crawford game, a player cannot double until after at least two rolls have been played by each side. It was common in tournament play in the s, but is now rarely used. There are many variants of standard backgammon rules. Some are played primarily throughout one geographic region, and others add new tactical elements to the game.

Variants commonly alter the starting position, restrict certain moves, or assign special value to certain dice rolls, but in some geographic regions even the rules and directions of the checkers' movement change, rendering the game fundamentally different.

Acey-deucey is a variant of backgammon in which players start with no checkers on the board, and must bear them on at the beginning of the game. The roll of is given special consideration, allowing the player, after moving the 1 and the 2, to select any desired doubles move. A player also receives an extra turn after a roll of or of doubles. Hypergammon is a variant of backgammon in which players have only three checkers on the board, starting with one each on the 24, 23 and 22 points.

The game has been strongly solved , meaning that exact equities are available for all 32 million possible positions. Nard is a traditional variant from Persia in which basic rules are almost the same except that even a single piece is "safe". All 15 pieces start on the 24th wedge. Nackgammon is a variant of backgammon invented by Nick "Nack" Ballard [18] in which players start with one less checker on the 6-point and midpoint and two checkers on the point.

Russian backgammon is a variant described in as: " In this variant, doubles are more powerful: four moves are played as in standard backgammon, followed by four moves according to the difference of the dice value from 7, and then the player has another turn with the caveat that the turn ends if any portion of it cannot be completed. Gul bara and Tapa are also variants of the game popular in southeastern Europe and Turkey. The play will iterate among Backgammon, Gul Bara, and Tapa until one of the players reaches a score of 7 or 5.

Coan ki is an ancient Chinese board game that is very similar. Plakoto , Fevga and Portes are three versions of backgammon played in Greece. Together, the three are referred to as Tavli. Misere backgammon to lose is a variant of backgammon in which the objective is to lose the game.

Tabla is a Bulgarian variant of Backgammon, played without the doubling cube. Other minor variants to the standard game are common among casual players in certain regions. For instance, only allowing a maximum of five checkers on any point Britain [25] or disallowing "hit-and-run" in the home board Middle East.

Backgammon has an established opening theory , although it is less detailed than that of chess. The tree of positions expands rapidly because of the number of possible dice rolls and the moves available on each turn. Recent computer analysis has offered more insight on opening plays, but the midgame is reached quickly.

After the opening, backgammon players frequently rely on some established general strategies, combining and switching among them to adapt to the changing conditions of a game. A blot has the highest probability of being hit when it is 6 points away from an opponent's checker see picture.

Strategies can derive from that. The most direct one is simply to avoid being hit, trapped, or held in a stand-off. A "running game" describes a strategy of moving as quickly as possible around the board, and is most successful when a player is already ahead in the race.

As the game progresses, this player may gain an advantage by hitting an opponent's blot from the anchor, or by rolling large doubles that allow the checkers to escape into a running game. The "priming game" involves building a wall of checkers, called a prime, covering a number of consecutive points.

This obstructs opposing checkers that are behind the prime. A checker trapped behind a six-point prime cannot escape until the prime is broken. Because the opponent has difficulty re-entering from the bar or escaping, a player can quickly gain a running advantage and win the game, often with a gammon. A "backgame" is a strategy that involves holding two or more anchors in an opponent's home board while being substantially behind in the race.

The backgame is generally used only to salvage a game wherein a player is already significantly behind. Using a backgame as an initial strategy is usually unsuccessful. For example, players may position all of their blots in such a way that the opponent must roll a 2 in order to hit any of them, reducing the probability of being hit more than once.

Many positions require a measurement of a player's standing in the race, for example, in making a doubling cube decision, or in determining whether to run home and begin bearing off. The minimum total of pips needed to move a player's checkers around and off the board is called the "pip count".

The difference between the two players' pip counts is frequently used as a measure of the leader's racing advantage. Players often use mental calculation techniques to determine pip counts in live play. Backgammon is played in two principal variations, "money" and "match" play.

Money play means that every point counts evenly and every game stands alone, whether money is actually being wagered or not. The format has a significant effect on strategy. In a match, the objective is not to win the maximum possible number of points, but rather to simply reach the score needed to win the match. For example, a player leading a 9-point match by a score of 7—5 would be very reluctant to turn the doubling cube, as their opponent could take and make a costless redouble to 4, placing the entire outcome of the match on the current game.

Conversely, the trailing player would double very aggressively, particularly if they have chances to win a gammon in the current game. In money play, the theoretically correct checker play and cube action would never vary based on the score. In , Emmet Keeler and Joel Spencer considered the question of when to double or accept a double using an idealized version of backgammon. In their idealized version, the probability of winning varies randomly over time by Brownian motion , and there are no gammons or backgammons.

