White - Pips 109
Black - Pips 98
Diagram 1. Black to Play 1-1
Something bad happened in between your first position and the second, which is diagrammed above. Somehow you ended up with a big stack on the 8pt. That will make it harder to get the distribution you want inside as you complete the bear in. Probably you rolled several 5s. If that is true, it may be that 10/5 or 8/3 would have been better than 13/8 for at least one or two of them.
For the 11 you have to play in Diagram 1, the table below lists all possible plays and their resulting EPCs. (EPC stands for effective pip count.) Note that the best of them, 8/7 8/5, unstacks the 8pt and puts checkers on points that need them. The second best, 8/6(2), unstacks the 8pt while making two crossovers. It puts too many checkers on the 6pt, but avoiding that turns out to be less important than having a diversified distribution outside. In fact, having as many as seven checkers on the 6pt may be ideal. See Diagram 2 below for an example.
Having checkers on the 7pt is problematic. It is useful in positions where the 6pt is light. That way you can efficiently play 7/6 when you roll an ace. In most positions, however, there is a danger that you will have to bear in too deeply when you crossover from the 7pt. In the table of Ideal Racing Positions linked below, there is only one position that has any checkers on the 7pt. These considerations explain why 8/6 8/7(2) turns out to be only 3rd-best in Diagram 1. That play puts too many checkers on both the 7pt and the 6pt.
EPC Table for Diagram 1
Code:
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No. Move EPC Difference % Difference
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1. 8/7, 8/5 101.22 -- --
2. 8/6(2) 101.277 0.0571141 0.0564259%
3. 8/6, 8/7(2) 101.277 0.0577823 0.0570861%
4. 10/9, 8/5 101.291 0.0711673 0.0703098%
5. 10/9, 8/6, 8/7 101.293 0.0736177 0.0727307%
6. 8/5, 6/5 101.303 0.0834381 0.0824328%
7. 8/6, 8/7, 4/3 101.34 0.120745 0.11929%
8. 8/5, 4/3 101.341 0.121497 0.120033%
9. 8/4 101.383 0.163573 0.161602%
10. 10/9, 8/7(2), 6/5 101.387 0.167073 0.16506%
11. 8/7(3), 6/5 101.409 0.189817 0.18753%
12. 8/6, 8/7, 5/4 101.411 0.191777 0.189466%
13. 8/7(2), 6/5(2) 101.415 0.195512 0.193156%
14. 8/7(2), 6/5, 4/3 101.435 0.21505 0.212459%
15. 10/9, 8/7, 6/5(2) 101.44 0.220601 0.217943%
16. 8/7(2), 6/4 101.454 0.234264 0.231441%
17. 10/9, 8/6, 4/3 101.474 0.254543 0.251476%
18. 8/7, 6/4, 6/5 101.474 0.254704 0.251635%
19. 10/9, 8/7(3) 101.478 0.258433 0.255319%
20. 10/9, 8/7, 6/4 101.478 0.258618 0.255502%
21. 10/9, 8/6, 5/4 101.491 0.271037 0.267771%
22. 8/7, 6/3 101.493 0.273363 0.270069%
23. 10/9, 8/7, 6/5, 4/3 101.495 0.275067 0.271753%
24. 8/7, 6/5(2), 4/3 101.511 0.291852 0.288335%
25. 8/6, 5/3 101.512 0.2921 0.28858%
26. 8/6, 4/2 101.516 0.296162 0.292593%
27. 10/6 101.518 0.298128 0.294536%
28. 8/7(3), 4/3 101.518 0.298881 0.29528%
29. 10/9, 8/7(2), 4/3 101.526 0.306345 0.302653%
30. 10/9, 8/7(2), 5/4 101.532 0.312467 0.308702%
31. 10/7, 6/5 101.54 0.320299 0.31644%
32. 8/7(4) 101.548 0.328809 0.324847%
33. 8/7(2), 5/3 101.549 0.328953 0.324989%
34. 8/7, 6/5, 4/2 101.553 0.333474 0.329456%
35. 10/7, 8/7 101.554 0.334614 0.330583%
36. 10/9, 6/4, 6/5 101.574 0.354886 0.35061%
37. 8/7(3), 5/4 101.576 0.356007 0.351718%
38. 8/7(2), 4/2 101.577 0.357217 0.352913%
39. 6/3, 6/5 101.59 0.370191 0.36573%
40. 10/9, 6/3 101.639 0.419859 0.4148%
41. 10/9, 6/5(2), 4/3 101.642 0.422537 0.417445%
42. 8/7, 6/5(3) 101.645 0.425366 0.420241%
43. 10/9, 8/7, 5/3 101.651 0.431822 0.426619%
44. 8/7, 4/1 101.68 0.460639 0.455089%
