BACKGAMMON BY THE BAY

Game #9

Open Division Final
San Mateo, California
18 May 1997
11 Point Match

Daniel Murphy (Black) vs. Kit Woolsey (White)
Score: 3 - 2

Analysis by Steve Clark

Each of the finalists of the May BGBB tourney finals has made a point of sharing his analytical backgammon insights with grateful students of the game. Daniel Murphy, Captain of the FIBS City Challenge San Francisco team and a recent semi-finalist in David Escoffery's FIBS Spring Tourney, is well-known for his informative and cogent, and frequently evocative, postings to rec.games.backgammon. Kit Woolsey has authored many articles and books on backgammon, is one of the co-authors of MatchQuiz, and is remembered fondly by all of us privileged to have been present at his in-person or on-FIBS match commentaries.


Play 1a
+-------------+---+-------------+
| X         O |   |   O       X |
| X         O |   |   O       X |
|           O |   |   O       X |
|           O |   |           X |  167
|           O |   |           X |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |           O |
|           X |   |           O |  167
|           X |   |   X       O |
| O         X |   |   X       O |
| O         X |   |   X       O |
+-------------+---+-------------+
    Black to play 65
Candidate Plays    Equities
24/13                +0.071
24/18 13/8           +0.028
SC: Black makes the normal play of 24/13. Kent Goulding (KG) often speaks of the merits of playing the split in this position, but no one really listens.

Black White
1. 65: 24/13
Play 1b
+-------------+---+-------------+
| X         O |   |   O       X |
|           O |   |   O       X |
|           O |   |   O       X |
|           O |   |           X |  167
|           O |   |           X |
|             |   |           X | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |           O |
|           X |   |           O |  156
|           X |   |   X       O |
| O         X |   |   X       O |
| O         X |   |   X       O |
+-------------+---+-------------+
    White to play 21
Candidate Plays    Equities
13/11 6/5            -0.141
13/11 24/23          -0.141
24/21                -0.163
13/10                -0.167
24/22 6/5            -0.183
24/22 24/23          -0.186
6/4 24/23            -0.207
8/5                  -0.216
8/6 24/23            -0.227
SC: Playing 13/11 is clear. It brings a builder down while making escape more difficult. The two candidates for the ace are 6/5, trying to build the 5 point but risking being hit, and 24/23, which makes it harder for Black to come in safely but does not build a board so easily. Either play is good here.

Black White
1. ... 21: 13/11 6/5
Play 2a
+-------------+---+-------------+
| X       O O |   |   O     O X |
|           O |   |   O       X |
|           O |   |   O       X |
|           O |   |           X |  164
|             |   |           X |
|             |   |           X | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |           O |  156
|           X |   |   X       O |
| O         X |   |   X       O |
| O         X |   |   X       O |
+-------------+---+-------------+
    Black to play 42
Candidate Plays    Equities
24/20* 13/11         +0.212
24/20*/18            +0.173
24/20* 8/6           +0.114
24/20* 6/4           +0.093
SC: Hitting and playing 13/11 is clear. Moving a builder to the 11 point early in the game is quite valuable. It provides diversification and interferes with your opponent's attempts to escape.

Black White
2. 42: 24/20* 13/11
Play 2b
+-------------+---+-------------+
|         X O |   |   O     O X |
|           O |   |   O       X |
|           O |   |   O       X |
|           O |   |           X |  184
|             |   |           X |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X | O |             |
|           X |   |           O |  150
|           X |   |   X       O |
| O         X |   |   X       O |
| O         X |   |   X     X O |
+-------------+---+-------------+
    White to play 31
Candidate Plays    Equities
Bar/22 6/5*          -0.233
Bar/24 8/5*          -0.290
SC: Here the hit on the 5 point should be made from the 6. This leaves White's builders spread around more evenly.

Not hitting here would be a big mistake. It is important to interfere with your opponent's attempts to escape when you are already behind. Hitting gives you a better chance of making the all-important 5 point. It keeps your opponent from making a point unless he rolls doubles. And since you are already well behind in the race, getting hit is not as bad as usual.


Black White
2. ... 31: Bar/22 6/5*
Play 3a
+-------------+---+-------------+
|         O O |   |   O     O X |
|           O |   |   O       X |
|           O |   |   O       X |
|             |   |           X |  180
|             | X |           X |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |           O |  155
|           X |   |   X       O |
| O         X |   |   X       O |
| O   O     X |   |   X     X O |
+-------------+---+-------------+
    Black to play 32
Candidate Plays    Equities
Bar/20*              +0.276
Bar/22 13/11         +0.201

Black White
3. 32: Bar/20*
Play 3b
+-------------+---+-------------+
|         X O |   |   O     O X |
|           O |   |   O       X |
|           O |   |   O       X |
|             |   |           X |  200
|             |   |           X |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X | O |             |
|           X |   |           O |  150
|           X |   |   X       O |
| O         X |   |   X       O |
| O   O     X |   |   X     X O |
+-------------+---+-------------+
    White to play 32
Candidate Plays    Equities
Bar/22 13/11         -0.292
Bar/23 8/5*          -0.298
Bar/22 24/22         -0.352
Bar/22 11/9          -0.350
Bar/22 8/6           -0.364
Bar/22 6/4           -0.365
SC: Here are two choices which are just about "pick 'em." Bar/22 13/11 puts your position together well, but the resulting position is clearly inferior. The alternative of Bar/23, 8/5 tries for more, but risks more as well.

