by Michael Strato
13 May 2000
"For those who aren't familiar with what the sets of 6 percentages referred to, they are, in order and for each move, Red's chance of a backgammon, Red's chance of a backgammon or a gammon, Red's chance of any win at all, White's chance of any win at all, White's chance of a gammon or backgammon, and White's chance of a backgammon."
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| 1. 24/23 13/11 Eq.: 0.002 0.5% 12.8% 49.9% 50.1% 12.3% 0.4% 2. 13/11 6/5 Eq.: -0.008 (-0.010) 0.5% 12.9% 49.7% 50.3% 13.0% 0.5% 3. 24/21 Eq.: -0.021 (-0.024) 0.4% 11.4% 49.2% 50.8% 12.0% 0.4% 4. 13/10 Eq.: -0.032 (-0.034) 0.5% 13.0% 48.3% 51.7% 12.8% 0.5% |
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| 1. 8/5 6/5 Eq.: 0.157 0.6% 16.0% 55.2% 44.8% 10.7% 0.4% 2. 24/23 13/10 Eq.: -0.008 (-0.165) 0.4% 12.7% 49.5% 50.5% 12.6% 0.4% 3. 13/9 Eq.: -0.015 (-0.172) 0.4% 13.0% 49.0% 51.0% 12.5% 0.4% 4. 24/20 Eq.: -0.021 (-0.178) 0.4% 11.4% 49.6% 50.4% 12.7% 0.4% 5. 13/10 6/5 Eq.: -0.028 (-0.185) 0.4% 12.9% 48.6% 51.4% 12.9% 0.4% |
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| 1. 24/21 13/11 Eq.: 0.016 0.5% 12.2% 50.8% 49.2% 12.1% 0.4% 2. 13/10 13/11 Eq.: -0.005 (-0.021) 0.5% 14.2% 49.3% 50.7% 13.2% 0.5% 3. 24/22 13/10 Eq.: -0.009 (-0.025) 0.5% 12.3% 49.7% 50.3% 12.5% 0.5% 4. 13/8 Eq.: -0.022 (-0.039) 0.4% 12.1% 49.1% 50.9% 12.5% 0.4% 5. 24/21 24/22 Eq.: -0.024 (-0.040) 0.4% 11.0% 49.5% 50.5% 12.5% 0.4% |
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| 1. 24/23 13/9 Eq.: -0.005 0.5% 13.1% 49.5% 50.5% 12.5% 0.5% 2. 13/8 Eq.: -0.025 (-0.020) 0.5% 12.4% 49.1% 50.9% 13.1% 0.5% 3. 24/20 24/23 Eq.: -0.025 (-0.021) 0.4% 11.2% 49.2% 50.8% 12.2% 0.4% 4. 13/9 6/5 Eq.: -0.031 (-0.026) 0.4% 13.0% 48.5% 51.5% 13.1% 0.4% 5. 24/20 6/5 Eq.: -0.046 (-0.041) 0.4% 11.6% 48.5% 51.5% 13.2% 0.4% |
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| 1. 8/4 6/4 Eq.: 0.106 0.6% 15.3% 53.4% 46.6% 11.5% 0.5% 2. 24/20 13/11 Eq.: 0.006 (-0.100) 0.5% 12.5% 50.3% 49.7% 12.5% 0.5% 3. 13/9 13/11 Eq.: 0.005 (-0.101) 0.6% 14.4% 49.6% 50.4% 13.1% 0.5% 4. 24/22 13/9 Eq.: 0.002 (-0.104) 0.4% 12.9% 49.9% 50.1% 12.5% 0.4% 5. 24/20 24/22 Eq.: -0.023 (-0.129) 0.3% 11.0% 49.6% 50.4% 12.5% 0.4% |
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| 1. 24/21 13/9 Eq.: 0.000 0.5% 12.9% 50.0% 50.0% 12.9% 0.5% 2. 24/20 13/10 Eq.: 0.000 (-0.000) 0.5% 12.5% 50.2% 49.8% 12.8% 0.5% 3. 13/9 13/10 Eq.: -0.003 (-0.003) 0.6% 14.3% 49.2% 50.8% 12.8% 0.5% 4. 24/20 24/21 Eq.: -0.004 (-0.004) 0.4% 11.2% 50.4% 49.6% 12.4% 0.4% 5. 13/6 Eq.: -0.051 (-0.052) 0.5% 12.7% 48.1% 51.9% 14.0% 0.5% |
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| 1. 24/23 13/8 Eq.: 0.015 0.5% 12.3% 50.3% 49.7% 11.4% 0.4% 2. 13/8 6/5 Eq.: -0.017 (-0.032) 0.5% 12.5% 49.2% 50.8% 12.5% 0.5% 3. 24/18 Eq.: -0.025 (-0.040) 0.4% 10.6% 49.7% 50.3% 12.6% 0.4% . 4. 13/7 Eq.: -0.061 (-0.075) 0.4% 12.0% 47.6% 52.4% 13.4% 0.5% 5. 24/23 8/3 Eq.: -0.123 (-0.138) 0.4% 11.2% 45.6% 54.4% 14.8% 0.5% |
