[2] Following the emergence of self-trained backgammon-playing neural networks, the suggested best opening moves for some rolls have changed significantly from the pre-bot expert opinions.
The table below summarizes the preferred moves for each of the 15 possible opening rolls, as selected by detailed computer simulations, referred to as "rollouts".
[3] The first column is the move that the rollout says gives the most equity (i.e. the average profit or loss that one would net, per game, by playing the position to conclusion an infinite number of times).
For instance, the opening move 8/2 6/2 for a roll of 6-4 was in the past greeted with disdain from experts (making the 2-point instead of trying for a higher home point), but turns out to be on average about as effective as the usual plays (24/14 and 24/18 13/9).
In the late 1990s Harald Johanni and Bill Robertie independently published the first lists based on computer rollouts with Robertie also providing some general principles:[14] In 2015 Jeremy Bagai published Mastering the Second Roll, a comprehensive analysis of 630 possible replies along with a set of rules to help aspiring players to remember the results.