This article originally appeared in the April 2001 issue of GammOnLine.
Thank you to Kit Woolsey for his kind permission to reproduce it here.

Peever's Errors vs. Kit Woolsey

By Paul Weaver
GamesGrid is the best place on the internet to play backgammon. GG has the best players, the best graphics, and the least lag of any of the internet backgammon servers.

Kit and I both play on GamesGrid, and I always enjoy playing matches with Kit for the following reasons:

(1) Kit is one of the very best match players in the world, and I enjoy the challenge of playing against the strongest possible competition.

(2) I enjoy the fact that Kit plays at a reasonably rapid pace. I become very bored when I play a match against a slow player, and make a mental note to never invite the slow player again. When a backgammon player makes 95% of his decisions quickly, he is entitled a few times a match, as Kit and I both do occasionally, to take a bit of extra time on an especially crucial decision.

(3) Kit always plays with perfect etiquette. He never complains when he has bad dice, not even when he recently fanned three consecutive shakes on my one point board. He is also always a gracious winner.

On September 26, 2000 Kit and I played a seven point match on GamesGrid. I kept my laptop busy for over a week rolling out positions from the match. Although Kit humbly gave me permission to discuss his mistakes, there are more than enough of my own errors to keep me occupied. The positions that follow are my own mistakes from the match with Kit.

                  POSITION 1

146








160

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Kit Woolsey 0



7 point match




Paul Weaver 0

           1. R  bar/21 8/5*               Eq.: -0.820
               0.3%   7.6%  33.3%    66.7%  26.5%   1.3%
               Live cube rollout: -0.815
               95% confidence interval:
                  - money cubeless eq.: -0.532 0.006,
                  - live cube: -0.815 0.015.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 117306 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           2. R  bar/21 6/3                Eq.: -0.935 (-0.115)
               0.2%   6.5%  31.8%    68.2%  27.4%   1.3%
               Live cube rollout: -0.934
               95% confidence interval:
                  - money cubeless eq.: -0.584 0.008,
                  - live cube: -0.934 0.017.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 99840 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           3. 3  bar/18                    Eq.: -0.915 (-0.096)
               0.2%   6.1%  32.9%    67.1%  28.9%   1.0%
               Full 3-ply, 100%.
           4. 2  bar/21 13/10              Eq.: -1.000 (-0.180)
               0.2%   6.2%  30.6%    69.4%  28.9%   1.1%
In Position 1 I have the unenviable task of playing a 43 from the roof. After entering with the forced 4, I played 6/3 (Position 1B) with the three, duplicating Kit's 2's while unstacking the 6-point. Unfortunately, my play also gives Kit free rein to attack my three exposed blots.

In colloquial terms, “When you know the other guy is going to hit you, it is better to get in the first punch, however weak it may be.”

Although the distribution after the hitting play B/21 8/5* (Position 1A) is admittedly ugly, putting Kit on the roof makes some of his numbers play worse than otherwise. He now fans with 66, he can no longer double switch with 11, nor can he point on my face with 64, 42, and 33. Also, his 31, 61, 62, and 63 play worse for him after the “ugly” hitting play.

                  POSITION 1A

151








153

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Kit Woolsey 0



7 point match




Paul Weaver 0

          Rollout      Money equity: 0.547
               1.5%  27.1%  66.9%    33.1%   7.5%   0.3%
               95% confidence interval:
                  - money cubeless eq.: 0.547 0.014,
                  - live cube no double: 0.755 0.014,
                  - live cube double take: 0.923 0.020.
               Rollout settings:
                  Full rollout,
                  1296 games (equiv. 30779 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  random seed, with race database.
          Evaluations
                1.  Double, take      0.940
                2.  No double         0.752  (-0.189)
                3.  Double, pass      1.000  (+0.060)
          Proper cube action: Double, take
          Live cube
                1.  Double, take      0.923
                2.  No double         0.755  (-0.169)
                3.  Double, pass      1.000  (+0.077)
          Proper cube action: Double, take

