NOTE: THIS IS A WORK IN PROGRESS, ADDITIONAL ROLLOUTS ARE STILL BEING CONDUCTED AND WILL BE ADDED AS THEY BECOME AVAILABLE.
I recently started reading Paul Magriel’s classic Backgammon. I had avoid this book because I knew that it was prebot and contained some errors. However I was struggling—even with reading Trice—to put to get clear in my mind some of the guiding principles that were being used to drive plays in various positions. After reading some comments online about Magriel’s book I decided to give it a try. I wanted to know – beyond the openings—were Magriel was not in agreement with the bots. My search turned up the following link at Hardy’s Backgammon pages: http://www.hardyhuebener.de/engl/magriels_irrtuemer.html. This is excellent information, however the rollouts are all cubeless and GNUBG 0-ply. So I decided to use this list as a starting point and reroll these positions in XG.
I choose money play, no Jacoby, cubeful, 3-ply for the rollout parameters. Money play without Jacoby was chosen because I believe it will give the best overall information for checker play in most money situations as well as most match play situations where the checker play is not score dependent. Using 3-ply was a practical consideration for doing the rollouts in a reasonable amount of time and still providing a high degree of accuracy. I screened the candidate plays using XG Roller + and included at least all the plays that were better than Margriel’s in the longer rollout. I used 1296 as the base number of games, but in some cases extended until the play either reached statistical significance (i.e. the confidence intervals between the top play and Magriel’s did not overlap) or until it was pretty clear that the plays were to close to call. For example in Position 12.1 the equity difference between Magriel’s play and the top play is 0.003, but both the top play and Magriel’s have confidence intervals of ±0.003 after 41,472 games, so this is a too close to call situation. Magriel’s plays are shown in bold italics in the rollout results.
There are some significant differences between these results and the GNUBG published at Hardy’s Backgammon Pages, undoubtedly due to differences in bots, plys, and choice of settings. This work is not intended as a criticism of the work done by the author of that site, therefore I will not go into a position by position comparison of the results from the two projects.
Position 12.1
| 1. | Rollout1 | 8/7 8/5 | eq: +0.364 | |||
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| 2. | Rollout1 | 7/6 7/4 | eq: +0.361 (-0.003) | |||
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| 3. | Rollout1 | 8/6(2) | eq: +0.354 (-0.010) | |||
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| 1 41472 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply |
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eXtreme Gammon Version: 1.13
Position 12.4
| 1. | Rollout1 | 10/9 6/4 | eq: +1.000 | |||
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| 2. | Rollout1 | 9/8 6/4 | eq: +0.982 (-0.018) | |||
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| 3. | Rollout1 | 9/7 6/5 | eq: +0.965 (-0.035) | |||
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| 4. | Rollout1 | 10/8 6/5 | eq: +0.893 (-0.107) | |||
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| 5. | 2 ply | 6/5 6/4 | eq: +0.889 (-0.111) | |||
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| 1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply |
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eXtreme Gammon Version: 1.13
Position 13.20
| 1. | Rollout1 | 24/18 13/11 | eq: -0.281 | |||
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| 2. | Rollout1 | 24/22 13/7 | eq: -0.306 (-0.026) | |||
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| 3. | Rollout1 | 24/22 24/18 | eq: -0.317 (-0.036) | |||
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| 4. | Rollout1 | 13/11 13/7 | eq: -0.411 (-0.130) | |||
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| 1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply |
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eXtreme Gammon Version: 1.13
Position 13.25B
| 1. | Rollout1 | 20/16 10/4 | eq: +1.421 | |||
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| 2. | Rollout1 | 20/14 10/6 | eq: +1.408 (-0.013) | |||
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| 3. | Rollout1 | 10/4 9/5 | eq: +1.405 (-0.017) | |||
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| 4. | Rollout1 | 20/14 9/5 | eq: +1.404 (-0.018) | |||
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| 5. | Rollout1 | 20/16 9/3 | eq: +1.402 (-0.020) | |||
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| 1 2592 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply |
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eXtreme Gammon Version: 1.13
Position 14.16
| 1. | Rollout1 | 8/4 6/4 | eq: +0.447 | |||
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| 2. | Rollout1 | 14/8 | eq: +0.305 (-0.142) | |||
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| 3. | Rollout1 | 7/1* | eq: +0.302 (-0.145) | |||
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| 1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply |
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eXtreme Gammon Version: 1.13
Position 16.9
Magriel only shows the 3, I placed a checker on the bar and made the other dice roll a 4 to arrive the position in Magriel.
| 1. | Rollout1 | Bar/21 13/10 | eq: -0.178 | |||
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| 2. | Rollout1 | Bar/21 8/5* | eq: -0.272 (-0.094) | |||
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| 1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply |
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eXtreme Gammon Version: 1.13
Position 17.8
| 1. | Rollout1 | 13/10 | eq: -0.606 | |||
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| 2. | Rollout1 | 24/23 13/11 | eq: -0.690 (-0.084) | |||
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| 3. | Rollout1 | 24/23 8/6 | eq: -0.720 (-0.114) | |||
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| 4. | Rollout1 | 8/5 | eq: -0.731 (-0.125) | |||
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| 5. | Rollout2 | 13/11 8/7 | eq: -0.740 (-0.134) | |||
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| 1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply 2 2592 Games rolled with Variance Reduction. |
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eXtreme Gammon Version: 1.13
Position 18.3
| 1. | Rollout1 | Bar/24 11/6 | eq: -0.810 | |||
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| 2. | Rollout1 | Bar/24 23/18 | eq: -0.891 (-0.082) | |||
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| 3. | XG Roller+ | Bar/24 13/8 | eq: -1.000 (-0.190) | |||
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| 4. | XG Roller+ | Bar/24 6/1 | eq: -1.000 (-0.190) | |||
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| 1 1296 Games rolled with Variance Reduction. Dice Seed: Random Moves and cube decisions: 3 ply |
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eXtreme Gammon Version: 1.13
Backgammon Camp 