Computer Backgammon

The first strong computer opponent was BKG 9.8. It was programmed by Hans Berliner in the late 1970s on a PDP-10 as an experiment in evaluating board positions. Early versions of BKG played badly even against poor players, but Berliner noticed that the critical mistakes the program made were always at phase changes. He applied basic principles of fuzzy logic to smooth out the transition between phase changes, and by July 1979, BKG 9.8 was ready to play against then current world champion Luigi Villa. It won the match, 7-1, becoming the first computer program to defeat a world champion in any game, although this was mostly a matter of luck, as the computer happened to get better dice rolls than its opponent in that match.

Beginning in the late 1980s, creators of backgammon-playing software began to have even more success with a neural network approach. TD-Gammon, developed by Gerald Tesauro of IBM, was the first of these computer programs to play at or near the expert level. This program’s neural network was trained using Temporal Difference learning applied to data generated from self-play.

This line of research has resulted in two modern commercial programs, Jellyfish and Snowie, the shareware BGBlitz (implemented in Java), and the free software GNU Backgammon, that play on a par with the best human players in the world. It is worth noting that without their associated “weights” tables which represent hours or even months of tedious neural net training, these programs play no better than a human child.

It is interesting to contrast the development of backgammon software with that of chess software:

For backgammon, neural networks work better than any other methods so far. For chess, brute force searching, with sophisticated pruning and other refinements, works better than neural networks.

Every advance in the power of computer hardware has significantly improved the strength of chess programs. In contrast, additional computing power appears to improve the strength of backgammon software only marginally.

For both backgammon and chess, it is at present unclear whether the best computer or the best human is best overall. For most other games, one or the other is unambiguously stronger.

Greek Tavli Variations for Backgammon Fans

If you’re interested in backgammon you may be interested to know that several different varieties of backgammon exist and are played in different parts of the world. One of these is known as Tavli.

Tavli is a Greek version of backgammon and gets its name from the Greek word for “board”. Three separate games make up Tavli, all offering different rules and sequences of play. However, all three are usually played in sets where players compete in order to win the best of three, five or seven games.

The first version of the game is known as Portes, which bears the most similarities to backgammon as it is commonly played in the western world. Players begin a game of Portes with checkers set up identically to those in a game of regular backgammon. However, players do not use a doubling cube for Portes meaning the game is played for fun rather than money. There is also no backgammon. Instead two points constitute a gammon and a normal win receives one point.

A second Tavli variation is known as Plakoto. The starting point of all checkers in a game of Plakoto deviates from the standard backgammon set up. A player must place his checkers on his opponent’s one point to begin the game and then move them around the board to his home area to bear off. There is also no “hitting” of blots in Plakoto. Instead, if you trap your opponent’s checker on a space it must remain there until you choose to remove your checker. This creates an interesting new twist on the game of backgammon. If your mother checker (the last checker on your starting point) is trapped by your opponent, you automatically lose the game along with two points.

The third Tavli variation known as Fevga also requires players to begin the game with all their checkers on one point on the board. Beginning on the point situated to their far right, each player must move his 15 checkers around the board and bear off once they are safely in his home board area. A major rule in Fevga is that your first checker must pass the point at which your opponent has started before you can move any of your other checkers. Like Plakoto, there is no hitting in the game and one checker is enough to dominate a point. Plakoto strategy differs from regular backgammon as the player is not permitted to erect a prime over six consecutive points. If your opponent gets stuck behind your prime, you are obliged to move a checker to enable him to play on.

While the rules deviate for each Tavli variation, there are some common points you should remember if you’re interested in trying a game. All Tavli games use one set of dice and players must determine who takes the first turn by rolling the dice for a high number. The first player must then roll the dice again to take his turn. One point is awarded to the first player who successfully bears all his checkers off the board. All Tavli variations rely on the enjoyment of the game alone, therefore no doubling cube is used for gambling purposes.