                  POSITION 1B
146








153

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Kit Woolsey 0



7 point match




Paul Weaver 0
          Rollout      Money equity: 0.603
               1.3%  28.7%  68.5%    31.5%   6.3%   0.3%
               95% confidence interval:
                  - money cubeless eq.: 0.603 0.024,
                  - live cube no double: 0.831 0.028,
                  - live cube double take: 1.091 0.035.
               Rollout settings:
                  Full rollout,
                  324 games (equiv. 9299 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  seed 100, with race database.
          Evaluations
                1.  Double, pass      1.000
                2.  No double         0.816  (-0.184)
                3.  Double, take      1.071  (+0.071)
          Proper cube action: Double, pass
          Live cube
                1.  Double, pass      1.000
                2.  No double         0.831  (-0.169)
                3.  Double, take      1.091  (+0.091)
          Proper cube action: Double, pass
Regardless of which play I make, my opponent has a strong double. After making the correct play, as shown in Position 1A, I have close take, according to the Snowie rollout. After making the incorrect passive play, B/21 6/3, as shown in Position 1B, the Snowie rollout indicates that I have a close pass. My passive play, B/21 6/3, was a blunder, giving up more than 0.10 in equity.

                  POSITION 2

157








173

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Kit Woolsey 1



7 point match




Paul Weaver 0

           1. R  bar/21 24/20 18/10        Eq.: -0.138
               0.4%  10.1%  45.9%    54.1%  11.3%   0.4%
               Live cube rollout: -0.135
               95% confidence interval:
                  - money cubeless eq.: -0.095 0.008,
                  - live cube: -0.135 0.014.
               Rollout settings:
                  Truncated rollout, depth 8,
                  188 games (equiv. 74537 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           2. R  bar/21 18/10 13/9         Eq.: -0.155 (-0.016)
               0.4%  11.4%  45.1%    54.9%  12.0%   0.5%
               Live cube rollout: -0.154
               95% confidence interval:
                  - money cubeless eq.: -0.104 0.008,
                  - live cube: -0.154 0.014.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 105426 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           3. R  bar/21 18/14 13/9(2)      Eq.: -0.156 (-0.017)
               0.4%  10.8%  45.4%    54.6%  12.0%   0.5%
               Live cube rollout: -0.158
               95% confidence interval:
                  - money cubeless eq.: -0.106 0.007,
                  - live cube: -0.158 0.012.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 114711 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           4. R  bar/21 24/20 13/9(2)      Eq.: -0.165 (-0.027)
               0.4%  10.7%  45.7%    54.3%  13.4%   0.6%
               Live cube rollout: -0.165
               95% confidence interval:
                  - money cubeless eq.: -0.114 0.007,
                  - live cube: -0.165 0.013.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 118085 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           5. 3  bar/21 13/9 6/2(2)        Eq.: -0.176 (-0.038)
               0.5%  12.9%  44.9%    55.1%  14.4%   0.6%
               Full 3-ply, 100%.

                  POSITION 2A
157








157

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Kit Woolsey 1



7 point match




Paul Weaver 0
Position 2 is a third roll position arising after the sequence 62/64/44. I played B/21, 24/20, 13/9(2), as shown in Position 2A.

This play makes the 9 point and facilitates Blue in linking his rear checkers if he is not attacked, but at the cost of leaving himself too vulnerable to White's attack. White's 21, 61, 62, and 63 allow White to hit two of Blue's checkers while leaving only one inner board blot, and White's 33 allows White to hit two of Blue's checkers while leaving no inner board blots.

                  POSITION 2B

157








157

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Kit Woolsey 1



7 point match




Paul Weaver 0
The correct play, B/21 24/20, 18/10, is shown in Position 2B. This play, which the rollout favored by a slim .016 margin, reduces Blue's exposure to White's double hitting numbers, leaves a spare on the midpoint, and gives Blue many return shots if White hits with a nine. If Blue is not hit, then all 36 of his numbers will allow him to either make a valuable offensive point, link his two rear checkers, or at least run one of the rear checkers to the safety of the midpoint.

