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Understanding The Backgammon Mathematics And Playing Techniques

Updated on April 28, 2014

Backgammon is unique

Learn the game right
Learn the game right | Source

Tackling the tricky side


The thrill of the game lies in the skill the player has. And in backgammon, it is very easy to acquire these skills because the whole game is dependent on correct estimation. If you are able to judge the board correctly , you are sure to make the right choices and win. The backgammon mathematics is simple. The roll of the dice depends on probability and luck. But the techniques of play and the estimation is done by using simple counting techniques that work very precisely. Of the many board games in existence today, backgammon is probably one of the oldest and indeed one of the quaintest. It is a two player board game and the winner is one who is able to bear off all his checkers or men off the board. Each player begins with fifteen pieces or checkers and these are arranged in a predefined manner. In the normal game each player has two checkers in the 24 position, three in the 8 position and five each in the 6 and 13 positions.

Match play

The game is played for a certain number of points and the person to reach the number wins. If one of the player is lagging by 3 points to reach the mark and the other is away by 7 points, one may use mathematics to arrive at the best estimate for a win. First kind of estimation is the pip count, that tells you how far ahead of the other one is. This is done by a) manual counting and by b) elimination. In the first method you count all the pips and total them up. You will low who leads and by how much. In the second, you just equate the equal positions and add only the ones that are different. This is faster and easier and will give the same result.

Understanding the backgammon mathematics

The backgammon mathematics has been derived based on probability and actual experience. It consists of arriving at the actual chances of wining based on the pip difference between the players and the total points required to win the game. The most common used method used is devised by Kit Woolsey. He further tells us of Neil Kazoroos who shows that one can calculate the percentage play using the "Neil's Numbers' (http://www.bkgm.com/articles/GOL/demo/equity.htm).


Neils Numbers

 
 
 
 
 
 
 
3
4
5
6,7
8,9,10
11,12,13,14
15
10
9
8
7
6
5
4
This approximate method will work even if you are not good at mathematics

Learn Ideal Game winning positions

Relaxing indoor board game
Relaxing indoor board game | Source

Find the Neil's number for the person who is trailing.If it is 6, the number is 7. Multiply this by the difference in the player's scores. if this is 2 then we get 2x 7 =14. Add 50 to get at the percentage, that is 64%. It is your chance of winning.

To find out whether to pass or double or play, we use the chance method. Here we estimate the chances of wining and the chances of losing. When the chances are say 60% for wining and 40% for losing, we would like to play. If the condition were reversed, we would reconsider the chances and sway that 1/4 of the time the losses would be gammons, but the rest of the time it would be wins. Thus when we win the percentage is 40% and if we lose it is one-fourth of 40% that is at 30%.

Next is to know how to make hits. The chances are all done for you on the table below.


Estimating your chances

Serial
Number that is required for the hit
Number of ways of doing this
1
1
11
2
2
12
3
3
14
4
4
15
5
5
15
6
6
17
7
7
6
8
8
6
9
9
5
10
10
3
11
11
2
12
12
3
Use the estimate always


This tells you how likely you are to make the hit.

Different Techniques for making wining play

Racing play: This is when one player will race all his checkers over the board and attempt to finish fast.

Priming game: Here one builds a wall of his checkers thus preventing the smooth movement of the opponents pieces.

Duplication: Here the player attempts to keep all his pieces at equal distances from the opposing pieces to reduce the chances of a hit.

Holding game: Here the opponents checkers are held in position to a corner of the board.

Game Play

The board itself has two portions for each player, one referred to as the home board having the 1 to 6 positions. The outermost point is numbered 1 and the inner most point is the 6 position. Points are long triangular markings on the board which are alternately dark and light. Each portion of the board has 6 points on each side of the board. There are thus 24 points in all. The outer board has the points 7 to 12 and the 13 point is referred to as the midpoint.

The number that is on the dice indicates the number of moves the player can make with the checkers. The checkers must be moved to an unoccupied position only, or if there is an opposite checker on the point it is 'hit'. The single checker of the opponent is called a 'blot'. Once the checker is hit, it is removed to the bar , the dividing portion of the game board between the home board and the outer board and remains in that place, till the player moves the checker back into the game through the throw of the dice. The player must move his checker according to the number that he has thrown. He may move any of his pieces. He is also free to move just one piece or checker two times provided the points they move to is unoccupied. If he is unable to move any of the pieces to any unoccupied points, he forfeits his turn. Further if the player throws a double, he is allowed to move the checkers twice so long as there is a place for him to move.

To win the player must clear the board of all his pieces before the opponent. To do this he must first bring his checkers to his home board. Only when he has accomplished this he is allowed to commence bearing off his checkers. The game begins when each of the player rolls a dice. The player who gets the bigger number is the first one to play. He makes a combined move of both the numbers that have just been rolled. In the probability that both the numbers are the same, the players have to roll the dice again. After that the play carries on with each player taking turns rolling the pair of dice.

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    • Porshadoxus profile image

      Porshadoxus 4 years ago from the straight and narrow way

      While I'm sure your math and illustrations are correct, the explanations were hard to follow. As I'm not a backgammon player, I felt lost throughout.

    • snerfu profile image
      Author

      Vivian Sudhir 14 months ago from Madurai, India

      Actually, it is simple Porshadoxus. You need to play it a little. Then you will find it comes naturally.

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