To reduce the possibility of cheating, most good quality backgammon sets use precision dice and a dice cup. Online cheating has therefore become extremely difficult. Early Muslim scholars forbade backgammon.

In State of Oregon v. Barr , a court case pivotal to the continued widespread organised playing of backgammon in the US, the State argued that backgammon is a game of chance and that it was therefore subject to Oregon's stringent gambling laws. Paul Magriel was a key witness for the defence, contradicting Roger Nelson, the expert prosecution witness, by saying, "Game theory, however, really applies to games with imperfect knowledge, where something is concealed, such as poker.

Backgammon is not such a game. Everything is in front of you. The person who uses that information in the most effective manner will win. Walker concluded that backgammon is a game of skill, not a game of chance, and found the defendant, backgammon tournament director Ted Barr, not guilty of promoting gambling.

Enthusiasts have formed clubs for social play of backgammon. A backgammon chouette permits three or more players to participate in a single game, often for money. One player competes against a team of all the other participants, and positions rotate after each game. Chouette play often permits the use of multiple doubling cubes. Backgammon clubs may also organize tournaments. Large club tournaments sometimes draw competitors from other regions, with final matches viewed by hundreds of spectators.

Winners at major tournaments may receive prizes of tens of thousands of dollars. Starting in January , tournament directors began awarding GammonPoints, [43] a free points registry for tournament directors and players, with GammonPoint awards based on the number of players and strength of field. The first world championship competition in backgammon was held in Las Vegas , Nevada in Tim Holland was declared the winner that year and at the tournament the following year.

For unknown reasons, there was no championship in , but in , Tim Holland again won the title. In , Lewis Deyong, who had promoted the Bahamas World Championship for the prior three years, suggested that the two events be combined. By the 21st century, the largest international tournaments had established the basis of a tour for top professional players. Major tournaments are held yearly worldwide. PartyGaming sponsored the first World Series of Backgammon in from Cannes and later the "Backgammon Million" tournament held in the Bahamas in January with a prize pool of one million dollars, the largest for any tournament to date.

The event was recorded for television in Europe and aired on Eurosport. In , the WBA collaborated with the online backgammon provider Play65 for the season of the European Backgammon Tour and with "Betfair" in When backgammon is played for money , the most common arrangement is to assign a monetary value to each point, and to play to a certain score, or until either player chooses to stop.

The stakes are raised by gammons, backgammons, and use of the doubling cube. Backgammon is sometimes available in casinos. Before the commercialization of artificial neural network programs, proposition bets on specific positions were very common among backgammon players and gamblers. The game is included in Clubhouse Games: 51 Worldwide Classics for the Nintendo Switch , a collection of tabletop games.

Backgammon software has been developed not only to play and analyze games, but also to facilitate play between humans over the internet. Dice rolls are provided by random or pseudorandom number generators. Real-time online play began with the First Internet Backgammon Server in July , [51] [52] but there are now a range of options, [53] many of which are commercial. Backgammon has been studied considerably by computer scientists. Neural networks and other approaches have offered significant advances to software for gameplay and analysis.

However, if a player still has any of their checkers on the bar or in their opponents home-board they are said to have been "backgammoned" and lose three times the value of the doubling cube. The Doubling Cube A doubling cube is a die marked with the numbers 2, 4, 8, 16, 32, and Gammons and Backgammons If a player hasn't borne-off any checkers before their opponent has borne-off all of theirs, then the player is said to have been "gammoned" and loses twice the value of the doubling cube.

If two identical values are thrown with the players initial throw when deciding who goes first, then the stakes are automatically doubled. The doubling cube is turned so 2 is face-up and kept halfway between the two players. Automatic doubling like this is usually limited to one time per game. A player who has doubled using the doubling cube may immediately double again as long as they haven't picked up their dice.

Their opponent must agree to the doubling, as with a single double, before it takes effect. This is known as a "Beaver". A gammon or backgammon isn't counted as double or triple when neither player has offered to double with the doubling cube. This rule is meant to speed up play, preventing players from not doubling and trying for a gammon. Known as the "Jacoby" rule because it was Oswald Jacoby, a Backgammon author, who invented and promoted the rule.

Commonly used in money games but never in match play. All rights reserved. Register and become a member.

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BLEACHER REPORT LAKERS CELTICS BETTING

Woolsey examines every possible score for the five point match and looks at cube and checker play strategy for each score. When you play a series of games to a specified number of points, this is called "match play. Tournament tactics differ in many ways from money games and chouette. In tournaments, the only objective is to defeat your adversary, and the difference in your scores is immaterial. I have stopped drilling match equity and take points. It just doesn't work for any but highly skilled players.