                  POSITION 3

131








167

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Kit Woolsey 1



7 point match




Paul Weaver 0

           1. R  bar/18                    Eq.: -0.839
               0.3%   6.7%  31.8%    68.2%  23.0%   1.3%
               Live cube rollout: -0.836
               95% confidence interval:
                  - money cubeless eq.: -0.536 0.011,
                  - live cube: -0.836 0.013.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 40988 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           2. R  bar/23 8/3*               Eq.: -1.000 (-0.161)
               0.3%   6.7%  26.6%    73.4%  27.9%   2.0%
               Live cube rollout: -1.000
               95% confidence interval:
                  - money cubeless eq.: -0.697 0.009,
                  - live cube: -1.000 0.000.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 61845 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           3. 3  bar/23 6/1                Eq.: -1.000 (-0.161)
               0.2%   5.4%  24.9%    75.1%  23.8%   1.0%
               Full 3-ply, 100%.
           4. 3  bar/23 13/8               Eq.: -1.028 (-0.189)
               0.1%   4.8%  22.0%    78.0%  28.8%   1.4%
               Full 3-ply, 100%.
           5. 2  bar/23 9/4                Eq.: -1.057 (-0.218)
               0.1%   4.8%  21.8%    78.2%  33.3%   2.0%

                  POSITION 3A
134








160

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Kit Woolsey 1



7 point match




Paul Weaver 0

                   POSITION 3B
131








160

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Kit Woolsey 1



7 point match




Paul Weaver 0

With his 52 from the bar, Blue must choose the least of the evils in Position 3. I incorrectly chose the hitting play, B/23, 8/3*, as shown in Position 3A. This play gives White 14 numbers to hit, sending a fourth checker of Blue's back, thereby increasing the chance that Blue will lose a gammon. Facing White's strongest possible four point board, Blue must realize that he is in no position to win the game immediately, and should therefore refrain from hitting loose in his board.

A better approach in this difficult position is shown in Position 3B. By playing B/18, Blue will not be risking a fourth checker back. In fact, after White's 12 missing numbers, Blue will have only two checkers back if he can move his 18-point blot to safety. After White's 24 hitting numbers, Blue will have a few lucky return shots. Even if he fans, he will have no more than three checkers back.

Blue's best strategy in Position 3 is to play quietly, hope to move the 18 point blot to safety, and strengthen his offensive position while waiting for a better attacking opportunity. My hitting play, B/23 8/3*, was a serious blunder.

If the cube were still in the center, Blue would have a comfortable take after playing B/18, but should pass after playing B/23, 8/3*.

                  POSITION 4
122








182

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Kit Woolsey 1



7 point match




Paul Weaver 0

           1. R  bar/24 6/3*               Eq.: -1.085
               0.2%   4.7%  24.7%    75.3%  41.8%   4.1%
               Live cube rollout: -1.101
               95% confidence interval:
                  - money cubeless eq.: -0.915 0.012,
                  - live cube: -1.101 0.005.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 41416 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           2. R  bar/24 8/7(2) 6/5         Eq.: -1.121 (-0.036)
               0.1%   3.7%  22.0%    78.0%  40.3%   3.2%
               Live cube rollout: -1.125
               95% confidence interval:
                  - money cubeless eq.: -0.958 0.011,
                  - live cube: -1.125 0.005.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 39753 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           3. R  bar/23 8/7(2)             Eq.: -1.124 (-0.039)
               0.1%   3.3%  20.4%    79.6%  37.9%   2.8%
               Live cube rollout: -1.117
               95% confidence interval:
                  - money cubeless eq.: -0.965 0.013,
                  - live cube: -1.117 0.005.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 29166 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           4. 3  bar/23 5/4(2)             Eq.: -1.116 (-0.031)
               0.1%   3.6%  19.4%    80.6%  35.9%   2.0%
               Full 3-ply, 100%.
           5. 3  bar/23 9/8(2)             Eq.: -1.116 (-0.031)
               0.1%   3.4%  19.3%    80.7%  35.6%   2.1%
               Full 3-ply, 100%.
           6. 3  bar/24 9/6                Eq.: -1.121 (-0.036)
               0.1%   4.3%  21.0%    79.0%  38.9%   2.6%
               Full 3-ply, 100%.
           7. 3  bar/24 9/8(2) 6/5         Eq.: -1.124 (-0.039)
               0.1%   3.8%  20.4%    79.6%  38.1%   2.3%
               Full 3-ply, 100%.
           8. 2  bar/23 6/4                Eq.: -1.136 (-0.051)
               0.1%   3.5%  20.5%    79.5%  39.8%   2.7%

