What this game is
Backgammon is the one classic game where dice and calculation live together as equals. You do not choose the roll, but you choose how to play it, and the whole game hides inside that choice.
On the surface it is a race: fifteen checkers have to travel round the board and come off before your opponent's do. In practice, for most of a game the two armies walk into each other and make life difficult. A lone checker can be hit and sent back to the start, and a wall of made points can lock an opponent up for several turns. Hence the decision behind almost every move: run, or keep contact.
Rules
- The board has 24 points and each side has 15 checkers. You play blue and travel from point 24 down to point 1, the computer plays red and runs the other way. The numbers are printed along the edges.
- The game opens with one die from each side: the higher number moves first and plays both dice. Equal numbers mean another roll.
- A roll of two dice is two moves. Each number is played separately: with two different checkers, or with one checker twice. A double gives four moves of that number.
- A checker may land on an empty point, on one of your own, or on a point holding exactly one enemy checker. That lone checker is called a blot: it is hit and goes to the bar.
- A point held by two or more enemy checkers is closed.
- While any of your checkers sits on the bar you must bring it in through your opponent's home first; nothing else may be moved. If neither number lets you enter, the turn is lost.
- Both numbers must be played whenever there is any way to play them. If only one can be played, it has to be the larger.
- Once all 15 of your checkers are home — on points 1 to 6 — bearing off begins. An exact number takes a checker off the matching point. A higher number takes one off the highest occupied point, but only when nothing is left further out.
- Bear all 15 off to win. If your opponent has borne none off it is a gammon, a double game; if on top of that he still has a checker on the bar or inside your home board it is a backgammon, a triple game. In the site-wide score all of these count as one win.
- Roll throws the dice, Undo takes back the last move inside the current turn, Done ends the turn. You move by clicking the destination point, or by clicking a die once a checker is picked up.
- There is no doubling cube here.
How to play better
- Make points instead of scattering checkers. Two checkers on one point are a wall: it cannot be hit and cannot be landed on. Points in your own home and an anchor in your opponent's home are worth most — from an anchor you will never sit on the bar with nowhere to enter.
- Build a prime, a run of consecutive made points. Four in a row already hurts; six in a row cannot be jumped by any roll at all.
- Count the pips, the distance each side still has to travel. Ahead in the race, trade and run, breaking contact. Behind, do the opposite: stay close and wait for a shot, because without contact a deficit can never be made up.
- A blot is not always a mistake, it is a question of price. Count how many of the 36 rolls reach it: from six points away that is 17 rolls out of 36, from seven it is only 6. Sometimes leaving a blot further out beats wrecking your position to leave none at all.
- Do not pile checkers up. Five on one point means three checkers taken out of play with nothing left to occupy.
- In the endgame watch out for wastage: checkers crammed onto the one and two points cannot use big numbers, and a race won on pips gets lost while bearing off.
A bit of history
Backgammon is one of the oldest board games still being played. Races along a track of squares decided by dice go back thousands of years; the Romans had their own version, and medieval Europe a whole family of games known collectively as tables. The modern rules are a late cast of that long tradition.
What made the game modern was a twentieth-century invention. In the 1920s the doubling cube appeared in New York: on your turn you may offer to double the stake, and your opponent must either accept or resign on the spot. Exactly who thought of it is not reliably known. The cube turned backgammon from a folk race into a game about estimating your own chances as a percentage — there is no cube here, so every game is played to the end.
In 1992 the game went through another revolution. Gerald Tesauro's TD-Gammon at IBM learned to play by playing itself a million and a half times: it was given the rules and no human knowledge of strategy at all. At its public debut it barely lost to the strongest players in the world, and its opening moves were so unexpected that professionals rewrote their opening theory.
This version follows the applet that ran on this site from 2005. Gammons and backgammons are recognised and announced, but the site-wide score is a simple one and any win is worth the same in it.
About the levels
On every turn the computer first builds every legal way to play the roll out in full — honouring both "play both dice" and "if only one, the larger" — and then chooses among the resulting positions. The level decides how deeply it checks them.
Easy judges a position by eye and fast: the pip difference, checkers on the bar and borne off, a penalty for its own blots and a small bonus for a blot you left behind. There is no looking ahead at all, which is why it happily leaves checkers where they can be hit.
Hard genuinely searches one ply. It takes the twenty best positions by static score and, for each, runs through all 21 distinct rolls of your reply — a double weighs 1/36, any other pair 2/36 — finds your best answer to each roll and averages the results. So the move is chosen not by how the position looks but by what it becomes on average after any die.
Expert does the same thing two plies deep: twenty candidates get a one-ply value, the best eight get a two-ply one in which the average over all 21 rolls is followed by another full average for the other side. It is given a budget of roughly eight tenths of a second for all that. On top of it, once the two armies have run past each other and nothing can be hit any more, Expert switches to a pure racing evaluation: pips plus wastage, the checkers piled up or buried on the near points that have nothing to do with a big number.
Hard and Expert value a position the same way: pips, made points, the home board, an anchor in the enemy home, the prime (which grows as the square of the chain), penalties for the bar and for an overloaded point, and above all the risk on every blot — the chance of being hit next roll, computed from a table of how many of the 36 rolls cover exactly that many pips.