Black White
3. ... 32: Bar/23 8/5*
Play 4a
+-------------+---+-------------+
|         O O |   |   O     O X |
|           O |   |   O       X |
|           O |   |           X |
|             |   |           X |  195
|             | X |           X |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |           O |  155
|           X |   |   X       O |
| O         X |   |   X       O |
| O O O     X |   |   X     X O |
+-------------+---+-------------+
    Black to play 51
Candidate Plays    Equities
Bar/20* 11/10        +0.323
Bar/20* 6/5          +0.277
Bar/20* 8/7          +0.262
Bar/24 13/8          +0.216
SC: Again the play is clear. Other aces after the hit leave White with too many chances to hit back in White's backcourt.

Black White
4. 51: Bar/20* 11/10
Play 4b
+-------------+---+-------------+
|         X O |   |   O     O X |
|           O |   |   O       X |
|           O |   |           X |
|             |   |           X |  215
|             |   |           X |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X | O |             |
|           X |   |           O |  149
|           X |   |   X       O |
| O         X |   |   X       O |
| O O O     X |   |   X   X   O |
+-------------+---+-------------+
    White to play 32
Candidate Plays    Equities
Bar/22 13/11         -0.353
Bar/23 8/5*          -0.___
Bar/22 23/21         -0.394
Bar/22 24/22         -0.401
Bar/23 13/10         -0.414
Bar/22 6/4           -0.421
Bar/23 11/8          -0.423
Bar/22 11/9          -0.430
Bar/23 24/21         -0.430
Bar/22 8/6           -0.439
SC: Now making the 22 and 11 points is clear, yielding White a defensible position. The alternative of hitting is no longer attractive. White has too few checkers in his front court to build much of board for a while, so hitting just weakens what little he has.

Black White
4. ... 32: Bar/22 13/11
Play 5a
+-------------+---+-------------+
|         X O |   |   O     O X |
|           O |   |   O     O X |
|           O |   |           X |
|             |   |           X |  21O
|             |   |           X |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  149
|           X |   |   X       O |
| O   O     X |   |   X       O |
| O O O     X |   |   X   X   O |
+-------------+---+-------------+
    Black to play 41
Candidate Plays    Equities
13/9 10/9            +0.334
20/15                +0.252
SC: What else.

Black White
5. 41: 13/9 10/9
Play 5b
+-------------+---+-------------+
|         X O |   |   O     O X |
|           O |   |   O     O X |
|           O |   |           X |
|             |   |           X |  21O
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  144
|           X |   |   X       O |
| O   O     X |   |   X X     O |
| O O O     X |   |   X X     O |
+-------------+---+-------------+
    White to play 63
Candidate Plays    Equities
11/5* 8/5            -0.329
11/5* 24/21          -0.363
11/5* 23/20          -0.365
11/5* 11/8           -0.379
11/5* 13/10          -0.388
24/15                -0.___
24/18 23/20          -0.394
24/18 24/21          -0.416
24/18 8/5*           -0.420
13/7 8/5*            -0.430
SC: Make the 5 point. Nothing else comes close.

Black White
5. ... 63: 11/5* 8/5
Play 6a
+-------------+---+-------------+
|         O O |   |   O     O X |
|         O O |   |           X |
|           O |   |           X |
|             |   |           X |  2O1
|             | X |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  149
|           X |   |   X       O |
| O   O     X |   |   X X     O |
| O O O     X |   |   X X     O |
+-------------+---+-------------+
    Black to play 32
Candidate Plays    Equities
Bar/22 13/11         +0.296
Bar/23 13/10         +0.279
Bar/22 8/6           +0.252
Bar/22 6/4           +0.230
SC: Notice how slotting on the 11 point comes out better than slotting on the 10. If you study rollouts, you will see this over and over.

Black White
6. 32: Bar/22 13/11
Play 6b
+-------------+---+-------------+
|     X   O O |   |   O     O X |
|         O O |   |           X |
|           O |   |           X |
|             |   |             |  2O1
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  144
|           X |   |   X       O |
| O   O     X |   |   X X     O |
| O O O     X |   |   X X   X O |
+-------------+---+-------------+
    White to play 65
Candidate Plays    Equities
24/18 8/3*           -0.328
24/18 23/18          -0.329
24/18 13/8           -0.341
11/5 8/3*            -0.347
13/7 8/3*            -0.379
11/5 13/8            -0.370
SC: The top four candidate plays come out close. White is going to have an inferior position regardless, because he has so many checkers back and not enough up front to build a strong board. With Black's board being so weak, the various reasonable plays come out about the same. The hitting plays interfere with Black's ability to build more points, and the structure plays give White a position from which to defend. I would not criticize any of the top four plays.

