In 1930, backgammon author Georges Mabardi called the two-point the “novice-point” when discussing an opening 6–4. More than half a century later, backgammon writer Bill Robertie was still explaining why making it spent useful checkers too far down the board. The five- and four-points were the prizes to fight for; the two-point could wait.
By 2001, analyst Kit Woolsey was describing how computer programs had established that same opening as a serious contender. You can follow the change in the dated expert commentary collected by Tom Keith: advice repeated across generations of books had become something players could test by having software play out thousands of games.
The dispute concerned the first move, with every checker still in its starting place. Even there, experienced players had more to learn about a game whose board has ancient roots.
What was wrong with making the two-point?
An opening 6–4 lets you move a checker from 8 to 2 and another from 6 to 2, making a new home-board point. In the notation below, that is 8/2 6/2: each pair of numbers gives a checker’s starting point and destination. Choose the three alternatives to see what each leaves behind.
Three ways to play the same opening 6–4
You are Ivory, moving from 24 toward 1. Choose a play to see the position after both moves. Each alternative starts from the original setup.
Gold outlines mark the destination points. Faded dice have been played. These boards compare three legal plays; they do not display an engine ranking or winning chances.
A checker that has reached 2 cannot come back to help make 4 or 5. Your new point also sits too far from the eight-point for both to belong to the same six-point prime. Running a back checker or bringing builders into play seemed to offer more useful progress.
Making the two-point gives you something valuable immediately, though: a second closed point in your home board. If you hit later, your opponent has fewer places to enter, and an attack has more chance of becoming a gammon. Woolsey singled out that gammon potential when discussing the move. The change in its reputation was a recognition that those benefits could pay for the checkers committed so far forward.
That does not make it the compulsory answer to every opening 6–4. The alternatives lead to different kinds of game, and match score changes the value of gammons. The historical reversal is that a move dismissed as a beginner’s error became a choice that strong players could defend.
How do you test an opening move?
A rollout compares moves by playing many games from the position each leaves and measuring the average points won and lost. Players had done this by hand, but a few evenings of rolling dice produce a small sample for a game with so much luck.
Computer rollouts made much larger comparisons practical. The program plays both sides, using fresh dice sequences across trials. It records single wins, gammons and backgammons as well as losses, because the play that wins most often may earn fewer points than a play that wins more gammons.
To compare openings, the scoring conditions need to stay the same. A match score that makes gammons especially valuable can favour a different choice from one where only winning the next game matters. The boards above show the legal alternatives; they are not a new rollout or a claim that we have proved one universally best.
The change came in the 1990s
Computers had already made backgammon news in 1979, when Hans Berliner’s BKG 9.8 beat world champion Luigi Villa in an exhibition match. Berliner’s own account acknowledged that Villa had played better overall and that the computer had enjoyed the better dice. The broader revision of opening advice came later, as stronger programs became useful partners for analysis.
At IBM, researcher Gerald Tesauro developed TD-Gammon, a neural network that learned through games against itself. In his 1995 paper, he described how rollouts published by Robertie in 1992 had persuaded leading players to reconsider openings such as 4–1 and 5–1. The familiar aggressive choice was to leave a checker alone on the five-point, hoping to cover it next turn. TD-Gammon favoured advancing one of the back checkers by a single point instead, and players began adopting that recommendation.
Programs such as JellyFish and Snowie brought neural-network analysis to players’ own computers, with tools that made rollouts more practical. David Montgomery’s account of JellyFish 2.0 describes its introduction of variance reduction in early 1996: a way to reduce the noise from the dice in rollout estimates, making more careful comparisons affordable.
In 2001, Jeremy Bagai published his own book, Classic Backgammon Revisited, using software to re-examine positions in five earlier books by other authors. As he explains in an interview about his book, he was examining works that had shaped his own play. Our article on learning backgammon follows that part of his story.
The computer result that disappeared
In his account of computer rollouts, Woolsey recalled testing opening plays with the early program Expert Backgammon. After 1,296 trials per play, an opening 4–2 appeared to be better spent bringing two checkers down from the midpoint than making the four-point, the standard play.
When he extended that comparison to more than 5,000 trials, making the four-point came out comfortably ahead. The smaller sample had happened to favour the unusual play, and its apparent advantage vanished as the comparison grew.
Woolsey also found a different problem when comparing programs: they sometimes gave substantially different rollout results because they handled the resulting positions differently. More trials could steady each program’s average while leaving that disagreement intact.
How a phone coach compares moves
More trials make a rollout’s average steadier, but a program that mishandles backgames can still undervalue a move that leads to one. Playing each trial to the end keeps those mistaken decisions in the result, however many games you run.
In CUBE Backgammon, a hint has to arrive while you are considering your turn, so the phone cannot settle every choice by playing thousands of complete games. Our engine combines a compact position evaluator with a search through possible replies. Training happens beforehand, using positions analysed by a stronger teaching engine. During play, the phone uses the learned estimates to help compare the boards that legal moves would leave.
During development, we once trained a network that agreed more often with GNU Backgammon’s preferred moves. A separate test that played out continuations found worse decisions overall, so we restored the previous version.
Historical sources: the dated book excerpts and expert comments in Tom Keith’s How to Play the Opening Rolls; Gerald Tesauro, Temporal Difference Learning and TD-Gammon (1995); Kit Woolsey, Computers and Rollouts (2000); David Montgomery, Variance Reduction (2000); Hans Berliner, Computer Backgammon (1980); and Jeremy Bagai’s 2001 interview. The boards are original renderings of the standard starting position and three legal 6–4 plays. They reproduce no historical rollout table and assert no current numerical ranking. The CUBE Backgammon section follows our published engine and development accounts.