Although sometimes it is claimed that Chess or Checkers has the greatest antiquity of all board games, it is now known that the board games found in ancient Egypt and Mesopotamia are instead closely related to this modern board game:

The game, of course, is Backgammon, and the illustration above shows the board and the initial arrangement of the men.
One off-putting thing about the traditional Backgammon board is that it is not clear where the board begins or ends. For the board as illustrated, the player with the light pieces moves in this direction:
1 1 1 1 1 1 1 2 2 2 2 2
--> 3 4 5 6 7 8 9 0 1 2 3 4
|
|
--- 1 1 1
2 1 0 9 8 7 6 5 4 3 2 1
and the player with the dark pieces moves in this direction:
1 1 1
--- 2 1 0 9 8 7 6 5 4 3 2 1
|
|
--> 1 1 1 1 1 1 1 2 2 2 2 2
3 4 5 6 7 8 9 0 1 2 3 4
The dividing line between the two halves of the board is called the bar, and represents the space before space 1 for each player.
The rules of Backgammon, as it is played today, are:
On each turn, a player rolls a pair of dice to move. The numbers on each of the two dice indicate individual moves, thus, a player may move two pieces in a turn, one by one of the numbers on the two dice, the other by the other number on the two dice. If one piece is moved, that piece must be able to stop on the intermediate space (or point) resulting from making the move indicated by one of the two dice.
If doubles are rolled, the player has four moves, rather than two, to make using the number shown on the two dice.
It is not possible to move one of one's own pieces to a point with two or more of the opponent's men on it.
It is possible to move one of one's own men to a point with only one of the opponent's men on it; this sends that man to the bar.
If any of one's own men are on the bar, all these men must be moved off the bar before any part of a dice roll may be used for any other type of move. However, once one has moved one's last man off of the bar, the remaining unused portion of the dice roll for that turn may then be used for other moves.
The object of the game is to move all one's men home, where home can be thought of as the 25th square of the board for each player. Moving men home is called bearing off, and is subject to the special rule that no man can be borne off unless all of one's men are in the last six points of the board.
When the player that has lost the game has not borne off any of his own men, this is gammon, and counts as a double loss; if, in addition to not having borne off any of his own men, he also has at least one man in the first six spaces of the board, or on the bar, this is backgammon, and counts as a triple loss.
No part of a roll may be discarded if it can be played, even if to do so is disadvantageous.
Initially, the value of a game is one point, or two if gammon, three if backgammon. Either player, if he feels himself ahead, may take the doubling cube, and present it to the other player in the position marked "2". The other player then has the choice of conceding the game at its old value, or accepting the doubling of the value of the game.
After the first double, only the opponent of the player who made the last most recent double may double; thus, each time one doubles, one gives the other player control of the doubling cube.
Doubling was added to backgammon during or before 1926, although the doubling cube was not used as the means of keeping track of doubles until 1931, as noted on this page. A game played on the backgammon board in the seventeenth century, called Ticktack, which was a close relative of Trictrac, had a similar doubling rule, except that the stake was increased by one point each time rather than doubled, but the game was only recently rediscovered from a suriving manuscript. This is discussed on this page.
Another page on that site leads to descriptions of many variants of Backgammon.
The ancient Romans played a game very similar to Backgammon, which was called Tabula.
As in Backgammon, both players have fifteen pieces; however, all of them start off the board.
Until all one's pieces are entered, it is not permitted to move past the first half of the board.
Both players move in the same direction.
Three dice are thrown for each turn, and the numbers on them are always what is played.
As in backgammon, all one's pieces have to be in the last six spaces before bearing off can commence. The same rules apply of being able to send an enemy singleton back to the start, and that a piece so sent must be reentered before any other move is made, apply as in Backgammon, as does the rule that one cannot move a man to a space occupied by two or more of the opponent's pieces, and the rule that the whole roll must always be played if possible.
This game was played with three dice on a board with three rows of twelve spaces. The rules have not survived, but it was likely played with rules very similar to those of Tabula.
This variant of Backgammon was played in the armed forces. It varied from regular backgammon in that a player who rolled doubles, in addition to counting the dice twice, also got a free turn. As well, a roll of 1-2 allowed the player to play a double of his choice in addition to that roll, and to also get a free turn. The 1-2 roll had to be played before the double.
All pieces start off the board in this game, and all of a player's pieces must be on the board before that player's pieces on the board can be moved.