Instead, I teach the concepts to beginner and intermediate players. Some strategies to employ toward the end of a close match. How does the score affect your checker and cube play? How important is a gammon for you or for your opponent?

What can you do to maximize your advantage or minimize your opponent's advantage? Phil leads the reader through the process of a making match-based cube decision. How the price of gammons affect cube decisions in match play. All of a sudden your opponent does something extremely irritating and rude: He doubles you! What do you do now? This article is for people who have enjoyed backgammon on a social level, or playing for small stakes with friends, but are ready to give tournament backgammon, or match play a try.

There are four match scores that are commonly recognized benchmarks from which checker play strategies for all other scores can be roughly interpolated or extrapolated: Money, double match point DMP , gammon save GS , and gammon go GG. A quick introduction to doubling decisions in match play. Hollands presents a match equity table and shows how to use it to estimate your take point in various match situations.

In tournament play, where matches are played to a specified number of points, proper doubling strategy is different than when games are played for money. This article presents a number of the considerations a player must make when handling the cube in match play. One of the strangest phenomena of match-play backgammon is the idea that at certain scores you can be "not good enough to double" and "too good to double" at the same time.

How can this be? Staying Ahead By Lasse H. Madsen How do you protect a lead in a long match; e. The focus of this article is on taking doubles. When do you accept an initial double? When do you accept a redouble? Charts show the patterns of how the match score influences take points, and the article develops some general guidelines along with some examples. Crawford and Beyond By Kit Woolsey In match play, the value of a gammon varies according to the score of the match.

This article looks at situations where the correct checker play depends on the score of the match. How long you can hold off doubling with an odd number of points to go in post-Crawford games. In a three-point match, life is a little more complex. Just as in the two-point match, the cube decisions at every score in the three-pointer are different to money play. Here are some examples of how to adjust your normal cubing strategy at this match score. In matches, optimal play is often affected by the score in the match.

The leader becomes more defensive. He wants to reduce the likelihood that the cube will reach a high level, and he wants to avoid gammonish positions. The trailer, on the other hand, is willing to double a little earlier than normal, and perhaps take cubes more aggressively. Only a 4-Cube By Kit Woolsey You have to be extra cautious when you have a big lead in the match and the cube starts flying. Before sending it over, see how things will look at the level your opponent will be potentially turning it back to.

If you do this, you can avoid giving away a match when you are a big favorite to win. This article discusses the concept of a frozen cube , situations where because of the match score one player or both will not want to turn the cube. The concept comes up more often than you might imagine. It is important to look ahead and see what the future ramifications of doubling or not doubling are. Sometimes the conclusions can be very unintuitive.

Memoriable Weekend By Kit Woolsey Some match-play cube decisions from the Chicago Memorial Day Tournament, How to use a match equity table to make correct doubling decisions in match play. The fourth in a series of articles for beginning and intermediate players. Articles about doubling strategy in match play. In match play, the score is the all-important factor, so let's start by looking at the shortest match length possible, the two-point match.

Playing a two-point match is a fun and popular game, both on the net and as a side event at tournaments. The interesting thing about playing at this score is that both your cube strategy and checker strategy are different from playing at any other score. Anthony Patz shows that when both players are two points away from winning the match, it can pay to double even when you are the underdog in the current game. How your doubling varies depending on the score of the match.

This is the fifth in a series of articles for beginning and intermediate players. Articles about the correct doubling strategy when both players both have two points to go in the match. Unusual cube actions when leading a match 2-away 4-away. Cube Decisions at 2-away 4-away By Kent Goulding For the most part, cube strategy is the same in match play as in money play. However, as a long match nears a conclusion, or in a short match 5 points or less , there are numerous situations where the score compels a total reevaluation of cube decisions.

Here is an extreme case that demonstrates the differences between match and money cube strategy. Getting Gammoned? Turn the Cube By Kent Goulding As tricky as cube decisions can be in money play, in match play they take on a whole new dimension. Someone who plays the cube brilliantly in a money game, but hasn't learned the nuances of match play, is at a tremendous disadvantage. When leading in the match, be careful about giving the opponent a powerful recube. Black was trailing 4-away 2-away when he turned the cube to two.

From White's swift acceptance and facial expression, it was obvious that he viewed the double as ill-advised and premature. After all, a two-point game was all that White needed to win the match. The Cube: Tournament vs. Money Play By Barclay Cooke Backgammon experts are cropping up everywhere these days. But while they become more and more proficient in moving their men, many still don't take time to study the vastly different tactics used in tournaments as opposed to money games, especially in the use of the doubler.

