CUBEBACKGAMMONJournal
Try game plans on interactive boards, experiment with dice, explore the game’s culture and read how we test the coach’s advice.
7 articles
Count your chances, understand a streak and put a bad run in perspective.
Measuring luck and skill
After a game, CUBE Backgammon shows the winner alongside estimates of who played better and whom the dice favoured. Building that analysis forces us to ask what separating luck from skill can actually mean in a single game.
Board size and dice
Some Roman gaming boards had 36 playing spaces, arranged as six words of six letters. By the fifth century, the Byzantine emperor Zeno was playing on a board with the familiar 24 points, though he used three dice.
Dice & probability · A pattern race
We do occasionally think about something other than backgammon, as long as it still involves two dice. The puzzle below is about probability rather than backgammon strategy. “Double, double, non-double” and “non-double, double, double” are equally likely in three preselected rolls. Keep rolling until either appears, however, and the second pattern wins with probability 35/36.
Backgammon dice · 1/2
A little dice counting helps with hits, getting off the bar and deciding how much risk to take.
Backgammon dice · 2/2
A double is a one-in-six roll. So why does a run of them feel like something that happens far too often?
Making your own chances
Two ways of playing the same 3–2 leave the same pip count, but different opportunities next turn. In our example, one arrangement lets 15 of the 36 rolls make a new point while keeping the existing ones; the other allows only five.
When results mislead
Even with a 55% chance of winning each match, you still have roughly a one-in-four chance of finishing behind after 20 matches.
11 articles
Find a plan and notice what a small change on the board can do.
Six games, ranked
Our order is blackjack, English checkers, backgammon, chess, Go, then full partnership bridge. The surprises are what dice do to backgammon’s search, why Go resisted position evaluation, and how hidden cards complicate bridge.
What a simulation is allowed to know
Building a backgammon engine raises a tempting question: how much can you settle by simulating more games? Bridge, a game my grandfather played brilliantly, shows why a simulation must also respect what the player can know.
Learning the game
Jeremy Bagai thought he had mastered backgammon within a week. Twelve years later, he published his own book correcting mistakes in five influential books he had learned from, written by authors such as Paul Magriel and Bill Robertie.
Playing from behind
When a comeback looks unlikely, bearing off just one checker can prevent a double or triple loss, but abandoning a good chance to hit can also be expensive.
A rule that catches new players
With a checker on the bar and a 6–1 to play, entering with the one can leave the six unusable. If the other order lets you play both dice, the rules require you to use it.
The score is part of the position
At 0–0, a chance to win two or three points can be worth taking a small risk. At 6–6 in a match to seven, one point already wins the match. The same board can call for a different move.
Choosing a plan as the game changes
Your opponent makes an anchor, and the checker you wanted to attack is suddenly protected. Follow that change on the board, then explore when to attack, block, run or wait.
Strategy · The doubling cube
Taking a double can put the whole match on one position, while passing leaves another route through the games that follow. A small bear-off example shows how those chances compare.
Reading the board
You don’t need to count fifteen checkers one by one. A few familiar groups can tell you how much ground each player has left to cover.
Reading the board
An extra exposed checker looks like an extra problem. Sometimes it gives your opponent fewer rolls that can hurt you.
The value of time
A hit can sometimes buy you time to wait for a chance, without giving up the points you need.
7 articles
How we build the coach, test its advice and measure its playing strength.
The estimate behind a move
Our backgammon engine cannot follow every possible game to its ending. It needs a useful estimate of what each unfinished position is worth, so it can compare the moves that lead there. That estimate is at the centre of its decisions.
Inside CUBE Backgammon · Randomness
For an ordinary computer match, CUBE Backgammon generates the dice sequence from a random starting value before the first roll. After the match, you can reproduce the sequence and check that the recorded rolls match it.
Inside CUBE Backgammon · Testing the coach
To improve CUBE Backgammon’s move advice, we trained the neural network that evaluates backgammon positions on more examples. It agreed more often with its teaching engine, GNU Backgammon, but chose worse moves in a separate test that played out possible continuations.
Inside CUBE Backgammon · A benchmark correction
To check whether a development version of CUBE Backgammon chose better moves, we asked Open Sage, another backgammon engine, to evaluate them. On half the positions, our code supplied the wrong player to roll and distorted the comparison.
Inside CUBE Backgammon · Playing strength
Our tests against GNU Backgammon provide evidence about CUBE Backgammon’s checker play. Here is what those results show and what we would need to compare the engine with professional players.
Inside CUBE Backgammon
Tap the Hint button to see the coach’s suggested move. Here’s how it chooses that move and finds an answer while you play.
Building CUBE Backgammon
We tested a development version of CUBE Backgammon’s coach on recorded tournament play. A second engine found that some suggested corrections were worse than the moves the players had made.
7 articles
The words, places and traditions that travel with the game.
Chance and self-play
The dice that frustrate backgammon players also helped an early neural network learn the game. They carried its practice games into new positions, giving a program playing against itself more varied experience.
The opponent who follows a rule
When we compare moves in CUBE Backgammon, we need to consider both future dice and an opponent who chooses how to use them. Blackjack keeps the uncertain cards but fixes the dealer’s behaviour, which changes the calculation considerably.
Computers and the opening roll
In the 1990s, computers transformed how people played backgammon, a game with centuries of history. Programs that could simulate thousands of games prompted leading players to rethink long-established advice, even about the opening moves.
Zeno at the tables
A poem records a Byzantine emperor rolling 2, 5 and 6 and ending up with eight exposed checkers. Reconstructing the position shows how the roll forced him to break all three of his pairs.
A game beneath the sea
When archaeologists excavated the Mary Rose, an English warship from Henry VIII’s navy that sank in 1545, they found a backgammon set among the tools in its carpenter’s cabin.
A bowl of matches beside the board
Some players in the backgammon boom of the 1920s and 1930s tracked doubles with ordinary matchsticks. Period guides show why they needed to agree on what each match meant, while a 1930 advertisement offers a more compact solution.
The language around the board
Some backgammon players in the Arab world and Turkey call the dice with words inherited from Persian, sometimes mixed with Turkish. A six and a five make a particularly good example.