The game consists of 30 checkers (15 white/ 15 black), 2 dice and the playing field. All checkers are distributed in the playing field at the start of the game according to the official rules. The player who opens the gaming table starts the game. The two opposing parties take turns during the course of the games to ensure there is no game-related advantage or disadvantage.
The checkers are moved only to the open points, by the number determined by the roll of the dice. The order and distribution of the rolled-for moves for the checkers is decided by the player, but all possible moves must be made. If a move cannot be made according to the number on the dice, then it expires and cannot be used in the next round.
Points are "open", when no, or at most one, opposing checker occupies the point, or if any number of the own player.s checkers are placed on the point. Points are "closed" when at least two opposing checkers are placed on them and hence moving the own checker to the fields, as a destination for a move, is not an option.
If both dice show the same number then the number of possible moves is doubled: in this case the checkers can be moved four times by the identical number shown on both dice.
A checker can be hit if it is the only opposing checker occupying a point. The own checker must be moved to the exact point occupied only by one opposing checker to hit it, and the hit checker can subsequently be removed from the playing field.
Before he can conduct any other moves, the opponent must bring his hit checker back into the starting quadrant by rolling the dice. If the opponent could only move his hit checker to an already blocked point, he must continue trying until his checker is back in the playing field.
Bearing off is the final phase of the game when all 15 checkers have reached the final quadrant, that is, the last 6 points.
Rolling a six allows a player to remove a checker from the point six, rolling a five allows a player to remove a checker from the point five, etc. It is furthermore allowed to use a higher rolled number for bearing off: a player can thus use a six to bear off a checker from point five, provided that at that moment none of the player.s checkers are located on point six.
The player who first bears off all of their 15 checkers wins the game.
Doubling cubes are used in the modes Normal game, price 5 Points, as well as price Single game.
This dice is called doubling cube and is labelled with the numbers 2, 4, 8, 16, 32 and 64.It is available to both players at the beginning of the game. If one of the players is under the impression of winning the game, he might offer the doubling cube to the opponent. The opponent loses the game if he rejects the doubling cube. If the opponent accepts the doubling cube then the result of the game is doubled. Subsequently, the player who accepts the doubling cube has the sole right to offer the cube again. The cube is turned as to show the current value of the power of two. Whoever has the right to the cube can double before rolling the dice. The player may roll the dice only when the opponent has accepted.
With the Normal Backgammon there is no investment and no point score that has to be attained; after there is a winner the parties can decide whether to start a new game or to stop playing.
With the set 3 Games price-game 2.50 ℂ or 5 ℂ are paid as an investment and 4.50 ℂ or 9 ℂ are paid to the winner respectively. If there is a tie then the investment will be returned minus 10%. The player who has attained the most points over the three games wins.
With the 5-points price-game 2.50 ℂ or 5 ℂ are paid as a investment and 4.50 ℂ or 9 ℂ are paid to the winner respectively. The player who first attains 5 points wins the game.
With the price Single game a single game is played and the score is settled according to points. A point is worth either 1 ℂ or 2 ℂ and there is a limit of either 10 ℂ or 20 ℂ. Every player pays the amount that was chosen as the limit and depending on how many points he attains, the winner of the game will be credited the respective amount minus 10% plus his investment. If the loser has not lost to the limit, the remaining value of his investment will be returned. Warning: If one of the players leaves the gaming table before the game has finished, then the opponent will automatically win the game and receive the winnings according to the potential points.
The ranking list is based on the Elo rating system, which is an objective rating system that enables the description of the relative skill levels of players through a rating number (short: Elo-number). It was developed by Dr Arpad Elo in the 60s and was first used in chess. By now the Elo system has also been introduced to Backgammon and has become the primary rating system. The Elo rating system is differentiated in the game modes Normal and Price, but there are no differences in the single game options (5 Points, Single Game, 3 Games).
This is the formula for the calculation of the Elo rating:
Every game is rated using a fixed point score. With a 5 Points price-game the point score is exactly 5, with the 3 Games price-game the point score is 4, with the Single price-game the point score is 2 and with the Normal game it is 1.
D = abs(EloOld1 - EloOld2) (This is the difference of the old Elo ratings)
P_u = 1/(10^(D*sqrt(n)/2000)+1) (Probability that the player with the lower Elo wins)
P = 1 - P_u (when the player with the lower Elo wins)
P = P_u (when the player with the higher Elo wins)
K = max ( 1 , 5 - experience/100 )
K is a factor that considers that players who have only played a few games up to date will have greater Elo variances. Hence, the sum of fixed point scores is carried over internally for every player (experience). For every player with more than 400 experience the value of K is always 1.
The new Elo of the winner now is :
EloNewWinner = EloOldWinner + 4 * K * sqrt(n) * P
The new Elo of the loser is:
EloNewLoser = EloOldLoser - 4 * K * sqrt(n) * P
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