It would seem that once the Crawford game in a match is reached or passed, cube decisions are trivial and checker play is considerably simplified. This is not necessarily the case. An understanding of the intricacies of the Crawford game can give the knowledgeable player that little extra edge which might make the difference.

I was kibitizing a point match at the European championships, along with Al Lorenz, one of Europe's best players. You're playing a point match, and you've got a very comfortable lead, You were doubled to two early on, and you took. Now you've broken contact, and you've got a big lead in the race, 26 pips. You'd like to redouble, but you don't know exactly when it's right to do so.

Match play injects several new variables into cube handling. But the match score and the cube size assume paramount importance. I hope the strategy I recommend appeals to your reason; it is rooted in calculations based on certain assumptions. Doubling strategy in match play differs somewhat from doubling strategy in money play. Most cube decisions are the same as for money, but a small number are different. Typically these include doubles beyond the two level, and doubles when one or both players are within four points of victory.

Across the Scores By Douglas Zare When we play backgammon matches, we face a series of decisions at one match score, and then move on to the next score. It is an enlightening exercise to do the reverse: Take one decision, and consider it at several match scores.

Dangerous Redoubles By Douglas Zare Backgammon match play is tricky since the points do not have the same value. It gets particularly interesting when the doubling cube is on 2 or higher, and those decisions are often very far from decisions in a money session. Match Equities. A match equity table tells you your chance of winning the match at each different score.

It is a useful tool in making doubling decisions. Woolsey's table is derived from a combination of empirical data and assumptions about gammon probability and the value of doubling potential. While it may not be totally accurate, the figures should be correct to within a percent or two. The table has proven to be of practical value, and is used by most experts today.

Mec26 is based on a small program published in by Claes Thornberg. Snowie Equities By Kit Woolsey This article describes how a match equity table can be derived mathematically if you assume a constant gammon rate and efficient cube usage. Lots of diagrams show the process step by step. Match Equities: Simplification vs.

Accuracy By Nigel Merrigan Nigel Merrigan compares three formulas for estimating match equity: Janowski's formula, Turner's formula, and his own Merrigan formula. He finds that his own formula does the best overall while still being reasonably easy to compute. Using these charts, you can visualize important characteristics of the possible scores in a match. Various match equity tables and formulas for estimating match equities. Committing a match equity table to memory By Fabrice Liardet Shortcuts are necessary if you want to memorize a match equity table.

Here are two separate methods, a very simple one for the Crawford equities, and a more difficult one for all the other equities in the table. Score cards By Fabrice Liardet Table of take points and gammon values at various match scores and gammon rates. In order to assess cube decisions late in the match, it is important to know what your match equity is at the potential scores.

The following table is the consensus of independent analyses by Bill Robertie, Danny Kleinman, and myself. A match equity table gives you the percentage chance of winning a match at any particular score. The problem is, how do you remember the table? Luckily help is at hand. I shall give two methods by which the match equity for any score in any length match can be calculated.

A computer model developed by the author generates this match-equity table. The primary model parameter is the probability of a gammon in a cubeless game, which has been calibrated from empirical results. If there is a heart to this book, it is Tables 13 to Table 13 is our benchmark table. Use it for any even match up to 25 points in length. In , I derived formulae for predicting match equities using the then current match equity tables.

I have since been able to derive suitable modifications to my formulae enabling all scores in a point match including Crawford and Post-Crawford to be predicted within 0. The Rockwell-Kazaross match equity table was a major achievement, obtaining all the match equities for a point match by direct rollout.

The next few pages contain charts indicating equities and cube actions in a match to 9 points between opponents of equal skill. I spent weeks calculating equities at various scores in a 9-point match and deriving cube strategies from these. I would have been spared all this labor had I known about Norman Zadeh's paper, "On Doubling in Tournament Backgammon," which had been submitted for publication one year earlier.

Some backgammon players with exceptional memories will learn a complete chart of take points for tournament doubles by heart. But most of us have only limited memories. Can we find some other method of determining how good our chances need be to justify taking the cube at a particular score? Dean Muench, one of the Chicago area's strongest backgammon players, has long sought shortcuts for estimating match equities.

Some tournament players have mastered match charts by rote, but in the middle of a match it is better to compute an estimate from a formula than to rely on a memorized chart. Here is Dean's formula. When you switch from regular backgammon to tournament play, you must make adjustments.

You must adapt your cube handling and checker play to certain special conditions occurring during matches. Here we consider some of these we lump together under the rubric of things that are "free" in backgammon matches. Inside the Database By Kit Woolsey I analyzed the data from Hal Heinrich's database of over matches to determine at each score the likely outcome of the next game.