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| 1. 24/22 13/8 Eq.: 0.005 0.5% 12.2% 50.3% 49.7% 12.4% 0.4% 2. 13/8 13/11 Eq.: 0.000 (-0.005) 0.5% 13.4% 49.9% 50.1% 13.1% 0.5% 3. 13/8 6/4 Eq.: -0.029 (-0.034) 0.4% 12.2% 48.6% 51.4% 12.2% 0.4% 4. 13/6 Eq.: -0.053 (-0.058) 0.4% 12.1% 47.8% 52.2% 12.9% 0.4% 5. 13/11 8/3 Eq.: -0.106 (-0.111) 0.4% 12.4% 46.0% 54.0% 15.0% 0.6% |
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| 1. 8/3 6/3 Eq.: 0.053 0.6% 15.3% 51.3% 48.7% 12.6% 0.5% 2. 24/21 13/8 Eq.: 0.025 (-0.028) 0.5% 12.5% 50.9% 49.1% 11.9% 0.4% 3. 13/8 13/10 Eq.: -0.002 (-0.054) 0.5% 13.6% 49.5% 50.5% 12.8% 0.5% 4. 24/16 Eq.: -0.007 (-0.059) 0.3% 10.7% 50.4% 49.6% 12.3% 0.4% 5. 13/5 Eq.: -0.027 (-0.079) 0.4% 13.0% 48.6% 51.4% 12.8% 0.4% |
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| 1. R 24/20 13/8 Eq.: 0.036 0.5% 12.6% 51.5% 48.5% 12.0% 0.4% 2. 13/8 13/9 Eq.: 0.013 (-0.023) 0.5% 13.6% 50.1% 49.9% 12.5% 0.5% 3. 24/15 Eq.: -0.006 (-0.042) 0.4% 10.6% 50.6% 49.4% 12.5% 0.5% 4. 13/4 Eq.: -0.041 (-0.077) 0.4% 12.6% 48.0% 52.0% 12.7% 0.4% 5. 13/8 6/2 Eq.: -0.066 (-0.102) 0.4% 12.0% 47.3% 52.7% 13.2% 0.5% |
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| 1. 13/7 8/7 Eq.: 0.093 0.5% 14.1% 53.2% 46.8% 11.1% 0.4% 2. 24/18 24/23 Eq.: -0.037 (-0.130) 0.4% 11.4% 49.3% 50.7% 13.8% 0.5% 3. 24/23 13/7 Eq.: -0.037 (-0.130) 0.4% 12.3% 48.3% 51.7% 12.6% 0.4% 4. 13/6 Eq.: -0.040 (-0.133) 0.4% 12.2% 48.2% 51.8% 12.6% 0.4% 5. 24/18 6/5 Eq.: -0.073 (-0.166) 0.3% 10.7% 48.0% 52.0% 14.1% 0.4% |
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| 1. 24/18 13/11 Eq.: 0.011 0.4% 11.9% 50.8% 49.2% 12.5% 0.4% 2. 24/16 Eq.: -0.004 (-0.015) 0.4% 11.0% 50.6% 49.4% 12.7% 0.5% 3. 13/5 Eq.: -0.020 (-0.031) 0.5% 13.0% 49.0% 51.0% 12.9% 0.5% 4. 24/18 24/22 Eq.: -0.046 (-0.057) 0.3% 10.4% 49.2% 50.8% 13.3% 0.4% 5. 13/7 13/11 Eq.: -0.049 (-0.061) 0.4% 12.9% 48.0% 52.0% 13.8% 0.5% |
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| 1. 24/18 13/10 Eq.: 0.002 0.4% 11.9% 50.5% 49.5% 12.6% 0.4% 2. 24/15 Eq.: -0.004 (-0.007) 0.4% 10.7% 50.6% 49.4% 12.4% 0.5% 3. 24/21 13/7 Eq.: -0.036 (-0.038) 0.4% 12.2% 48.6% 51.4% 13.0% 0.4% 4. 24/18 24/21 Eq.: -0.038 (-0.041) 0.3% 10.6% 49.5% 50.5% 13.6% 0.4% 5. 13/4 Eq.: -0.041 (-0.043) 0.4% 12.6% 48.0% 52.0% 12.7% 0.4% |
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| 1. 24/14 Eq.: 0.011 0.4% 10.9% 51.0% 49.0% 11.9% 0.4% 2. 24/18 13/9 Eq.: 0.006 (-0.005) 0.4% 12.5% 50.4% 49.6% 12.6% 0.4% 3. 8/2 6/2 Eq.: 0.004 (-0.008) 0.6% 14.1% 49.9% 50.1% 13.5% 0.5% 4. 24/20 13/7 Eq.: -0.035 (-0.047) 0.4% 12.2% 48.5% 51.5% 12.7% 0.4% 5. 24/18 24/20 Eq.: -0.043 (-0.054) 0.3% 10.4% 49.4% 50.6% 13.6% 0.4% |
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| 1. 24/13 Eq.: 0.060 0.4% 10.8% 53.2% 46.8% 11.3% 0.4% 2. 3 24/18 13/8 Eq.: 0.026 (-0.034) 0.4% 11.7% 51.4% 48.6% 11.9% 0.4% 3. 3 13/7 13/8 Eq.: -0.038 (-0.098) 0.4% 12.7% 48.2% 51.8% 13.0% 0.4% 4. 2 13/2 Eq.: -0.067 (-0.127) 0.4% 12.7% 47.2% 52.8% 13.8% 0.5% 5. 2 24/18 8/3 Eq.: -0.127 (-0.187) 0.4% 10.5% 46.0% 54.0% 15.3% 0.5% |
Links to more info on Opening Rolls:
Kit Woolsey On Opening Rolls
Bernhard Kaiser On One-Point Matches
Backgammon Galore's Backgammon Newsgroup Archive On Opening Rolls
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