                  POSITION 4A
125








178

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Kit Woolsey 1



7 point match




Paul Weaver 0

                   POSITION 4B
122








178

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Kit Woolsey 1



7 point match




Paul Weaver 0

Only one roll after the loose hit from the bar was wrong in Position 3, the loose hit from the bar becomes correct in Position 4. I managed to make the wrong play in both positions, hitting when it was wrong in Position 3, and then playing safe when the hit was correct in Position 4.

The relevant difference between Positions 3 and 4 is that in Position 4 White is threatening to complete a 6-prime. If Blue chooses a non-hitting play, as shown in Position 4B, then White will have 20 rolls that cover his 7 point, thereby trapping four of Blue's checkers behind a 6-prime.

By putting White on the bar with B/24, 6/3*, as shown in Position 4A, Blue can reduce White's numbers that cover his 7 point from 20 to 11. Preventing White from completing his 6-prime is Blue's overriding concern in Position 4, and the Snowie rollout indicates that the hitting play is correct by .036 over B/24, 6/5, 8/7(2) and correct by .039 over B/23, 8/7(2).

                  POSITION 5

             Blue on Roll, Cube Action
134








117

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Kit Woolsey 3



7 point match




Paul Weaver 0

          Rollout      Money equity: 0.981
               2.8%  45.3%  78.1%    21.9%   5.9%   0.2%
               95% confidence interval:
                  - money cubeless eq.: 0.981 0.023,
                  - live cube no double: 1.175 0.016,
                  - live cube double take: 2.131 0.033.
               Rollout settings:
                  Full rollout,
                  324 games (equiv. 11591 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  seed 100, with race database.
          Evaluations
                1.  No double         1.193
                2.  Double, pass      1.000  (-0.193)
                3.  Double, take      2.129  (+0.936)
          Proper cube action: Too good to double, pass     17%
          Live cube
                1.  No double         1.175
                2.  Double, pass      1.000  (-0.175)
                3.  Double, take      2.131  (+0.956)
          Proper cube action: Too good to double, pass     16%

                  POSITION 5A
134








135

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Kit Woolsey 3



7 point match




Paul Weaver 0

                  POSITION 5B
129








109

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Kit Woolsey 3



7 point match




Paul Weaver 0

          3-Ply        Money equity: 0.553
               0.4%   9.1%  74.9%    25.1%   3.9%   0.2%
                1.  Double, take      0.923
                2.  No double         0.901  (-0.022)
                3.  Double, pass      1.000  (+0.077)
          Proper cube action: Double, take
In Position 5, the rollout suggests that Blue will win a gammon in 45% of the games that are played to conclusion. Blue's 55 on his previous shake has taken him abruptly from not good enough to double to too good to double.

Blue should hit loose with any 5. Even if White hits back with a deuce, Blue will still be able to cash the position as long as White enters only one checker (see Position 5A).

If White manages to anchor, as shown in Position 5B after the sequence Blue:62/White:32, then Blue should double and White has a close take. Although Blue is slightly worse off in Position 5B after a double/take than he would have been if he had cashed in Position 5, his 45% gammon winning chances in Position 5 make it worthwhile for him to play on for a gammon.