From these distributions, I wrote a computer program to generate a new match equity table. The results conform both with Heinrich's database and my own intuition much better than the previous tables. Thanks to Hal Heinrich, we finally have a large database from which we can determine empirically vital information such as likelihood of gammons and the value of cube leverage to the trailer in the match. Using this data, I have constructed a new match equity table.

Joseph Heled, the developer of the Gnu Backgammon neural nets doesn't use the default match equity table shipped with Gnu BG, and instead uses Mec No one knew what this was, so he explained that it was based on a small program published in by Claes Thornberg. Rockwell-Kazaross was developed by rolling out every score in a point match almost 39, times using GNU 2-ply Supremo.

I then carefully extrapolated out to 25 points. In match play, particularly when making doubling decisions, it is useful to know one's match equity. This is the probability that one will win the match from a given score, assuming perfect play by both players. A chart of 13 different match equity tables devised over the years and 7 formulas for estimating the match equity at different scores. Users can select different tables from the chart and see how one match equity table compares to another.

Small rounding errors in match equity tables may cause rather big errors when calculating takepoints. This means you have to use match equity tables with sufficient accuracy to get satisfying results. A description and evaluation of several popular methods of making cube decisions in noncontact positions. This article introduces the "Keith" count, an accurate formula for making race cube decisions. Trice introduces the term "effective pip count" and describes some clever methods of calculating it in different types of positions.

In positions where it applies, the effective pip count is a very accurate method of making cube decisions in noncontact positions. There are several methods for adjusting the pip count to penalize wasteful formations, and the effective pip count epc is the best that I have encountered.

It not only allows me to assess most races to within a pip, but it provides a framework for learning. Introduction the the effective pip count EPC. Thorp Edward O. Thorp examines the proper checker play and cube actions when both players have just one or two checkers left to bear off.

Even in these simple games, some very tricky decisions crop up. Thorp provides tables that allow for perfect play, and gives rules of thumb to help players make correct decisions over the board. Often a game will come down to one player having two checkers left versus an opponent with one or two checkers left. Since this is common, one can benefit by memorizing a table of these cube actions. This article presents some guidelines to make memorizing the table easier.

Many of our games will end in a race, with no hitting possible and gammons out of the question, so it is important to know how to handle the cube, or we will give away large amounts of our precious equity. Introduction to equity and basic concepts of doubling, Woolsey's Rule of doubling, the Jacoby Paradox, and cube racing formulas. Knowing both players' pipple count gives a good idea of your racing chances.

Unfortunately, the calculations are quite tedious and "almost certainly not worth the effort at the table". Seret develops a method of estimating a pipple count based on: 1 the numbers of men on each of the 6 points home-board points, 2 the shape of the distribution, and 3 which points have no checkers on them.

How to calculate exact game winning chances during bearoff By Joachim Matussek A linear formula for calculating the EPC for bearoff positions up to 8 checkers is introduced. Two correction terms give an improved accuracy for the estimated EPC. The average error of the estimate is 0. Article revised July After contact has been broken and the game is a pure race, it is easier to estimate your winning chances and make accurate doubling decisions.

Here are some articles on handling the cube in races. By Bob Floyd Some rules of thumb for when to double and when to take in a racing bearoff where you and your opponent have the same position. By Kent Goulding A look at a famous bearoff position where both sides have stacks and gaps, trying to decide which side is favored. Proper use of the doubling cube is probably the most important and most difficult part of backgammon.

One reason it is so difficult is that it is normally hard to prove whether a particular doubling decision is correct or not. There is, however, one important part of backgammon where art gives way to science, and doubling decisions can be determined precisely. The purpose of this article is to elaborate doubling cube theory in money games for running positions in which there is little or no wastage. The specific purposes are: to present the optimal approach; to analyze three known approaches proposed so far; and to propose a new approach.

After looking into how adjusted pip counts and decision criteria work in general, we present a more formal framework that allows us to parametrize and optimize adjusted pip counts and the corresponding decision criteria. The outcome is a new method resulting in both less effort and fewer errors for your cube handling in races compared to existing methods.

This article explains three flaws in Axel Reichert's "Improved Cube Handling in Races" and comments on other topics of Reichert's article. Finally, the article gives some suggestions on how to further improve the existing theory on cube handling in races for money games. Backgammon Races By Chris Bray This short monograph summarises the development of formulae for racing situations, the work of other backgammon theoreticians who have led us to where we are today.

In particular I must acknowledge the work of Walter Trice. How far behind can you be in a pure race and still have a take? All criteria in terms of such a percentage deficit must be inaccurate. A blot has the highest probability of being hit when it is 6 points away from an opponent's checker see picture. Strategies can derive from that.

