Game #9
Open Division Final
San Mateo, California
18 May 1997
11 Point Match
Daniel Murphy (X) vs. Kit Woolsey (O)
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 |
+-------------+---+-------------+
|
|
X to play 65
Candidate Plays Equities
24/13 +0.071
24/18 13/8 +0.028
|
|
SC:
|
X 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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 X to come in safely
but does not build a board so easily.
Either play is good here.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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 O'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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X to play 32
Candidate Plays Equities
Bar/20* +0.276
Bar/22 13/11 +0.201
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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 O with too many chances
to hit back in O's backcourt.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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 O a defensible position.
The alternative of hitting is no longer attractive.
O has too few checkers in his front court
to build much of board for a while,
so hitting just weakens what little he has.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X to play 41
Candidate Plays Equities
13/9 10/9 +0.334
20/15 +0.252
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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.
O 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 X's board being so weak,
the various reasonable plays come out about the same.
The hitting plays interfere with X's ability to build more points,
and the structure plays give O a position from which to defend.
I would not criticize any of the top four plays.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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.
X 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 O has so many return shots.
Even with his misses,
O will be able to make valuable points.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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.
X 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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.
X will probably be hit if he plays Bar/18,
but O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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 X's lack of inner points gives O a fair amount
of flexibility in his plays here.
O can build a very useful 9 point,
or he can try for an advanced anchor.
O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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 X has no board.
As a result,
a trailer on the 23 point is not in very much danger
and will interfere with X 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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:
|
O can make a bunch of funny plays here with impunity,
like 18/15/13/11 or 13/8,
because X has no board.
Most everyone, like O does,
will make one of the more mundane plays without noticing the funny stuff.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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.
O 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.
O's move comes out second best
because X 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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 X would have the weaker board
and be prostrate before O'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 O already has a reasonable board.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O to play 43
Candidate Plays Equities
14/10 14/11 +0.389
14/7 +0.318
|
|
SC:
|
O can afford to slot the back of the prime,
because X has so many blots.
If X had a better board,
this would be a more interesting problem.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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 O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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 O will leave no big shot.
Actually,
X should make the 2 point here.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O to play. Double or roll?
Equity (centered)
O 88.5% G 0.1% BG 0.0%
X 11.5% G 0.2% BG 0.0%
Equity (O): +0.769
Equity (X owns cube )
O 69.5% G 1.0% BG 0.0%
X 30.5% G 0.3% BG 0.0%
Equity (X): -0.406
Equity (cubeless)
O 73.4% G 1.9% BG 0.0%
X 26.6% G 0.7% BG 0.0%
Equity (O): +0.479
|
|
SC:
|
Should O double?
It is a general rule of thumb that you need a normal racing lead
to double a 4-point holding game.
O, 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 O 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 O 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).
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O 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 O's position for the bearoff.
This is always an important consideration and is often ignored.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
X 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+
|
|
O to play. Double or roll?
Equity (centered)
O 90.3% G 0.1% BG 0.0%
X 9.7% G 0.1% BG 0.0%
Equity (O): +0.805
Equity (X owns cube )
O 70.3% G 2.0% BG 0.0%
X 29.7% G 0.3% BG 0.0%
Equity (X): -0.422
Equity (cubeless)
O 74.0% G 2.0% BG 0.0%
X 26.0% G 0.6% BG 0.0%
Equity (O): +0.495
|
|
SC:
|
Here is the double.
O's position has improved slightly from the last roll.
Strong double.
|
|
JF:
|
I would have doubled (level 7 evaluation).
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+ +---+
|
|
X to play. Accept or pass?
Equity (centered)
O 90.3% G 0.1% BG 0.0%
X 9.7% G 0.1% BG 0.0%
Equity (O): +0.805
Equity (X owns cube )
O 70.3% G 2.0% BG 0.0%
X 29.7% G 0.3% BG 0.0%
Equity (X): -0.422
Equity (cubeless)
O 74.0% G 2.0% BG 0.0%
X 26.0% G 0.6% BG 0.0%
Equity (O): +0.495
|
|
SC:
|
Clear take.
|
|
JF:
|
I would have accepted (level 7 evaluation).
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+ +---+
|
|
O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+ +---+
|
|
X 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 O will not leave a blot on his next roll.
As a result,
X will be able to correct any little errors next turn.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+ +---+
|
|
O 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:
|
O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+ +---+
|
|
X 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 O's ace and deuce points.
Even so,
it does not gain much equity.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+ +---+
|
|
O 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 O's blocking power,
and the resulting position is poorly diversified.
As a result,
7/1 3/2 becomes more attractive.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+ +---+
|
|
X 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+ +---+
|
|
O 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 X from escaping.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+ +---+
|
|
X to play 63
Candidate Plays Equities
21/12 -0.504
21/15 5/2 -0.560
21/15 4/1 -0.562
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+ +---+
|
|
O 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.
|
| |
X
|
O
|
|
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 |
+-------------+---+-------------+ +---+
|
|
X to play. Double or roll?
Equity (X owns cube )
X 89.0% G 0.0% BG 0.0%
O 11.0% G 0.0% BG 0.0%
Equity (X): +0.780
Equity (O owns cube )
X 75.3% G 0.0% BG 0.0%
O 24.7% G 0.0% BG 0.0%
Equity (O): -0.505
Equity (cubeless)
X 77.6% G 0.0% BG 0.0%
O 22.4% G 0.0% BG 0.0%
Equity (X): +0.553
|
|
SC:
|
Easy double.
|
|
JF:
|
I would have doubled (level 7 evaluation).
|
| |
X
|
O
|
|
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 | | |
+-------------+---+-------------+
|
|
O to play. Accept or pass?
Equity (X owns cube )
X 89.0% G 0.0% BG 0.0%
O 11.0% G 0.0% BG 0.0%
Equity (X): +0.780
Equity (O owns cube )
X 75.3% G 0.0% BG 0.0%
O 24.7% G 0.0% BG 0.0%
Equity (O): -0.505
Equity (cubeless)
X 77.6% G 0.0% BG 0.0%
O 22.4% G 0.0% BG 0.0%
Equity (X): +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).
|
| |
X
|
O
|
|
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 | | |
+-------------+---+-------------+
|
|
|
|
|
X 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:
- level 5
- 7776 games (36x216)
- horizon 7
- seed 518
Standard deviations of equity estimates were between 0.002 and 0.007.
Parameter values for rollouts on cube decisions were:
- level 5
- 23328 games (36x648)
- full game
- seed 518
- settlement limit 0.550
Standard deviations of equity estimates were between 0.004 and 0.006.
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BackGammon By the Bay