If Blue cashes in Position 5, he wins exactly 1.0; if he plays on, he will win about 1.18, on average, according to the Snowie rollout. My not playing on for the gammon was a serious blunder.

                  POSITION 6

157








160

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Kit Woolsey 3



7 point match




Paul Weaver 1

           1. R  24/14                     Eq.: -0.159
               0.3%   9.7%  47.2%    52.8%  15.6%   0.6%
               Live cube rollout: -0.162
               95% confidence interval:
                  - money cubeless eq.: -0.118 0.008,
                  - live cube: -0.162 0.012.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 112264 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           2. R  8/2* 6/2                  Eq.: -0.207 (-0.048)
               0.5%  13.9%  43.9%    56.1%  15.9%   0.7%
               Live cube rollout: -0.216
               95% confidence interval:
                  - money cubeless eq.: -0.144 0.008,
                  - live cube: -0.216 0.013.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 122120 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.

                  POSITION 6A

157








150

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Kit Woolsey 3



7 point match




Paul Weaver 1

                  POSITION 6B

159








150

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Kit Woolsey 3



7 point match




Paul Weaver 1

                  POSITION 6C

161








167

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Kit Woolsey 3



7 point match




Paul Weaver 1

           1. 3  8/2* 6/2                  Eq.:  0.034
               0.5%  13.9%  50.5%    49.5%  12.1%   0.4%
               Full 3-ply, 100%.
           2. 3  24/14                     Eq.: -0.102 (-0.136)
               0.3%   9.4%  48.5%    51.5%  13.2%   0.4%
               Full 3-ply, 100%.
As a response to the opening roll after the sequence 51/64, it is well known that Blue should point on White's face, playing 8/2*, 6/2 with 64 in Position 6C. Although the 2 point is a deep point, the hit is correct because it leaves no return shots while giving White four fanning numbers and providing White with only four numbers from the bar (11, 33, 44, and 55) that make a new offensive point. In fact, all other plays are blunders, giving up more than 0.10 in equity.

Position 6, however, is quite different. White owns his 5 point, Blue owns his 7 point, and Blue's 8-point is stripped. If Blue makes his deuce point, as shown in Position 6B, then he will have to leave a blot on his 8 point, giving White five return shots that send a third checker back. Even if he is not hit, Blue may have a difficult time cleaning up the blot on his 8 point, especially if White rolls one of his six numbers (32, 43, 54) that give him an advanced anchor.

Running with 24/14, as shown in Position 6A, is a better play. Notice the partial duplication of 2's. White's 42, 32, 21, and 22, play well in any case, leaving only four nonduplicated hitting 2's (52 and 62). After running, Blue will have either one or two checkers back, but after hitting 8/2* 6/2 Blue will have either two or three checkers back.

Blue must respect the strength of White's 5 point and make the play that minimizes contact, trying to capitalize on his 7 pip racing advantage. My play, 8/2* 6/2, gives up about 0.05 in cubeless equity.

                  POSITION 7

132








116

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Kit Woolsey 4



7 point match




Paul Weaver 1

           1. R  13/5                      Eq.:  0.215
               0.6%  13.3%  54.7%    45.3%   5.8%   0.3%
               Live cube rollout: 0.180
               95% confidence interval:
                  - money cubeless eq.: 0.173 0.013,
                  - live cube: 0.180 0.021.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 38106 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           2. R  8/2 4/2                   Eq.:  0.172 (-0.043)
               0.5%  11.4%  54.4%    45.6%   7.8%   0.4%
               Live cube rollout: 0.151
               95% confidence interval:
                  - money cubeless eq.: 0.125 0.012,
                  - live cube: 0.151 0.020.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 46024 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           3. R  8/2 8/6                   Eq.:  0.160 (-0.055)
               0.5%  12.2%  53.9%    46.1%   7.9%   0.4%
               Live cube rollout: 0.143
               95% confidence interval:
                  - money cubeless eq.: 0.121 0.012,
                  - live cube: 0.143 0.021.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 39128 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.