The most direct one is simply to avoid being hit, trapped, or held in a stand-off. A "running game" describes a strategy of moving as quickly as possible around the board, and is most successful when a player is already ahead in the race. As the game progresses, this player may gain an advantage by hitting an opponent's blot from the anchor, or by rolling large doubles that allow the checkers to escape into a running game.

The "priming game" involves building a wall of checkers, called a prime, covering a number of consecutive points. This obstructs opposing checkers that are behind the prime. A checker trapped behind a six-point prime cannot escape until the prime is broken. Because the opponent has difficulty re-entering from the bar or escaping, a player can quickly gain a running advantage and win the game, often with a gammon. A "backgame" is a strategy that involves holding two or more anchors in an opponent's home board while being substantially behind in the race.

The backgame is generally used only to salvage a game wherein a player is already significantly behind. Using a backgame as an initial strategy is usually unsuccessful. For example, players may position all of their blots in such a way that the opponent must roll a 2 in order to hit any of them, reducing the probability of being hit more than once.

Many positions require a measurement of a player's standing in the race, for example, in making a doubling cube decision, or in determining whether to run home and begin bearing off. The minimum total of pips needed to move a player's checkers around and off the board is called the "pip count". The difference between the two players' pip counts is frequently used as a measure of the leader's racing advantage. Players often use mental calculation techniques to determine pip counts in live play.

Backgammon is played in two principal variations, "money" and "match" play. Money play means that every point counts evenly and every game stands alone, whether money is actually being wagered or not. The format has a significant effect on strategy.

In a match, the objective is not to win the maximum possible number of points, but rather to simply reach the score needed to win the match. For example, a player leading a 9-point match by a score of 7—5 would be very reluctant to turn the doubling cube, as their opponent could take and make a costless redouble to 4, placing the entire outcome of the match on the current game. Conversely, the trailing player would double very aggressively, particularly if they have chances to win a gammon in the current game.

In money play, the theoretically correct checker play and cube action would never vary based on the score. In , Emmet Keeler and Joel Spencer considered the question of when to double or accept a double using an idealized version of backgammon. In their idealized version, the probability of winning varies randomly over time by Brownian motion , and there are no gammons or backgammons. To reduce the possibility of cheating, most good quality backgammon sets use precision dice and a dice cup. Online cheating has therefore become extremely difficult.

Early Muslim scholars forbade backgammon. In State of Oregon v. Barr , a court case pivotal to the continued widespread organised playing of backgammon in the US, the State argued that backgammon is a game of chance and that it was therefore subject to Oregon's stringent gambling laws.

Paul Magriel was a key witness for the defence, contradicting Roger Nelson, the expert prosecution witness, by saying, "Game theory, however, really applies to games with imperfect knowledge, where something is concealed, such as poker. Backgammon is not such a game.

Everything is in front of you. The person who uses that information in the most effective manner will win. Walker concluded that backgammon is a game of skill, not a game of chance, and found the defendant, backgammon tournament director Ted Barr, not guilty of promoting gambling. Enthusiasts have formed clubs for social play of backgammon. A backgammon chouette permits three or more players to participate in a single game, often for money. One player competes against a team of all the other participants, and positions rotate after each game.

Chouette play often permits the use of multiple doubling cubes. Backgammon clubs may also organize tournaments. Large club tournaments sometimes draw competitors from other regions, with final matches viewed by hundreds of spectators.

Winners at major tournaments may receive prizes of tens of thousands of dollars. Starting in January , tournament directors began awarding GammonPoints, [43] a free points registry for tournament directors and players, with GammonPoint awards based on the number of players and strength of field. The first world championship competition in backgammon was held in Las Vegas , Nevada in Tim Holland was declared the winner that year and at the tournament the following year.

For unknown reasons, there was no championship in , but in , Tim Holland again won the title. In , Lewis Deyong, who had promoted the Bahamas World Championship for the prior three years, suggested that the two events be combined. By the 21st century, the largest international tournaments had established the basis of a tour for top professional players.

Major tournaments are held yearly worldwide. PartyGaming sponsored the first World Series of Backgammon in from Cannes and later the "Backgammon Million" tournament held in the Bahamas in January with a prize pool of one million dollars, the largest for any tournament to date.

The event was recorded for television in Europe and aired on Eurosport. In , the WBA collaborated with the online backgammon provider Play65 for the season of the European Backgammon Tour and with "Betfair" in When backgammon is played for money , the most common arrangement is to assign a monetary value to each point, and to play to a certain score, or until either player chooses to stop.

