Backgammon online

How to play backgammon

The board is 24 points: a row of 12 facing a row of 12. You and your opponent travel them in opposite directions, so the two armies pass through one another on the way round. Each side starts with 15 checkers: 2 on your furthest point, 5 on your thirteenth, 3 on your eighth, 5 on your sixth. Bring all 15 into the six points of your home board, take them off, and the game is yours.

Two dice, and the server throws them. Neither side picks a number and neither side can throw again, so the roll that arrives is the roll you play. They come to you as two separate moves, and you may spend them on one checker or on two. A double is the exception. Rolling the same number on both dice gives you four moves of it instead of two, which is how the board stores the throw. Double sixes carries you 24 pips, counting a pip for each point a checker crosses, and can settle a game on its own.

Two of your checkers on a point make it yours and shut the other side out of it. One checker on its own is a blot, and an enemy checker landing there knocks it to the bar to begin its lap again. Once everything you own is home you start bearing off, and the side that clears all 15 wins. You move by choosing a checker and then a point: touch one of your own and the places it can legally go light up, which is the engine showing you what the throw allows.

One difference from the tournament game is there before anybody has moved. The standard game has each side roll a single die to decide who goes, and those two unlike numbers become the opening move, so nobody can open on a double. Here Ivory opens by throwing two dice like anybody else, which means this board can, and a tournament board cannot.

Every die you can play, you must play

The standard rules say you must move according to both dice if it is at all possible. This board enforces it. You do not get to play the number you like and quietly drop the other, and across a real table that is a rule the two of you have to police between you.

Before it accepts a move the engine plays your whole go out ahead of you, works out the largest number of dice any sequence could consume, and then allows only the moves that keep that number reachable. If both dice can be played, you must play both, in whichever order makes that possible. If only one of them can be played, it has to be the higher. If a double lets you make 3 of your 4 moves and no more, you make 3 and the turn ends there.

So a move that looks reasonable is sometimes refused, because playing it would strand the other die, and the order you are moving in can be forced even when the choice of checker is not. When a throw gives you nothing at all the turn passes by itself, without sitting there waiting for you to notice.

The bar, and the walk back

Being hit is the most expensive thing that happens in a game. The checker comes off the point and goes to the bar, the brass strip down the middle of the board, and it starts the whole lap again from the far end.

From the bar there is one way back: into the far quarter, on the number you throw, onto a point the other side does not already block with two of its own. Until all of your own checkers are off the bar, nothing else you own may move, so a single blot left standing can freeze your whole board for a turn or three. Hitting costs you a move. Being hit costs you most of a lap.

Bearing off, and how the game ends

Once all 15 of your checkers are inside your home board, and none of them is on the bar, you can start taking them off. A die takes a checker off the point of that exact number. A die larger than any point you still occupy will remove one from your furthest occupied point, but only when nothing of yours is further back than that.

Get hit while bearing off and the checker goes to the bar, and nothing comes off again until it is home. The first side to take off all 15 wins, and here the scoring stops at that. Finishing while your opponent still has checkers sitting in your home board is a gammon or a backgammon in the tournament game, worth double or triple the stake. This board counts none of it. One game, one winner.

The doubling cube is about a hundred years old, and this board has none

The most famous object in backgammon is the newest thing in it. The doubling cube was introduced in the 1920s in New York City, among the members of gaming clubs on the Lower East Side, and whoever thought of it is not recorded. Before it existed, a double was recorded by putting common parlour matches on the bar. What the cube did was turn a race into a running argument about the odds: offer it, and your opponent either takes at twice the stake or gives up the game at the current one. That is what turned backgammon into the expected value problem the twentieth century played.

This board does not have one. There is no cube on the table, no offer to double, no match play and no stake. The rules file that the server and both sides of a game all run has four player actions in it, and none of them is a double.

The optional rules people ask about go with it, because all of them are cube rules. The beaver, where the side being doubled accepts and immediately doubles back while keeping the cube. The raccoon stacked on top of the beaver. The Murphy rule, where identical numbers on the opening throw turn the cube without anybody offering. None of them exists without a cube, so none of them is here. What is left is the older game underneath: the race, the hitting, and nothing riding on it.

How far back backgammon goes

The family is old and backgammon itself is not, and that difference is where most of the confusion about its age sits. The earliest attested relative is Roman: ludus duodecim scriptorum, the twelve line game, mentioned by Ovid in the Ars Amatoria somewhere between 1 BCE and 8 CE. Tabula, the earliest game anybody can identify as a tables game, is described in an epigram about the Byzantine emperor Zeno, who reigned in the late fifth century, preserved by Agathias a hundred years later. The name backgammon appears in a letter of 1647.

The Zeno epigram is unusually good evidence because it records a real position and a real throw. It gives 15 pieces a side, both sides running the same way round the board, three dice where we use two, and a piece standing alone and vulnerable to capture. Four rules of the modern game, attested in the fifth century. What it does not settle is whether a hit piece had to come back in before anything else moved, whether everything had to be home before bearing off, or whether there was a bar at all. Those parts of our game arrive later, and nobody can say when. Scholars read tabula as a trimmed down ludus duodecim scriptorum, which is the likeliest account rather than a thing anybody wrote down.