                  POSITION 7A

132








108

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Kit Woolsey 4



7 point match




Paul Weaver 1

                  POSITION 7B

132








108

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Kit Woolsey 4



7 point match




Paul Weaver 1

                  POSITION 7C

132








108

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Kit Woolsey 4



7 point match




Paul Weaver 1

Blue leads by 24 pips in Position 7 after playing his 62, but he has no spares on his 20 point, midpoint, or 8 point. One of these points has to go, but which one? I believe that many, if not most, strong players would make the wrong play in Position 7.

The correct play, 13/5, as shown in Position 7A, involves leaving a voluntary double shot, giving White 24 hitting numbers. However, these 24 numbers are far from winners, because White has a blot in his board that can be covered with only 4 of the 24 hitting numbers. After being hit, Blue will have both attacking and racing chances.

But why leave a 24 number shot when there are safer plays? Blue must look ahead and see that if he waits to leave a shot, his lead in the race in the mutual holding game may soon turn into a liability instead of an asset. Blue's only safe play, 8/2 8/4 (Position 7C), leaves him with no safe 6's next turn, except for 66. It will be worse for Blue if he plays a 6 from his midpoint on his next turn than this turn because he may have two blots in his board instead of one, he will not have his 8 point, and White will probably be closer to covering his 2 point blot.

The compromise play that I made, 8/2 4/2 (Position 7B), is slightly better than the safe play 8/2 8/4, but it still has the weakness of leaving Blue with few good options on his next roll.

The Snowie rollout indicates that 13/5 is better than 8/2 4/2 by 0.043 and better than 8/2 8/6 by 0.055.

                  POSITION 8

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Paul Weaver 1

           1. R  13/8 13/9                 Eq.:  0.169
               0.3%   9.4%  54.4%    45.6%   5.4%   0.3%
               Live cube rollout: 0.113
               95% confidence interval:
                  - money cubeless eq.: 0.128 0.011,
                  - live cube: 0.113 0.018.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 49294 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           2. R  20/15 8/4                 Eq.: -0.044 (-0.213)
               0.7%  14.8%  49.0%    51.0%  15.7%   0.8%
               Live cube rollout: -0.085
               95% confidence interval:
                  - money cubeless eq.: -0.031 0.014,
                  - live cube: -0.085 0.024.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 41674 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.
           3. R  13/4                      Eq.: -0.056 (-0.225)
               0.4%  11.1%  47.7%    52.3%   8.8%   0.5%
               Live cube rollout: -0.089
               95% confidence interval:
                  - money cubeless eq.: -0.023 0.016,
                  - live cube: -0.089 0.027.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 27071 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  settlement 0.550 at 4 pts,
                  seed 100, with race database.

                  POSITION 8A

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7 point match




Paul Weaver 1

                  POSITION 8B

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7 point match




Paul Weaver 1

Paul Magriel sometimes refers to a checker play error of 0.10 or more as a “whopper”, and a checker play error of 0.20 or more as a “double whopper.” My error is Position 8 was my only “double whopper” of the match.

With a 54 to play in Position 8, the only “safe” plays require the unacceptable concession of Blue's breaking a point in his inner board. Blue needs to keep his 5 point board in order to have an advantage if there is an exchange of hits within the next few rolls.

The best play, 13/8 13/9 (shown in Position 8A) leaves Blue's blot exposed to 11 numbers. This is an acceptable risk, because only 5 of these numbers also cover White's deuce point blot. Even after White rolls one of his 5 hit and cover numbers, Blue's anchor and standing in the race will keep him in the game. If missed, Blue has a good chance of being able to play his next two rolls safely while maintaining his five point board.

I chose 20/15 8/4 (Position 8B) because I thought I was running out of time and I was seduced by the duplication of White's 3's. This play gives White nine numbers that both hit and cover, putting Blue on the roof against a four point board without an anchor. Even if Blue is missed, he has no guarantee of being able to clean up his two blots on his next rolls.