The stakes are raised by gammons, backgammons, and use of the doubling cube. Backgammon is sometimes available in casinos. Before the commercialization of artificial neural network programs, proposition bets on specific positions were very common among backgammon players and gamblers. The game is included in Clubhouse Games: 51 Worldwide Classics for the Nintendo Switch , a collection of tabletop games. Backgammon software has been developed not only to play and analyze games, but also to facilitate play between humans over the internet.

Dice rolls are provided by random or pseudorandom number generators. Real-time online play began with the First Internet Backgammon Server in July , [51] [52] but there are now a range of options, [53] many of which are commercial. Backgammon has been studied considerably by computer scientists. Neural networks and other approaches have offered significant advances to software for gameplay and analysis.

The first strong computer opponent was BKG 9. Early versions of BKG played badly even against poor players, but Berliner noticed that its critical mistakes were always at transitional phases in the game. He applied principles of fuzzy logic to improve its play between phases, and by July , BKG 9. It won the match 7—1, becoming the first computer program to defeat a world champion in any board game.

Berliner stated that the victory was largely a matter of luck, as the computer received more favorable dice rolls. In the late s, backgammon programmers found more success with an approach based on artificial neural networks. Its neural network was trained using temporal difference learning applied to data generated from self-play. Tesauro proposed using rollout analysis to compare the performance of computer algorithms against human players.

The rollout score of the human or the computer is the difference of the average game results by following the selected move versus following the best move, then averaged for the entire set of taken moves. The strength of these programs lies in their neural networks' weights tables, which are the result of months of training. Without them, these programs play no better than a human novice.

For the bearoff phase, backgammon software usually relies on a database containing precomputed equities for all possible bearoff positions. Computer-versus-computer competitions are also held at Computer Olympiad events. The history of backgammon can be traced back nearly 5, years to its origins in Mesopotamia modern-day Iraq , [2] [3] [4] [5] the world's oldest set of dice relatable to the game having been discovered in the region.

It used tetrahedral dice. Various other board games spanning from the 10th to 7th centuries BCE have been found throughout modern day Iraq, Syria, Egypt and western Iran. Today the game in various forms continues to be commonly played in Iraq, Lebanon, Egypt, Syria, Jordan throughout the Arab world. In the modern Arab Levant and Iraq, the game is commonly called tawle , which means table. This may represent a shared name origin with the Roman or Byzantine variant of the game.

It is also commonly referred to by shesh besh shesh meaining six in Hebrew , Aramaic and Northwest Semitic , and besh meaning five in Turkish , amongst Arabs as well as by some Kurdish, Persian and Turkish speakers. Shesh Besh is commonly used to refer to when a player scores a 5 and 6 at the same time on dice.

An older game resembling backgammon may have also been played in the easternmost part of the prehistoric Iranian plateau , far from Mesopotamia. The rules of this game, like others found in Egypt, have yet to be deciphered. It is however made from ebony, a material more likely to be found in the Indian subcontinent which indicates such board games may be more widespread than once thought.

In the 11th century Shahnameh , the Persian poet Ferdowsi credits Burzoe with the invention of the tables game nard in the 6th century. He describes an encounter between Burzoe and a Raja visiting from India. The Raja introduces the game of chess , and Burzoe demonstrates nard , played with dice made from ivory and teak.

Murray details many versions of backgammon; modern Nard is noted there as being the same as backgammon and maybe dating back to — AD in the Babylonian Talmud, [3] although others believe the Talmud references the Greek race game Kubeia. Irvine, on the first written mention of earlier variants of backgammon—writes:. The use of dice for the game is another indication of its Indic origin since dice and gambling were a favorite pastime in ancient India.

According to the historical legend, the Indian king Dewisarm sends his minister Taxritos to Persia with the game of chess , and a letter challenging Sasanian King Khosrow I to solve the riddle or rationale for the game. Khosrow asks for three days to decipher the game, but initially, no-one in the court is able to make any progress.

On the third day, Khosrow's minister, Wuzurgmihr, successfully rises and explains the logic of the game. As a reciprocal challenge, Wuzurgmihr constructs the game of backgammon and delivers it to the Indian king who is unable to decipher the game.

There are two games of nardi commonly played:. Short nardi : Set-up and rules are the same as backgammon. Long nardi : A game that starts with all fifteen checkers placed in one line on the point and on the point. The two players move their checkers in opposing directions, from the point towards the 1-point, or home board.

In long nardi , one checker by itself can block a point. There is no hitting in long nardi. The objective of the game is bearing all checkers off the board, and there is no doubling cube. Like today, each player had 15 checkers and used cubical dice with sides numbered one to six. The only differences from modern backgammon were the use of an extra die three rather than two and the starting of all pieces off the board with them entering in the same way that pieces on the bar enter in modern backgammon.

