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tom@bkgm.com

## Motif Backgammon Statistics

These statistics are the result of 100,289 games played on Motif Backgammon between June 1, 1996 and November 1, 1996.

## Roll Totals

This table shows the number of dice rolls in all games against Motif. The number of pips is the total numeric value rolled, counting twice for doubles. With random dice, you would expect to see an average of about 8.167 pips per roll.

Rolls Pips Pips/Roll
Players 1,612,834   13,167,843   8.164
Motif 1,624,332   13,259,678   8.163
Total 3,237,166   26,427,521   8.164

## Distribution of Doubles Rolls

The next table shows the distribution of doubles rolls for all players and for Motif. The rate is the average number of times out of 36 that each roll appears.

Players Motif Total

RollsRate
RollsRate
RollsRate
 44,710 0.998 44,661 0.997 44,703 0.998 44,945 1.003 44,886 1.002 44,679 0.997
 45,133 1 45,022 0.998 45,259 1.003 45,294 1.004 45,160 1.001 44,713 0.991
 89,843 0.999 89,683 0.997 89,962 1 90,239 1.004 90,046 1.001 89,392 0.994
Total
 268,584 5.995
 270,581 5.997
 539,165 5.996

## Distribution of Mixed Rolls

The next table shows the distribution of mixed rolls for all players and for Motif. The rate is the average number of times out of 36 that each roll appears.

Players Motif Total

RollsRate
RollsRate
RollsRate
 89,951 2.008 90,079 2.011 89,448 1.997 89,841 2.005 90,048 2.01 89,592 2 89,252 1.992 89,467 1.997 89,443 1.996 89,921 2.007 89,335 1.994 89,416 1.996 89,482 1.997 89,253 1.992 89,722 2.003
 90,278 2.001 89,967 1.994 90,281 2.001 90,617 2.008 90,165 1.998 90,333 2.002 90,347 2.002 90,488 2.005 90,319 2.002 90,155 1.998 90,061 1.996 90,171 1.998 90,600 2.008 89,966 1.994 90,003 1.995
 180,229 2.004 180,046 2.002 179,729 1.999 180,458 2.007 180,213 2.004 179,925 2.001 179,599 1.997 179,955 2.001 179,762 1.999 180,076 2.003 179,396 1.995 179,587 1.997 180,082 2.003 179,219 1.993 179,725 1.999
Total
 1,344,250 30.005
 1,353,751 30.003
 2,698,001 30.004

## Favorite Ways to Play the Opening Rolls

 24/23, 13/11 24/21 13/10 24/22, 24/23 13/11, 6/5
 27% 26% 15% 12% 11%
 8/5, 6/5
 95%
 13/8 13/10, 13/11 24/21, 13/11 24/21, 24/22
 38% 27% 18% 10%
 13/8 24/23, 13/9 24/20, 24/23 13/9, 6/5
 48% 20% 18% 9%
 8/4, 6/4
 95%
 13/9, 13/10 24/20, 13/10 24/20, 24/21 13/6 24/21, 13/9
 25% 24% 21% 18% 10%
 24/23, 13/8 24/18 13/8, 6/5 13/7
 66% 17% 9% 6%
 13/8, 13/11 24/22, 13/8 13/6
 46% 32% 19%
 8/3, 6/3
 86%
 24/20, 13/8 13/8, 13/9 24/15
 43% 33% 22%
 13/7, 8/7
 92%
 24/16 24/18, 13/11 13/5 24/18, 24/22 13/7, 13/11
 53% 19% 9% 8% 6%
 24/15 24/18, 13/10 24/18, 24/21 13/7, 13/10
 63% 17% 10% 7%
 8/2, 6/2 24/14 24/18, 13/9
 62% 24% 6%
 24/13
 95%

## Attempting to Enter from the Bar

The next table shows the success rate of entering a checker from the bar. The rate shown is the average number of times out of 36 that a checker is entered.

Open
Points
Players Motif Total
TriesRate
TriesRate
TriesRate
 1 2 3 4 5 6
 74,531 10.993 98,905 20.066 93,053 27.097 76,233 32.052 45,110 35.058 616 36
 51,668 10.966 68,328 20.015 76,259 26.944 69,026 32.055 44,903 34.969 598 36
 126,199 10.982 167,233 20.045 169,312 27.028 145,259 32.053 90,013 35.013 1,214 36

## Roll Totals in Pure Race Positions

This table shows the number of dice rolls by each player and the average pips per roll in positions where the opposing forces are disengaged.

Rolls Pips Pips/Roll
Players 259,368   2,117,652   8.165
Motif 269,658   2,203,113   8.170
Total 529,026   4,320,765   8.167

## Probability of Winning the Race

This table shows the probability of the on-roll player winning the game at various pipcounts and leads over his opponent, in positions where the opposing forces are disengaged.

1-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 101-110
-20
-15
-10
-5
Even
+5
+10
+15
+20
+25
+30
---
---
5.9
29.6
74.9
92.8
97.5
98.8
99.7
99.7
100.0
0.0
3.8
14.8
42.6
63.7
81.3
90.5
95.1
98.1
99.4
99.6
3.4
11.6
27.0
45.1
64.2
77.7
88.3
94.0
97.2
98.0
98.9
7.5
17.1
29.5
45.0
65.1
75.5
85.9
91.5
95.8
97.3
98.6
10.7
19.9
31.3
46.4
62.8
73.0
83.2
90.4
93.3
96.7
99.2
11.9
22.8
34.0
47.7
59.9
72.5
80.4
88.4
92.6
95.9
97.8
14.1
25.0
35.9
47.5
59.7
69.1
78.8
86.6
90.6
95.9
97.9
16.2
25.2
35.0
47.5
60.6
69.9
79.6
85.8
92.2
94.1
95.5
18.1
24.5
34.0
46.6
59.7
69.0
76.3
83.8
91.9
93.6
90.3
16.7
27.7
35.1
46.4
59.8
69.1
74.5
82.1
91.1
---
---
18.5
25.7
36.3
46.9
61.6
65.3
68.0
---
---
---
---

Last Updated: September 2004