Black White
6. ... 65: 24/18 8/3*
Play 7a
+-------------+---+-------------+
|     O   O O |   |         O X |
|         O O |   |           X |
|           O |   |           X |
|             |   |             |  190
|             | X |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  147
|           X |   |   X       O |
|     O     X |   |   X X     O |
| O O O     X |   | O X X   X O |
+-------------+---+-------------+
    Black to play 42
Candidate Plays    Equities
Bar/21 13/11         +0.335
Bar/21 11/9          +0.341
Bar/23 11/7*         +0.284
Bar/23 13/9          +0.274
SC: The tie in the two top plays demonstrates that the 11 point has just about as much value as having an extra builder on the 9 point. Black really needs inner board points here, rather than the 11 point. He also needs to get those checkers off the 6 point so as to better combat the back game. Even so, making the 11 point comes in for a tie in the equities.

Hitting on the 7 point is close, but does not accomplish as much as usual because White has so many return shots. Even with his misses, White will be able to make valuable points.


Black White
7. 42: Bar/23 11/7* 62: Bar/23 24/18*
Play 8a
+-------------+---+-------------+
|   X O   O O |   |         O X |
|         O O |   |           X |
|           O |   |           X |
|             |   |             |  189
|             | X |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  159
|           X |   |   X       O |
|   O O     X |   |   X X     O |
|   O O     X |   | O X X     O |
+-------------+---+-------------+
    Black to play 54
Candidate Plays    Equities
Bar/21 13/8          +0.233
Bar/21 23/18         +0.226
Bar/16               +0.209
Bar/21 9/4           +0.041
SC: This demonstrates what was wrong with hitting on the 7 point last turn. Black has no trouble coming in and moving about, but is unable to build anything useful. It is hard to see any superiority in the top three candidate plays.

Black White
8. 54: Bar/16
Play 8b
+-------------+---+-------------+
|   X O   O O |   |     X   O X |
|         O O |   |           X |
|           O |   |           X |
|             |   |             |  189
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  150
|           X |   |   X       O |
|   O O     X |   |   X X     O |
|   O O     X |   | O X X     O |
+-------------+---+-------------+
    White to play 43
Candidate Plays    Equities
13/9* 6/3            -0.120
22/18 6/3            -0.252
SC: With rolls like this, backgammon is an easy game.

Black White
8. ... 43: 13/9* 6/3
Play 9a
+-------------+---+-------------+
|   X O   O O |   |     O   O X |
|     O   O O |   |           X |
|             |   |           X |
|             |   |             |  182
|             | X |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  159
|           X |   |   X         |
|   O O     X |   |   X X     O |
|   O O     X |   | O X X     O |
+-------------+---+-------------+
    Black to play 43
Candidate Plays    Equities
Bar/18               +0.079
Bar/21 13/10         +0.020
SC: No point in creating a third loose checker. Black will probably be hit if he plays Bar/18, but White is too far back to be really threatening. The blot on the 10 point is just an invitation to have a third checker sent back.

Black White
9. 43: Bar/21 13/10
Play 9b
+-------------+---+-------------+
|   X O X O O |   |     O   O X |
|     O   O O |   |           X |
|             |   |             |
|             |   |             |  182
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  157
|           X |   |   X         |
|   O O     X |   |   X X     O |
|   O O     X |   | O X X X   O |
+-------------+---+-------------+
    White to play 32
Candidate Plays    Equities
18/15* 11/9          +0.041
18/15* 23/21         +0.031
18/15* 22/20         +0.023
18/15*/13            +0.006
SC: Again Black's lack of inner points gives White a fair amount of flexibility in his plays here. White can build a very useful 9 point, or he can try for an advanced anchor. White may have flexibility, but this does not mean that he has a significant advantage, even after the hit. He still is too far back to be more than a very small favorite.

Black White
9. ... 32: 18/15* 11/9
10. 21: Bar/24 23/21
Play 10b
+-------------+---+-------------+
| X   O X O O |   |     O     X |
|     O X O O |   |     O     X |
|             |   |             |
|             |   |             |  177
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  164
|           X |   |   X         |
|   O O     X |   |   X X     O |
|   O O     X |   |   X X O   O |
+-------------+---+-------------+
    White to play 54
Candidate Plays    Equities
23/18 22/18          +0.027
23/18 15/11          -0.045
22/13                -0.048
23/14                -0.054
SC: No second choice.

Black White
10. ... 54: 23/18 22/18
11. 21: 24/21
Play 11b
+-------------+---+-------------+
|     O X O O |   |     O     X |
|     O X O O |   |     O     X |
|       X     |   |             |
|             |   |             |  168
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  161
|           X |   |   X         |
|           X |   | O X X     O |
|   O O     X |   | O X X O   O |
+-------------+---+-------------+
    White to play 41
Candidate Plays    Equities
22/18 15/14          +0.052
23/18                +0.052
15/11 23/22          +0.029
15/11 22/21          +0.016
18/14 15/14          +0.001
15/10                -0.015
13/9 23/22           -0.026
SC: There is little to choose between the two top plays. Whits does not want to build the 22 point here. His 5's and 6's will be blocked, and he probably will be wanting to escape from it next roll.