Zeno, who was white, had a stack of seven checkers, three stacks of two checkers and two "blots", checkers that stand alone on a point and are therefore in danger of being put outside the board by an incoming opponent checker. Zeno threw the three dice with which the game was played and obtained 2, 5 and 6. As in backgammon, Zeno could not move to a space occupied by two opponent black pieces.

The white and black checkers were so distributed on the points that the only way to use all of the three results, as required by the game rules, was to break the three stacks of two checkers into blots, exposing them and ruining the game for Zeno. In Roman times, this game was also known as alea , and a likely apocryphal Latin story linked this name, and the game, to a Trojan soldier named Alea.

Race board games involving dice have existed for millennia in the Near East and eastern Mediterranean, including the game senet of Ancient Egypt. Senet was excavated, along with illustrations, from Egyptian royal tombs dating to BC. The usual Tavla rules are same as in the neighboring Arab countries and Greece, as established over a millennium ago, [68] but there are also many quite different variants. Players try to flip their pieces over the opponents' pieces to beat them.

Backgammon is popular among Greeks. It is a game in which Greeks usually tease their opponent and create a lively atmosphere [77]. Portes: Set-up and rules the same as backgammon, except that backgammons count as gammons 2 points and there is no doubling cube.

Plakoto : A game where one checker can trap another checker on the same point. Asodio: Also known as Acey-deucey , where all checkers are off the board, and players enter by rolling either doubles or acey-deucey. These games are played one after another, in matches of three, five, or seven points. Players use the same pair of dice in turns.

After the first game, the winner of the previous game starts first. There is no doubling cube. Over time it was replaced by other games such as xiangqi Chinese chess. In Japan, ban-sugoroku is thought to have been brought from China in the 6th century, and is mentioned in Genji monogatari.

As a gambling game, it was made illegal several times. By the 13th century, the board game Go , originally played only by the aristocracy, had become popular among the general public. In Korea, it is called Ssang-ryuk or Jeopo.

The jeux de tables 'Games of Tables' , predecessors of modern backgammon, first appeared in France during the 11th century and became a favorite pastime of gamblers. In , Louis IX issued a decree prohibiting his court officials and subjects from playing. In Spain , the Alfonso X manuscript Libro de los juegos , completed in , describes rules for a number of dice and table games in addition to its extensive discussion of chess.

A wooden board and checkers were recovered from the wreck of the Vasa among the belongings of the ship's officers. Some surviving artworks are Cardsharps by Caravaggio the backgammon board is in the lower left and The Triumph of Death by Pieter Bruegel the Elder the backgammon board is in the lower right.

In the 16th century, Elizabethan laws and church regulations prohibited playing tables, but by the 18th century, backgammon was popular among the English clergy. In English, the word "backgammon" is most likely derived from "back" and Middle English : gamen , meaning "game" or "play".

The earliest use documented by the Oxford English Dictionary was in The most recent major development in backgammon was the addition of the doubling cube. The popularity of backgammon surged in the mids, in part due to the charisma of Prince Alexis Obolensky who became known as "The Father of Modern Backgammon". He also established the World Backgammon Club of Manhattan, devised a backgammon tournament system in , then organized the first major international backgammon tournament in March , which attracted royalty, celebrities and the press.

Cigarette, liquor and car companies began to sponsor tournaments, and Hugh Hefner held backgammon parties at the Playboy Mansion. Board and committee members include many of the top players, tournament directors and writers in the worldwide backgammon community. From Wikipedia, the free encyclopedia.

One of the oldest board games for two players. For other uses, see Backgammon disambiguation. A backgammon set, consisting of a board, two sets of 15 checkers, two pairs of dice, a doubling cube, and dice cups. Play media. Main article: Tables board game. This section may be confusing or unclear to readers. In particular, the picture is incorrect because it does not take into account that when rolling doubles, a given distance may be traveled using the rolled number 3 or 4 times.

Please help clarify the section. There might be a discussion about this on the talk page. November Learn how and when to remove this template message. See also: List of World Backgammon champions. See also: Nard game. The Metropolitan Museum of Art Bulletin. New Series 1 9 : — Hacker Art Books. Backgammon For Dummies. Backgammon to Win. Lulu Com. Backgammon Galore!. Rules of play describe a particular variation of backgammon and on this there is no disagreement among international tournaments.

In fact, tournament rules sets do not usually specify these rules but might instead refer, as in the US Rules, to the 'commonly accepted rules of backgammon. Gaming Guide - Gambling in Europe. To start the game, each player throws a single die. This determines both the player to go first and the numbers to be played.

Retrieved Archived from the original on Artificial Intelligence.

Backgammon is one of the oldest known board games.

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