45. 10/9, 8/7, 4/2 101.688 0.468116 0.462476%
46. 8/6, 4/3(2) 101.688 0.468862 0.463213%
47. 6/5, 4/1 101.692 0.472791 0.467095%
48. 8/7, 6/5, 4/3(2) 101.715 0.49514 0.489174%
49. 6/2 101.716 0.496784 0.490798%
50. 10/9, 6/5, 4/2 101.717 0.49729 0.491298%
51. 6/4, 6/5(2) 101.719 0.499087 0.493074%
52. 8/7, 5/2 101.721 0.501285 0.495245%
53. 8/7, 6/4, 5/4 101.725 0.505407 0.499317%
54. 8/7(2), 4/3(2) 101.729 0.50911 0.502976%
55. 6/5(2), 4/2 101.735 0.515344 0.509135%
56. 10/9, 6/5(3) 101.736 0.51614 0.509921%
57. 10/8, 6/5(2) 101.736 0.516284 0.510064%
58. 6/4(2) 101.749 0.529354 0.522976%
59. 8/7, 5/3, 4/3 101.769 0.549149 0.542532%
60. 6/3, 5/4 101.77 0.550554 0.54392%
61. 6/3, 4/3 101.772 0.552209 0.545555%
62. 10/7, 4/3 101.772 0.552756 0.546096%
63. 10/7, 5/4 101.774 0.554422 0.547742%
64. 10/8, 6/4 101.776 0.555943 0.549244%
65. 8/7, 4/2, 4/3 101.798 0.578531 0.571561%
66. 10/9, 6/4, 5/4 101.798 0.578697 0.571725%
67. 8/7(2), 5/4(2) 101.803 0.582936 0.575912%
68. 8/7, 5/3, 5/4 101.806 0.586142 0.57908%
69. 10/8, 6/5, 4/3 101.808 0.587931 0.580847%
70. 10/9, 4/1 101.812 0.591989 0.584856%
71. 10/9, 8/7, 5/4(2) 101.825 0.605079 0.597789%
72. 6/5, 4/2, 4/3 101.829 0.609708 0.602361%
73. 10/9, 8/7, 4/3(2) 101.832 0.612167 0.604791%
74. 10/9, 6/5, 4/3(2) 101.863 0.64324 0.635489%
75. 6/5(3), 4/3 101.874 0.654518 0.646631%
76. 8/6, 5/4(2) 101.882 0.662171 0.654193%
77. 10/9, 5/2 101.892 0.672392 0.66429%
78. 6/5(2), 4/3(2) 101.901 0.681879 0.673663%
79. 5/1 101.916 0.696772 0.688376%
80. 4/1, 4/3 101.956 0.736688 0.727812%
81. 5/2, 4/3 101.957 0.737437 0.728551%
82. 10/9, 5/3, 4/3 102.018 0.798483 0.788862%
83. 10/9, 5/3, 5/4 102.027 0.807392 0.797663%
84. 10/8, 5/3 102.03 0.810691 0.800923%
85. 10/9, 4/2, 4/3 102.063 0.843517 0.833353%
86. 5/3(2) 102.092 0.872499 0.861986%
87. 10/8, 4/2 102.099 0.87903 0.868439%
88. 4/2(2) 102.205 0.985561 0.973686%
89. 5/2, 5/4 102.213 0.993842 0.981867%
90. 6/5(4) 102.221 1.00176 0.989687%
91. 6/4, 5/4(2) 102.355 1.13552 1.12184%
92. 10/8, 4/3(2) 102.383 1.16381 1.14979%
93. 5/3, 4/3(2) 102.396 1.17621 1.16204%
94. 10/8, 5/4(2) 102.44 1.22001 1.20531%
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White - Pips 0
Black - Pips 79
Diagram 2. ideal Bear-in Position in a Non-contact Race
In many racing positions, the ideal checker arrangement minimizes EPC. To that end, it is worth knowing a couple of reference positions. The one above, with a 7-5-3 distribution, is the one you should have been aiming for when you began the bear in. See
Ideal Racing Positions for a list of other ideal positions.
In practice, you won't always be able to reach an ideal position. Here are some of the things to keep in mind: Making crossovers is important, but is not always the top priority. Stay diversified outside. Work to reach a wedge shape, such as the ones shown in Diagrams 2 and 3. A smaller, but similarly shaped wedge is often best for the checkers that remain outside. Diagrams 2, 3, and 4, all of which show wedges, are ideal at their respective pip counts when all 15 checkers are still in play on or below the 11pt.
As the number of checkers outside diminishes, the wedge is no longer best. Shapes with a hump towards the rear are better. Diagrams 5 and 6 are examples of this. Beginning from either one, Black has a good chance to reach the 7-5-3 distribution of Diagram 2.
Black - Pips 70
Diagram 3. Woolsey's Wedge
Black - Pips 130
Diagram 4. Woolsey's Wedge in the outfield
Black - Pips 113
Diagram 5. Later on, a humped shape replaces the wedge outside.
Black - Pips 103
Diagram 6. Still later, a small hump remains.
Mike