In the pre-computer backgammon age, the technique of rolling positions out by hand and/or playing them as propositions was the only way to learn the game; but the value of these techniques was quite limited nonetheless. Even days and days of painstaking rollouts were inadequate to get to the truth of many complicated backgammon positions, and every expert had a long list of puzzles that he knew he had never adequately solved. In the late 1980s, for example, I played a proposition with a well-known Las Vegas expert for a solid week:
The obvious play, I thought, was to make the four point with 10/4, 6/4. But my opponent (who had mysteriously produced this position out of thin air) said he liked 23/17, 10/8. That looked all wrong to me, and I agreed to play him even though I suspected that he had done some prior work on the position.
Worse than a Whopper
Over the course of the week we played about 130 trials of the prop (amounting to 260 or so actual games). The result: a total wash! His play and my play, over the course of that week, won an equal number of points. It was not until years later, when I fed this position to the bots, that I found out I had been right all along. My opponent’s play was what Paul Magriel calls a “double whopper: worse than the correct play by more than .2 points per game (a plain “whopper” is an error of between .1 and .2 points per game).
Best Proposition Player
The best backgammon proposition player of all was the American Mike Svobodny. “Svobo” had an uncanny knack for staying with a play or cube when it was right and getting away from it when it was wrong. But sometimes even he was bewildered by short term volatilities. Mike once played this very unusual position with Black on roll being paid one point per game to hold a 2 cube.
In this super-swingy position both sides can be gammoned. But the odds are with White. Black leaves double and triple shots with a multitude of rolls.
As the backgammon game began, White went on a super-hot streak, racking up 100 points in a row before Mike could win a game! Mike was about to quit (he was asking himself why he hadn’t quit before he decided to play) but he knew that he had not gotten his fair share of jokers. He decided to try a few more games, and sure enough, he rolled a few 2-2s and 6-6s, got missed a few times when he left triple shots, and won a few freak games after being hit. The whole hundred points came back to him, and then some! It was absolutely impossible to tell from these results what the position was worth, but the bots nowadays say that this was a pretty fair result: it is a small pass with Black on roll.
Things Lost with Backgammon Computers
Finally, after years of wandering in the dark, we backgammon experts were saved when the neural networks, Jellyfish and Snowie were developed. My game took a quantum leap upwards as I gleefully sat in front of the computer, greedily gobbling up the answers to all the riddles that had plagued me for years. But the bad news was that all those players over whom I had always had a big edge, who had never done a stitch of work in their lives, now had access to all the answers as well!