So the shape here is a family, not a line of descent. The Royal Game of Ur is the same kind of game, a race along a track run on dice with pieces that can be sent back, and its boards were cut around 2600 BCE. Nobody has the documents that would join it to the Roman evidence. The gap between the two is roughly twice the gap between that evidence and now.

Backgammon strategy starts with one number

We counted this against our own rules instead of taking it from a book. Put a lone checker a set distance in front of an enemy checker on an otherwise empty board, run all 36 throws through the engine, and count the throws that can reach it.

One point away, 11 of 36 hit. Three points away, 14. Six points away, 17, which is the highest number anywhere on the board and close to a coin toss. Then it falls off a cliff. Seven points away is hit by 6 throws. Eight by 6, nine by 5, ten by 3, eleven by 2.

So the most useful number in the game is the difference between six and seven. Six can be thrown on one die and seven cannot, so anything past six needs two numbers to combine. A blot six points in front of an enemy checker sits on the most dangerous square on the board, and one more point of distance cuts the risk to about a third. Counting and judging risk are the two skills this game rewards, and both of them start there. Whatever else there is to master in backgammon, this is the part that costs one sentence to learn.

How many legal opening moves there are

There are 21 distinct opening throws: 15 unlike pairs and 6 doubles. Running each of them through our own reducer and counting the distinct positions you could leave the board in gives 447 in total.

They are nothing like evenly spread. Double twos give 75 distinct opening plays and double threes 73, while double fives give 4, six and five give 7, and one and five give 8. Some throws are a real decision and some are close to a formality, which is why opening theory in backgammon is a short list and not a library. The two throws with the widest fork in them are also the two a tournament opening can never hand you, since it cannot start on a double at all.

The game a neural network learned by playing itself

Gerald Tesauro, at IBM's Thomas J. Watson Research Center, built a program that learned backgammon from games it played against itself, with no human opening book supplied to it. TD-Gammon was a neural network trained by temporal difference learning, correcting its estimate of a position against the estimate that followed it. Version 1.0 arrived in 1991 and finished 13 points down over 51 games against grandmasters. Version 2.1, in 1993, played 40 games against Bill Robertie and finished one point down, which put it at the level of the best in the world. Kit Woolsey judged its positional sense, and particularly the way it weighed risk against safety, better than his own or anybody's.

Then it did the rarer thing. On the opening throws of 2-1, 4-1 and 5-1, human authority slotted a checker on the five point. TD-Gammon preferred splitting the back checkers, 24 to 23. Tournament players tried it, found it worked, and within a few years slotting had gone out of the tournament game. A program had taught its own teachers the opening.

Our computer opponent is not that. It is a one move evaluator. It takes each legal move available, plays it a single step forward, and scores the position it lands in based on a handful of counts: checkers borne off count heavily, your checkers on the bar count for it, its own count against it, distance from home is a cost, a lone checker is a small penalty and a point held by two or more is a small credit. A strong bot would look several throws deeper and weigh what it found with something it had learned. This one stops at the step in front of it, and it has no difficulty settings. It is on every board here so that each game can be played through and tested by one person before it ships. That is how everything on this shelf gets checked.

Classic backgammon online, and what classic leaves out

Classic here means the board most people picture: 24 points in two rows of 12, ivory against ebony in a walnut frame, 15 checkers a side and the standard opening setup. What it leaves out is the machinery that usually comes attached to a free board, the coins and the daily rewards and the levels to climb, and the advertising between games.

It also means a ruleset you can check. One rules file runs on the server and on both sides of a game, so what the board allows is the same whoever is sitting at it. Where this table departs from the tournament standard it departs in exactly two places, and both are named on this page instead of buried in a settings menu: the cube it does not have, and the way the opening throw is made. That is what classic backgammon online means on this table, the standard game with two departures written down where you can read them.

Play backgammon online with friends, or on one screen

Multiplayer here is a link and two seats. Open a table and the board gives you an address to pass on, and the person following it arrives in the other chair. Neither of you signs up for anything, neither of you installs anything, and there is no app to find: it is a web page with a board on it. The board itself is one drawing that scales to the screen it is on, so a phone gets the same 24 points as a laptop.

The room outlives the sitting. A table stays open for 48 hours after the last move, and there is no clock and no time limit on a move, so a game does not have to be finished in one evening. Play your go, close the tab, and come back the next day: the device you opened the table on remembers it and lists it waiting for you. The privacy of it is structural. The room exists because you sent the link to it, and what the server holds of the game goes when the room does. That suits backgammon, where a game is a run of small decisions and not one long think.

Two player backgammon works on one screen as well, so when you are both in the same room you do not need two devices. Set it out once and pass it back and forth. If you would rather meet the game in private, try the computer.

There are no online backgammon tournaments on this site, no ladder and no rating, and nothing here is played for money. What the table does give you is the standard game with the rules enforced by the engine, so neither of you has to referee, and a seat open at it. Most of the games in this collection are public domain boards rebuilt because they are open and not because they are famous. Backgammon is one of the exceptions. It is here because it is the one board game you already know.