Using Hedge to Get Ahead in Craps

Of all the games you can play in the casino craps is perhaps the most physically challenging. True, it doesn’t take an Olympic bench presser to roll the dice onto the table. View this from a mental aspect. Your brain is operating at a million miles per second and you’re using every thinkable trick in the book to come out on top. This is all tremendous pressure for some. It may not hit you immediately but later on your body will reap the effects. Winning at craps takes planning and great technique. Online craps doesn’t exactly measure up to the intensity of the casino version but can be rather challenging as well. If there’s a chance of handicapping the dealer, why not do it? The hedge system was created just for that and is an easy way to get ahead of the game.


Rumor goes that the (Parity) hedge system was created by a team of Las Vegas geniuses. When they weren’t on the job advancing technology, they were at the casino testing other strategies. Combining mathematics into the game of craps, this group developed a system to slowly but surely move ahead of Las Vegas dealers. They performed in stealth mode in order stay under casino radars. While the hedge procedure eventually slipped into the hands of other gamblers, it is said that this innovative team was never found out and their identities remain a mystery to this day.

Using a hedge bet is rather common in online craps games. This process is done by breaking a single bet down into two separate gambles. The reason for this is to increase winning odds and keep a player in the game for a longer amount of time. That extra bet has the ability to cancel out the original. While the amounts aren’t normally much money, it is profit and could get you on a hot streak.


Depending on the website, you typically win money or credit for both your individual bet and the hedge. For instance, if your don’t pass wage is for $20 on a point of six or eight, you can make an additional bet on that same number at $18. If a seven happens to roll, your winnings total $20 even though you lost $18 in the process. Still you earned a profit of $2, small but positive just the same. Via the online crap table you’re usually rewarded your $20 for the original bet plus the additional $20 on the hedge. Similar scenario: say the point is at four or ten. You have the option to bet on either number for $15. Seven rolls across the table; win twenty and lose fifteen, a five dollar plus. If you’re lucky enough to make point, you lose twenty but move $7 ahead of that with your hedge bet.

Many play online craps strictly for recreational purposes. When no physical money is on the line, you’re open to a variety of options and techniques. You’re not liable to break the dealer by placing hedge bets but slowly stacking chips is very possible. Many people are using the system effectively. Why not give this method a try and see if it works for you?

Saint Vincent and The Grenadines Casinos

The Caribbean conjures up images of beautiful islands, with perfect white sandy beaches, swaying palm trees and the deep blue ocean glittering under an endlessly sunny sky. And Saint Vincent and the Grenadines, a former British colony that since 1979 has enjoyed its independence, does not disappoint. Yet when the sun finally sets, Saint Vincent and the Grenadines Casinos offer the gambling visitor a way of continuing the party into the small hours of the morning.

There are two Saint Vincent and the Grenadines Casinos, one in the capital Kingstown, which is found on the largest island, Saint Vincent, and the other at Carenage Bay, which is located on a small island called Canouan, which is part of the group of islands known as the Grenadines.

First let’s pay a visit to the capital Kingstown, the chief port and largest city, albeit a capital city with just 15,000 inhabitants. Here gamblers will find the country’s largest casino, the Emerald Valley Resort and Casino, located in Penniston Valley. The casino offers 50 slot machines and eight table games, including three tables of Blackjack, two tables of Caribbean Stud Poker (and if you can’t play Caribbean Stud Poker in the Caribbean, where you can you play it?), three tables of Roulette, and finally the dice-based game, Craps. To spend their winnings (or help forget the losses) visitors will find the resort has an American restaurant, a DJ Bar, and a whole range of sports facilities including a nine hole golf course, swimming, tennis, horse riding facilities and a 24 room hotel.

The second casino on Saint Vincent and the Grenadines is in Carenage Bay, on the island of Canouan, and is part of the Raffles Resort hotel. This luxurious establishment enjoys 300 acres of private grounds and its own white sandy beaches, with accommodation consisting of 156 villas for the guests. The casino is located in the Villa Monte Carlo, which in addition offers a gourmet restaurant and a ballroom. US entrepreneur Donald Trump manages the casino, based in the Trump Club Privee, and it offers six tables playing Blackjack, Roulette and Craps, all in European-style gaming experience.

So whether in Kingstown or Canouan, Saint Vincent and the Grenadines Casinos offer a great choice for those who like to try to beat the odds in luxurious and beautiful surroundings.