Black White
11. ... 41: 22/18 15/14
12. 62: 21/13
Play 12b
+-------------+---+-------------+
|     O X O O |   |     O     X |
|     O X O O |   |     O     X |
|             |   |           X |
|             |   |             |  163
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  153
|           X |   | O X         |
|           X |   | O X X     O |
|   O       X |   | O X X   O O |
+-------------+---+-------------+
    White to play 54
Candidate Plays    Equities
18/9                 +0.001
23/14                -0.008
18/13 14/10          -0.008
14/5                 -0.015
13/8 18/14           -0.036
23/18 14/10          -0.060
14/9 13/9            -0.070
18/13 18/14          -0.085
23/18 13/9           -0.089
SC: 23/14 seems automatic here. The reason the other plays come out equal is that Black has no board. As a result, a trailer on the 23 point is not in very much danger and will interfere with Black slotting inner board points. Even if you are aware of this possibility at the table, 23/14 is clearly good and few players would be able to resist it.

Black White
12. ... 54: 23/14
Play 13a
+-------------+---+-------------+
|     O X O O |   |     O     X |
|     O X O O |   |     O     X |
|             |   |           X |
|             |   |             |  154
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  153
|           X |   | O X         |
|           X |   | O X X   O O |
|           X |   | O X X   O O |
+-------------+---+-------------+
    Black to play 63
Candidate Plays    Equities
13/4                 -0.018
8/2 6/3              -0.059
9/3 9/6              -0.064
9/3 6/3              -0.108
9/3 8/5              -0.111
SC: 13/4 is automatic. It leaves no shots and starts the best point available under the circumstances.

Black White
13. 63: 13/4
Play 13b
+-------------+---+-------------+
|     O X O O |   |     O     X |
|     O X O O |   |     O     X |
|             |   |             |
|             |   |             |  154
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  144
|           X |   | O X         |
|           X |   | O X X   O O |
|       X   X |   | O X X   O O |
+-------------+---+-------------+
    White to play 32
Candidate Plays    Equities
18/15 13/11          -0.022
14/11 13/11          -0.023
13/8                 -0.026
18/13                -0.026
14/9                 -0.040
13/10 13/11          -0.037
9/6 13/11            -0.087
9/6 9/7              -0.107
SC: White can make a bunch of funny plays here with impunity, like 18/15/13/11 or 13/8, because Black has no board. Most everyone, like White does, will make one of the more mundane plays without noticing the funny stuff.

Black White
13. ... 32: 18/13
Play 14a
+-------------+---+-------------+
|     O X O O |   |     O     X |
|     O X O O |   |     O     X |
|             |   |             |
|             |   |             |  149
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|           X |   |             |
|           X |   |             |  144
|           X |   |   X       O |
|           X |   | O X X   O O |
|       X   X |   | O X X   O O |
+-------------+---+-------------+
    Black to play 52
Candidate Plays    Equities
8/3 6/4              -0.013
6/1 6/4              -0.046
8/3 4/2              -0.094
6/1 4/2              -0.099
9/4 6/4              -0.116
SC: Make a point and then slot the best point you can. These type of plays should be fairly automatic.

Black White
14. 52: 8/3 6/4
Play 14b
+-------------+---+-------------+
|     O X O O |   |     O     X |
|     O X O O |   |     O     X |
|             |   |             |
|             |   |             |  149
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|           X |   |             |  137
|           X |   |           O |
|       X   X |   | O X X   O O |
|     X X   X |   | O X X   O O |
+-------------+---+-------------+
    White to play 42
Candidate Plays    Equities
13/9 13/11           -0.008
13/7                 -0.047
14/8                 -0.071
9/5 13/11            -0.131
SC: This is one of the more interesting positions of the game. White plays 13/7 because it minimizes shots and leaves only one blot. The rollouts favor 13/9 13/11, even though this leaves more blots and more shots. White's move comes out second best because Black will want to hit and start to escape. The other play does not offer such favorable opportunities for this.

When you see a result like this, it is important to recognize that the result is an exception to the general principles enumerated above.


Black White
14. ... 42: 13/7
Play 15a
+-------------+---+-------------+
|     O X O O |   | O   O     X |
|     O X O O |   |     O     X |
|             |   |             |
|             |   |             |  143
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|           X |   |             |  137
|           X |   |             |
|       X   X |   | O X X   O O |
|     X X   X |   | O X X   O O |
+-------------+---+-------------+
    Black to play 31
Candidate Plays    Equities
6/3 6/5              +0.024
8/5 6/5              -0.004
6/3 9/8              -0.041
9/6 9/8              -0.062
6/2                  -0.065
SC: Hitting can be rejected, because Black would have the weaker board and be prostrate before White's onslaught. Once the hit is rejected, the principle of making a point and slotting the next-best point again comes to the fore. Often making the 5 point is right even when leaving a blot, but here there is no particular need to take the risk when White already has a reasonable board.