The Snowie rollout indicates that the size of my “double whopper” blunder was 0.213.

                  POSITION 9

             Blue on Roll, Cube Action

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7 point match




Paul Weaver 1

          Rollout      Money equity: 0.482
               1.4%  18.9%  67.4%    32.6%   6.6%   0.4%
               95% confidence interval:
                  - money cubeless eq.: 0.482 0.026,
                  - live cube no double: 0.951 0.027,
                  - live cube double take: 0.992 0.029.
               Rollout settings:
                  Full rollout,
                  324 games (equiv. 7037 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  seed 100, with race database.
          Evaluations
                1.  Double, take      0.993
                2.  No double         0.890  (-0.103)
                3.  Double, pass      1.000  (+0.007)
          Proper cube action: Double, take
          Live cube
                1.  Double, take      0.992
                2.  No double         0.951  (-0.041)
                3.  Double, pass      1.000  (+0.008)
          Proper cube action: Double, take

In Position 9 Blue has several advantages: he leads by 20 pips, has a stronger board, has a well-placed builder on his 10 point, and has almost escaped one of his back checkers. I correctly doubled.

For money, the double/no double is a very close issue. The Snowie rollout indicates that Blue's equity is very close to 0.73 whether he doubles or leaves the cube in the center.

At the given match score (Blue needs 6, White needs 2), Blue's gammons are very useful but White's gammons do not help him at all once the cube has been turned. Also, White has no recube vig. For these reasons Blue will double much earlier and White will also pass much earlier at the given score than for money. The rollout indicates that the take/pass is a marginal decision at the given score.

These rollout results provide us with a very useful piece of information: a position with a 19% gammon rate, worth .73 for money, and a marginal initial double for money, is a marginal take/pass at the 2-away/6-away score.

At the 2-away/4-away score Position 9 would be a huge pass.

                  POSITION 10

              Blue on Roll, Cube Action

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7 point match




Paul Weaver 4

          Rollout      Money equity: 0.284
               0.8%  23.0%  57.2%    42.8%   9.5%   0.2%
               95% confidence interval:
                  - money cubeless eq.: 0.284 0.028.
               Rollout settings:
                  Full rollout,
                  324 games (equiv. 8762 games),
                  played 3-ply (medium, 33%),
                  seed 100, with race database.
                1.  Double, take      0.710
                2.  No double         0.589  (-0.121)
                3.  Double, pass      1.000  (+0.290)
          Proper cube action: Double, take

Although Blue trails by 9 pips in Position 10, he is still the favorite in the position because of his stronger board and White's two exposed blots. Blue has 11 numbers that hit White's blot on Blue's 11 point, and 9 additional numbers that point on White's face. Blue's 6's cover his 7 point, and 66 is a joker. Indeed, 23% of the games will result in Blue winning a gammon.

Blue doubles much earlier at this score (Blue needs 3, White needs 2) than for money for the same reasons given in the discussion of Position 9: White's gammons with the cube turned do not count, and White has no recube vig.

Although the double would be early for money, giving up about 0.13, at the given score the double is mandatory. My failure to double cost me about 0.12. White's current lead in the race, and Blue's two back checkers still on the 24 point make the position a clear take.

                  POSITION 11

             Blue on Roll, Cube Action

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7 point match




Paul Weaver 4

          Rollout      Money equity: 0.329
               0.7%  24.4%  58.7%    41.3%   9.1%   0.4%
               95% confidence interval:
                  - money cubeless eq.: 0.329 0.027,
                  - live cube no double: 0.707 0.027,
                  - live cube double take: 0.828 0.034.
               Rollout settings:
                  Full rollout,
                  324 games (equiv. 8350 games),
                  played 3-ply (medium, 33%), cube 3-ply,
                  seed 100, with race database.
          Evaluations
                1.  Double, take      0.828
                2.  No double         0.664  (-0.164)
                3.  Double, pass      1.000  (+0.172)
          Proper cube action: Double, take
          Live cube
                1.  Double, take      0.828
                2.  No double         0.707  (-0.121)
                3.  Double, pass      1.000  (+0.172)
          Proper cube action: Double, take

Position 11 arose from Position 10 after Blue's 43 and White's 62. The same concepts discussed mentioned in Position 10 also apply in Position 11, but once again I failed to double.

