Backgammon
Backgammon is an old, very popular board [1]game of both skill and
[2]chance (dice rolling) in which players race their stones from one side
of the board to the other. It often involves betting (but can also be
played without it) and is especially popular in countries of Near East
such as Egypt, Syria etc. (where it is kind of what [3]chess is to our
western world or what [4]shogi and [5]go are to Asia). It is a very old
game whose predecessors were played by old Romans and can be traced even
as far as 3000 BC. Similarly to [6]chess, [7]go, [8]shogi and other
traditional board games backgammon is considered by [9]us to be one of the
best games as it is [10]owned by no one, highly [11]free, cheap, simple
yet deep and entertaining and can be played even without a [12]computer,
just with a bunch of [13]rocks; compared to the other mentioned board
games backgammon is unique by involving an element of chance and being
only played on [14]1 dimensional board; it is also relatively simple and
therefore noob-friendly and possibly more relaxed (if you lose you can
just blame it on rolling bad numbers).
Rules
Here we'll summarize the common rules, keep in mind there may be some
variations, like extra rules on competitive level and so on. The rules
seem quite complex and arbitrary at first, but by playing you'll see
they're really pretty simple and sometimes quite intuitive (furthermore
the game, at least on casual level, mostly doesn't require such hard
thinking as e.g. chess, so it even feels more relaxed, you can focus on
the rules well).
There are two players, black and white, each moving circular stone discs,
or just stones of his color, here we'll use {# for black stones and (O for
white ones. There are two six sided dice in the game. The board has 24
places (vertical lines, traditionally drawn as long triangles) which
stones can occupy. The following shows the board, the initial setup of
stones, the directions in which players move and their goals.
black's direction
.------------ - - - -
| ___________________________
| |{# ; ; ;(O ; |(O ; ; ; ;{# | white's goal
| |{# : : :(O : |(O : : : :{# |
| |{# . . .(O . |(O . . . . . |
V |{# . . . . . |(O . . . . . |
|{# |(O |
| | |
|(O |{# |
^ |(O . . . . . |{# . . . . . |
| |(O . . .{# . |{# . . . . . |
| |(O : : :{# : |{# : : : ;(O |
| |(O ; ; ;{# ; |{# ; ; ; ;(O | black's goal
| """""""""""""""""""""""""""
'------------ - - - -
white's direction
The goal of each player is to get all his stones to his goal -- the goal
is one place beyond the last place on the board in the direction of his
movement. Whoever does this the first wins.
The first six places on one's path are called the home board, the last six
are called the outer board.
At start both players roll the dice (each one rolls one), whoever rolls
the bigger number starts and has to use (details below) the numbers that
were just rolled for his first turn (if the numbers were the same, they
roll again). After the first player finishes his round, the other player
rolls both dice, makes his turn, then the first player does the same again
and so on, the players just take turns in rolling dice and playing.
A turn is played by rolling the two dice, resulting in numbers X (one die)
and Y (the other one). The player then moves two stones (he can choose
which), one by X places, the other by Y places. He can also move the same
stone, but the move still counts as moving twice, i.e. first moving the
stone by X, then moving it again by Y, or vice versa (this may be
important in regards to rules explained later). If X and Y are the same,
the numbers are doubled, so the player gets 4 numbers to play: X, X, X, X
-- for example rolling 2 and 2, the player can move 4 stones, each by 2,
or 1 stone by 8 (in separate steps) or 1 stone by 2 and other one by 6 and
so on. Moves cannot be skipped by choice, the player has to move "as much
as he can", i.e. if he can at least partially use the numbers he rolled,
he has to (also if there is a choice between higher and lower number
rolled, he has to use the higher number etc.).
Movement: players move their stones in opposite directions by the number
of steps they roll, in a kind of horseshoe shaped path (as shown above --
topologically the board is just a 1D line, it's just curved to nicely fill
the board) -- notice that on one end the stones jump from one side of the
board to the other side. Stones can walk over stones of same color and can
even stay on the same place -- if more than one stones occupy the same
place, they are "stacked" and protected against being taken. A stone can
move over enemy stones (even if multiple stacked enemy stones), but can
end on such place only if there is exactly one enemy stone, in which case
it is taken -- it is removed and placed in the middle of the board.
Remember that a stone that is moving by a sum of rolled numbers counts as
several discrete moves, so if a stone is moving e.g. by 3 + 3 steps, it's
not the same as moving by 6 because after the first 3 steps taken it
mustn't land on stacked enemy stones (but it can land on one enemy stone
and take it).
A stone that's been taken (placed in the middle of the board) is seen as
being one place before the player's starting place (the opposite of one's
goal), and can be returned to the game (appearing in the enemy home board)
-- in fact it HAS TO be returned to the game before any other move can be
made by the player whose stone it is, i.e. if a player has any stones out
of the game because the opponent has taken them, he cannot move any other
stones until he returns all his stones back to the game.
Once the player has all his stones in the enemy home board, he can start
bearing off, i.e. getting the stones to the goal (i.e. before this his
stones aren't allowed to reach the goal). The goal is seen as a place one
after the final board square in the direction of the player's movement --
if the stone gets to the goal, it is placed on the board border. Here
there are a bit more complex rules: normally a stone may reach the goal
only if it steps on it exactly, i.e. a stone on the very last place can
only get to the goal by rolling 1, the stone before it by rolling 2 etc.
However the stone furthest away from the goal may also use a value higher
than this, i.e. if there is a stone 3 places before the goal AND it is the
last one back, it may finish with 3, 4, 5 or 6. During bearing off the
player may also use the lower rolled value first, even if it wouldn't
fully utilize the higher value (exception to a rule mentioned above).
Details
Despite chance playing some role, skill is highly important and there
exist strategies and tactics that maximize once chance of winning -- for
example a basic realization is that the different sums you may roll don't
have the same probabilities, e.g. 8 can be achieved by 2 + 6 or 2 + 2 + 2
+ 2, but 3 only as 2 + 1 -- one can account for this. The highest
probability to take the enemy stone with one's own stone is when the
stones are 6 places apart. Taking enemy stone while having own stones
stacked in all places in enemy home board makes opponent unable to play
(he is required to return the stone to play but there is no number that
can do it for him). There is also some opening theory.
The game is internationally governed by WBGF (World Backgammon
Federation), similarly to how chess is governed by FIDE.
Who was the best player ever? There doesn't seem to be a clear consensus,
but Masayuki Mochizuki (Japan) seems to come up very often as an answer to
the question, other names include Paul Magriel, Nack Ballard etc.
Backgammon was the first board game in which the world champion at the
time (Luigi Villa) was defeated by [15]computer -- this happened in 1979.
This was perhaps thanks to the element of chance.
As for backgammon computer engines the best [16]free as in freedom one
seems to be [17]GNU backgammon, using [18]neural networks, apparently
beyond the strength of best human players. The Extreme Gammon engine is
probably a bit stronger (currently said to be the strongest) but it is
[19]proprietary and therefore unusable.
Some statistics about the game: there are 18528584051601162496 legal
positions. Average branching factor (considering all possible dice rolls)
is very high, somewhere around 400, which is likely why space search isn't
as effective as in chess and why neural networks greatly prevail. Average
number of moves in a game seem to be slightly above 20.
TODO
Links:
1. game.md
2. randomness.md
3. chess.md
4. shogi.md
5. go.md
6. chess.md
7. go.md
8. shogi.md
9. lrs.md
10. public_domain.md
11. free.md
12. computer.md
13. rock.md
14. 1d.md
15. computer.md
16. free_software.md
17. gnu.md
18. neural_network.md
19. proprietary.md