Black White
15. 31: 6/3 6/5 62: 13/7 13/11
Play 16a
+-------------+---+-------------+
|     O X O O |   | O   O   O X |
|     O X O O |   | O   O     X |
|             |   |             |
|             |   |             |  135
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|             |   |             |  133
|             |   |             |
|     X X   X |   | O X X   O   |
|     X X X X |   | O X X   O   |
+-------------+---+-------------+
    Black to play 63
Candidate Plays    Equities
8/2 8/5              -0.035
9/3 9/6              -0.071
SC: Again, make the point and slot the next-best point.

Black White
16. 63: 9/3 9/6
Play 16b
+-------------+---+-------------+
|     O X O O |   | O   O   O X |
|     O X O O |   | O   O     X |
|             |   |             |
|             |   |             |  135
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|             |   |             |  124
|     X     X |   |             |
|     X X   X |   | O X     O   |
|     X X X X |   | O X     O   |
+-------------+---+-------------+
    White to play 55
Candidate Plays    Equities
18/8(2)              +0.352
18/13(2) 14/9(2)     +0.278
SC: Make the prime. Primes win.

Black White
16. ... 55: 18/8(2)
Play 17a
+-------------+---+-------------+
|     O X O O |   | O O O   O X |
|     O X O O |   | O O O     X |
|             |   |             |
|             |   |             |  115
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|             |   |             |  124
|     X     X |   |             |
|     X X   X |   |   X     O   |
|     X X X X |   |   X     O   |
+-------------+---+-------------+
    Black to play 22
Candidate Plays    Equities
8/2 3/1              -0.360
8/6 5/1 3/1          -0.371
8/4 3/1              -0.372
8/4 8/6 3/1          -0.373
8/2 6/4              -0.378
8/2 8/6              -0.379
5/1 4/2 3/1          -0.379
8/2 4/2              -0.383
4/2(2) 3/1(2)        -0.384
8/6 4/2(2) 3/1       -0.465

Black White
17. 22: 8/2 3/1
Play 17b
+-------------+---+-------------+
|     O X O O |   | O O O   O X |
|     O X O O |   | O O O     X |
|             |   |             |
|             |   |             |  115
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|             |   |             |  116
|           X |   |             |
|     X X   X |   |         O   |
| X X X X X X |   |   X     O   |
+-------------+---+-------------+
    White to play 43
Candidate Plays    Equities
14/10 14/11          +0.389
14/7                 +0.318
SC: White can afford to slot the back of the prime, because Black has so many blots. If Black had a better board, this would be a more interesting problem.

Black White
17. ... 43: 14/10 14/11
Play 18a
+-------------+---+-------------+
|     O X O O |   | O O O O O X |
|     O X O O |   | O O O   O X |
|             |   |             |
|             |   |             |  108
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|             |   |             |  116
|           X |   |             |
|     X X   X |   |             |
| X X X X X X |   |   X         |
+-------------+---+-------------+
    Black to play 21
Candidate Plays    Equities
8/5                  -0.453
13/11 6/5            -0.456
13/11 8/7            -0.459
13/11 13/12          -0.460
13/10                -0.461
5/2                  -0.465
4/2 6/5              -0.470
3/1 6/5              -0.470
4/2 8/7              -0.472
5/3 8/7              -0.474
SC: So many plays come out even in the rollouts because White will not leave a shot next roll (except on 66). In principle, the best move must involve 6/5. I would play 13/11 6/5 without giving this position much thought.

Black White
18. 21: 13/11 6/5
Play 18b
+-------------+---+-------------+
|     O X O O |   | O O O O O X |
|     O X O O |   | O O O   O   |
|             |   |             |
|             |   |             |  108
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|             |   |             |  113
|             |   |             |
|     X X X X |   |             |
| X X X X X X |   |   X     X   |
+-------------+---+-------------+
    White to play 63
Candidate Plays    Equities
11/5 10/7            +0.468
10/1                 +0.455
SC: Do you risk a joker (not a real strong joker), or do you weaken your position slightly? Pick 'em.

Black White
18. ... 63: 11/5 10/7
Play 19a
+-------------+---+-------------+
|     O X O O |   | O O O   O X |
|     O X O O |   | O O O       |
|         O   |   | O           |
|             |   |             |   99
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|             |   |             |  113
|             |   |             |
|     X X X X |   |             |
| X X X X X X |   |   X     X   |
+-------------+---+-------------+
    Black to play 63
Candidate Plays    Equities
8/2 13/10            -0.480
11/5 13/10           -0.485
13/4                 -0.485
13/7 8/5             -0.485
8/2 6/3              -0.486
11/2                 -0.486
13/7 5/2             -0.486
13/7 4/1             -0.486
13/7 11/8            -0.489
11/5 4/1             -0.498
SC: All plays are equal because White will leave no big shot. Actually, Black should make the 2 point here.