Blue now has a 3 point board with several attacking jokers (33 66 64 62 53 44 and 22) and he should hit loose with several other numbers. Blue will win a gammon in 24% of the games played to conclusion.

Although once again the double would be premature for money, it is mandatory at the match score (Blue needs 3, White needs 2). Failing to double costs Blue equity in the range of 0.12 to 0.16.

                  POSITION 12

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Paul Weaver 4

           1. R  13/10 8/2*                Eq.:  0.326
               0.8%  23.5%  55.2%    44.8%  11.0%   0.5%
               95% confidence interval:
                  - money cubeless eq.: 0.231 0.010.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 77641 games),
                  played 3-ply (medium, 33%),
                  seed 100, with race database.
           2. R  24/21 8/2*                Eq.:  0.291 (-0.035)
               0.8%  22.3%  54.9%    45.1%  10.6%   0.5%
               95% confidence interval:
                  - money cubeless eq.: 0.218 0.009.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 93145 games),
                  played 3-ply (medium, 33%),
                  seed 100, with race database.
           3. R  24/15                     Eq.:  0.226 (-0.100)
               0.6%  15.7%  55.3%    44.7%   9.8%   0.4%
               95% confidence interval:
                  - money cubeless eq.: 0.168 0.009.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 70714 games),
                  played 3-ply (medium, 33%),
                  seed 100, with race database.
           4. R  24/21 13/7                Eq.:  0.208 (-0.118)
               0.7%  18.8%  53.8%    46.2%  10.4%   0.4%
               95% confidence interval:
                  - money cubeless eq.: 0.162 0.010.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 66329 games),
                  played 3-ply (medium, 33%),
                  seed 100, with race database.
           5. R  24/18 13/10               Eq.:  0.206 (-0.120)
               0.7%  16.7%  54.7%    45.3%  10.9%   0.5%
               95% confidence interval:
                  - money cubeless eq.: 0.154 0.010.
               Rollout settings:
                  Truncated rollout, depth 8,
                  324 games (equiv. 58922 games),
                  played 3-ply (medium, 33%),
                  seed 100, with race database.

                  POSITION 12A

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7 point match




Paul Weaver 4

                  POSITION 12B

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7 point match




Paul Weaver 4

In Position 12, after incorrectly failing to double, I rolled a 63. In making the beginner's play 24/15 (Position 12B) I failed to take advantage of the strength of my three point board, and I gave my opponent more good numbers than if I had hit loose with 13/10 8/2*.

Although it is frequently incorrect to break the 8 point to hit loose with a 6, in Position 12 the loose hit is correct by a large margin. After hitting 8/2* with the 6, bringing down a builder with 13/10 (shown in Position 12A) is better than splitting with the 3 because it reduces the number of double hits White has from the roof.

Why is the loose hit (13/10 8/2*) better than the running play (24/15)? After the running play, 34 of White's 36 numbers (all except 51) play constructively, allowing White to either hit or make a new point. After White makes a new point, it will be much riskier for Blue to attack. With Blue's current three to one advantage in inner board points, the time to attack is now.

After hitting loose with 13/10 8/2*, White will have 15 return shots, 9 fans, and 12 misentries. Blue's stronger board will keep him in the game after White hits one of the 15 return shots, Blue will retain both attacking and racing options after the 12 misentries, and Blue is in the driver's seat with his sights on a gammon after the 9 fans.

My beginner's running play was a blunder of “whopper” proportion, costing equity of about 0.10.

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