Black White
19. 63: 11/5 13/10
Play 19b
+-------------+---+-------------+
|     O X O O |   | O O O   O   |
|     O X O O |   | O O O       |
|         O   |   | O           |
|             |   |             |   99
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|             |   |             |  104
|         X   |   |             |
|     X X X X |   |             |
| X X X X X X |   |   X   X     |
+-------------+---+-------------+
    White to play. Double or roll?
Equity (centered)
White 88.5%  G  0.1%  BG 0.0%
Black 11.5%  G  0.2%  BG 0.0%
Equity (White): +0.769

Equity (Black owns cube)
White 69.5%  G  1.0%  BG 0.0%
Black 30.5%  G  0.3%  BG 0.0%
Equity (Black): -0.406

Equity (cubeless)
White 73.4%  G  1.9%  BG 0.0%
Black 26.6%  G  0.7%  BG 0.0%
Equity (White): +0.479
SC: Should White double? It is a general rule of thumb that you need a normal racing lead to double a 4-point holding game. White, with only a five pip advantage, does not have that lead. In compensation, however, he has a five-point prime and his checkers are as well placed as possible. As a result he has a cubeless equity of 0.479.

In positions such as this one, where the gammon percentages are low, this equity makes for a strong double, and White has one here. It is possible he thought his equity was lower because that is the normal situation when coming in against a 4-point game. Another possibility is that White might have thought that conservative cube decisions were justified if he felt he was the stronger player.

In any event this is a position, and a problem, well worth looking at.
 

JF: I would have doubled (level 7 evaluation).

Black White
19. ... Roll
Play 19b
+-------------+---+-------------+
|     O X O O |   | O O O   O   |
|     O X O O |   | O O O       |
|         O   |   | O           |
|             |   |             |   99
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|             |   |             |  104
|         X   |   |             |
|     X X X X |   |             |
| X X X X X X |   |   X   X     |
+-------------+---+-------------+
    White to play 31
Candidate Plays    Equities
11/8 7/6             +0.431
11/8 3/2             +0.431
11/7                 +0.421
5/2 7/6              +0.411
5/2 3/2              +0.411
7/3                  +0.395
5/1                  +0.391
9/6 9/8              +0.340
SC: All the reasonable plays come out the same. Note that 11/8 3/2 does well. The reason is that 3/2 improves White's position for the bearoff. This is always an important consideration and is often ignored.

Black White
19. ... 31: 11/8 7/6
Play 20a
+-------------+---+-------------+
|     O X O O |   | O O O       |
|     O X O O |   | O O O       |
|         O O |   |   O         |
|             |   |             |   95
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|             |   |             |  104
|         X   |   |             |
|     X X X X |   |             |
| X X X X X X |   |   X   X     |
+-------------+---+-------------+
    Black to play 21
Candidate Plays    Equities
5/2                  -0.504
5/3 8/7              -0.508
8/6 5/4              -0.509
10/7                 -0.510
8/6 10/9             -0.511
8/6 3/2              -0.511
5/3 10/9             -0.511
8/6 4/3              -0.512
4/2 10/9             -0.514
4/2 8/7              -0.514
3/1 10/9             -0.519
SC: My favored play of 5/2 did not even make the top 20 favorite plays in JellyFish level 5 evaluation.

Black White
20. 21: 8/6 10/9
Play 20b
+-------------+---+-------------+
|     O X O O |   | O O O       |
|     O X O O |   | O O O       |
|         O O |   |   O         |
|             |   |             |   95
|             |   |             |
|             |   |             | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | |   |
|             |   |             | +---+
|             |   |             |
|             |   |             |  101
|         X X |   |             |
|     X X X X |   |             |
| X X X X X X |   |     X       |
+-------------+---+-------------+
    White to play. Double or roll?
Equity (centered)
White 90.3%  G  0.1%  BG 0.0%
Black  9.7%  G  0.1%  BG 0.0%
Equity (White): +0.805

Equity (Black owns cube)
White 70.3%  G  2.0%  BG 0.0%
Black 29.7%  G  0.3%  BG 0.0%
Equity (Black): -0.422

Equity (cubeless)
White 74.0%  G  2.0%  BG 0.0%
Black 26.0%  G  0.6%  BG 0.0%
Equity (White): +0.495
SC: Here is the double. White's position has improved slightly from the last roll. Strong double.
 
JF: I would have doubled (level 7 evaluation).

Black White
20. ... Double -> 2
Play 21a
+-------------+---+-------------+
|     O X O O |   | O O O       |
|     O X O O |   | O O O       |
|         O O |   |   O         |
|             |   |             |   95
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |  101
|         X X |   |             |
|     X X X X |   |             | +---+
| X X X X X X |   |     X       | | 2 |
+-------------+---+-------------+ +---+
    Black to play. Accept or pass?
Equity (centered)
White 90.3%  G  0.1%  BG 0.0%
Black  9.7%  G  0.1%  BG 0.0%
Equity (White): +0.805

Equity (Black owns cube)
White 70.3%  G  2.0%  BG 0.0%
Black 29.7%  G  0.3%  BG 0.0%
Equity (Black): -0.422

Equity (cubeless)
White 74.0%  G  2.0%  BG 0.0%
Black 26.0%  G  0.6%  BG 0.0%
Equity (White): +0.495
SC: Clear take.
 
JF: I would have accepted (level 7 evaluation).

Black White
21. Accept
Play 21b
+-------------+---+-------------+
|     O X O O |   | O O O       |
|     O X O O |   | O O O       |
|         O O |   |   O         |
|             |   |             |   95
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |  101
|         X X |   |             |
|     X X X X |   |             | +---+
| X X X X X X |   |     X       | | 2 |
+-------------+---+-------------+ +---+
    White to play 65
Candidate Plays    Equities
8/2 6/1              +0.546
7/1 7/2              +0.532
SC: Clearing the 7 point is stronger than it seems. In many related positions it can be the right move, but not here, and few players would seriously consider it.

Black White
21. ... 65: 8/2 6/1
Play 22a
+-------------+---+-------------+
| O O O X O O |   | O O O       |
|     O X O O |   | O O O       |
|         O   |   |             |
|             |   |             |   84
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |  101
|         X X |   |             |
|     X X X X |   |             | +---+
| X X X X X X |   |     X       | | 2 |
+-------------+---+-------------+ +---+
    Black to play 41
Candidate Plays    Equities
9/4                  -0.592
6/2 9/8              -0.594
9/5 3/2              -0.598
6/2 5/4              -0.600
5/1 9/8              -0.601
5/1 3/2              -0.607
6/1                  -0.610
5/1 5/4              -0.613
6/2 4/3              -0.614
6/2 6/5              -0.617
SC: Positions like this one just prove than all plays come out the same. The reason that all rollouts tend to come out the same is that White will not leave a blot on his next roll. As a result, Black will be able to correct any little errors next turn.

Black White
22. 41: 6/2 9/8
Play 22b
+-------------+---+-------------+
| O O O X O O |   | O O O       |
|     O X O O |   | O O O       |
|         O   |   |             |
|             |   |             |   84
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |   96
|         X   |   |             |
|   X X X X X |   |             | +---+
| X X X X X X |   |   X         | | 2 |
+-------------+---+-------------+ +---+
    White to play 42
Candidate Plays    Equities
9/5 9/7              +0.553
5/1 3/1              +0.522
7/3 7/5              +0.517
SC: White can afford to clear from the rear because he has gained a more significant racing lead. If the race were closer at this point, the other possible plays would become more attractive. Even here, they are quite close to being correct. Each of these positions must be judged as to how the race stands.

Black White
22. ... 42: 9/5 9/7
Play 23a
+-------------+---+-------------+
| O O O X O O |   | O O         |
|     O X O O |   | O O         |
|         O   |   | O           |
|         O   |   |             |   78
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |   96
|         X   |   |             |
|   X X X X X |   |             | +---+
| X X X X X X |   |   X         | | 2 |
+-------------+---+-------------+ +---+
    Black to play 61
Candidate Plays    Equities
21/14                -0.572
21/15 8/7            -0.573
21/15 5/4            -0.577
21/15 2/1            -0.594
8/1                  -0.607
8/2 5/4              -0.609
21/15 6/5            -0.614
SC: Running here works only because of the blots on White's ace and deuce points. Even so, it does not gain much equity.

Black White
23. 61: 8/1
Play 23b
+-------------+---+-------------+
| O O O X O O |   | O O         |
|     O X O O |   | O O         |
|         O   |   | O           |
|         O   |   |             |   78
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |   89
|         X   |   |             |
| X X X X X X |   |             | +---+
| X X X X X X |   |             | | 2 |
+-------------+---+-------------+ +---+
    White to play 61
Candidate Plays    Equities
7/1 3/2              +0.601
8/2 8/7              +0.567
7/1 2/1              +0.564
SC: 8/2 seems to be best because it clears from the rear. Here, however, it reduces White's blocking power, and the resulting position is poorly diversified. As a result, 7/1 3/2 becomes more attractive.

Black White
23. ... 61: 7/1 3/2
Play 24a
+-------------+---+-------------+
| O O O X O O |   | O O         |
| O O   X O O |   | O O         |
|         O   |   |             |
|         O   |   |             |   71
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |   89
|         X   |   |             |
| X X X X X X |   |             | +---+
| X X X X X X |   |             | | 2 |
+-------------+---+-------------+ +---+
    Black to play 42
Candidate Plays    Equities
6/2 6/4              -0.679
5/1 6/4              -0.679
6/2 5/3              -0.681
6/2 3/1              -0.701
5/1 5/3              -0.694
6/2 4/2              -0.704
5/1 4/2              -0.705
5/1 3/1              -0.717
SC: As I said, it does not seem to matter what you play.

Black White
24. 42: 6/2 6/4
Play 24b
+-------------+---+-------------+
| O O O X O O |   | O O         |
| O O   X O O |   | O O         |
|         O   |   |             |
|         O   |   |             |   71
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |   83
|   X   X X   |   |             |
| X X X X X   |   |             | +---+
| X X X X X   |   |             | | 2 |
+-------------+---+-------------+ +---+
    White to play 31
Candidate Plays    Equities
6/3 6/5              +0.568
5/1                  +0.566
8/5 8/7              +0.533
5/2 3/2              +0.529
SC: Would you be able to play 6/3 6/5? I sure would have a tough time. 8/5 8/7 is very poorly diversified and 5/1 has a lot of wastage. Even so, 5/1 is tied for the lead because it does the most to prevent Black from escaping.

Black White
24. ... 31: 8/5 8/7
Play 25a
+-------------+---+-------------+
| O O O X O O |   | O           |
| O O   X O O |   | O           |
|         O   |   | O           |
|         O   |   |             |   67
|         O   |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |   83
|   X   X X   |   |             |
| X X X X X   |   |             | +---+
| X X X X X   |   |             | | 2 |
+-------------+---+-------------+ +---+
    Black to play 63
Candidate Plays    Equities
21/12                -0.504
21/15 5/2            -0.560
21/15 4/1            -0.562
SC: No second choice.

Black White
25. 63: 21/12 64: 7/1 5/1
26. 66: 21/3 12/6
Play 26b
+-------------+---+-------------+
| O O O   O O |   | O           |
| O O     O O |   | O           |
| O       O   |   |             |
| O       O   |   |             |   57
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |   50
|   X X X X   |   |             |
| X X X X X   |   |             | +---+
| X X X X X X |   |             | | 2 |
+-------------+---+-------------+ +---+
    White to play 41
Candidate Plays    Equities
7/3 5/4              -0.508
7/3 7/6              -0.546
7/3 6/5              -0.589
7/2                  -0.600
SC: Time after time you will see players move 7/3 7/6. Even many of the best players in the world will do this wrong. If you are doubtful about the best play here, study this position over and over. Slotting the 4 and 5 points is a must. The lower points can mostly be ignored, but the 4 and 5 points are critical.

Black White
26. ... 41: 7/3 5/4
Play 27a
+-------------+---+-------------+
| O O O O O O |   | O           |
| O O O   O O |   |             |
| O       O   |   |             |
| O           |   |             |   52
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |   50
|   X X X X   |   |             |
| X X X X X   |   |             | +---+
| X X X X X X |   |             | | 2 |
+-------------+---+-------------+ +---+
    Black to play. Double or roll?
Equity (Black owns cube)
Black 89.0%  G  0.0%  BG 0.0%
White 11.0%  G  0.0%  BG 0.0%
Equity (Black): +0.780

Equity (White owns cube)
Black 75.3%  G  0.0%  BG 0.0%
White 24.7%  G  0.0%  BG 0.0%
Equity (White): -0.505

Equity (cubeless)
Black 77.6%  G  0.0%  BG 0.0%
White 22.4%  G  0.0%  BG 0.0%
Equity (Black): +0.553
SC: Easy double.
 
JF: I would have doubled (level 7 evaluation).

Black White
27. Double -> 4
Play 27b
+-------------+---+-------------+ +---+
| O O O O O O |   | O           | | 4 |
| O O O   O O |   |             | +---+
| O       O   |   |             |
| O           |   |             |   52
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |   50
|   X X X X   |   |             |
| X X X X X   |   |             |
| X X X X X X |   |             |
+-------------+---+-------------+
    White to play. Accept or pass?
Equity (Black owns cube)
Black 89.0%  G  0.0%  BG 0.0%
White 11.0%  G  0.0%  BG 0.0%
Equity (Black): +0.780

Equity (White owns cube)
Black 75.3%  G  0.0%  BG 0.0%
White 24.7%  G  0.0%  BG 0.0%
Equity (White): -0.505

Equity (cubeless)
Black 77.6%  G  0.0%  BG 0.0%
White 22.4%  G  0.0%  BG 0.0%
Equity (Black): +0.553
SC: This probably is a money take, but not much of one. It is very close between a pass and a take.
 
JF: I would have accepted (level 7 evaluation).

Black White
27. ... Pass
Play 28a
+-------------+---+-------------+ +---+
| O O O O O O |   | O           | | 4 |
| O O O   O O |   |             | +---+
| O       O   |   |             |
| O           |   |             |   52
|             |   |             |
|             |   |             |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
|             |   |             |
|             |   |             |
|             |   |             |   50
|   X X X X   |   |             |
| X X X X X   |   |             |
| X X X X X X |   |             |
+-------------+---+-------------+
   
Black went on to win the match, 11-4.


The game was recorded on tape by Richard McIntosh, and transcribed by Steve Clark.

Rollouts were made by Richard McIntosh, using JellyFish Analyzer 2.02. Rollout results show equities for the player on move. Candidate plays were better than or within 0.100 equity of the actual plays, evaluated at level 7.

Parameter values for rollouts on moves were:

Standard deviations of equity estimates were between 0.002 and 0.007.

Parameter values for rollouts on cube decisions were:

Standard deviations of equity estimates were between 0.004 and 0.006.

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