Game #4
Open Division Final
San Mateo, California
15 December 1996
11 Point Match
Blake Sorem (Black) vs. Kevin Mansfield (White)
Score: 2 - 0
Analysis by Ron Karr
Going into the final round of December's Backgammon by the Bay tournament,
two players were left standing in the Open division:
Kevin Mansfield,
a finalist in last month's tournament,
and Blake Sorem,
recent winner of the Super 16
at the Gammon Associates tournament in Los Angeles.
As we pick up the action,
Blake has just won the first game to take a 2-0 lead.
| Play 1b |
|
|
White to play 65
Candidate Plays Equities
24/13 +0.069
24/18 13/8 +0.024
|
| |
Black
|
White
|
|
1.
|
|
65: 24/13
|
|
| Play 2a |
|
|
Black to play 32
Candidate Plays Equities
24/21 13/11 -0.117
13/10 13/11 -0.128
13/10 24/22 -0.139
13/10 6/4 -0.164
13/8 -0.183
|
|
RK:
|
There are two standard plays with this roll.
Playing 13/11 13/10 concentrates on building up Black's front position,
while 24/21 13/11 improves the coverage of White's outer board
and increases Black's chances to make an advanced anchor.
When the opponent has escaped a back checker,
the balance usually swings in favor of splitting the back checkers,
to make it more difficult for him to play safely;
building up one's own board is slightly less important
when the opponent has only one checker back.
The rollouts agree,
but not by much;
and the alternate split of 24/22 13/10 isn't far behind.
|
| |
Black
|
White
|
|
2.
|
32: 24/21 13/11
|
|
|
| Play 2b |
|
|
White to play 53
Candidate Plays Equities
8/3 6/3 +0.073
13/8 24/21 +0.024
|
|
RK:
|
Making a new point has the highest priority.
There is no urgency to escape the back checker.
|
| |
Black
|
White
|
|
2.
|
...
|
53: 8/3 6/3
|
|
| Play 3a |
|
|
Black to play 54
Candidate Plays Equities
13/8 24/20 -0.228
6/1* 24/20 -0.243
11/6 24/20 -0.246
11/6 13/9 -0.263
6/1* 13/9 -0.296
|
|
RK:
|
Black must choose between relatively non-constructive plays.
Running a back checker into the outfield is not desirable,
since it risks being hit,
and the gains if the checker is missed are small,
since White is still ahead in the race and with a better board.
Playing 24/20 provides good coverage of White's outer board,
which is important because of all the checkers on the midpoint.
If White attacks on either the 4 or 5 points,
Black has the chance to hit back or make the other point.
Moving 11/6 with the 5 is unnecessarily conservative;
the checker on 11 is in a relatively safe and useful place.
Hitting loose on the 1 point would put a checker out of play
and risk losing serious ground in the race.
It's sometimes done as a tempo move,
to prevent the opponent from using his entire roll;
in this position White doesn't have a lot of great numbers,
so this isn't necessary.
|
| |
Black
|
White
|
|
3.
|
54: 13/8 24/20
|
31: 8/5* 6/5
|
|
| Play 4a |
|
|
Black to play 62
Candidate Plays
Bar/17*
|
|
RK:
|
Black can't anchor but manages to eliminate one of White's builders.
|
| |
Black
|
White
|
|
4.
|
62: Bar/17*
|
|
|
| Play 4b |
|
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White to play. Double or roll?
Equity (center cube)
Black 39.6% G 1.1% BG 0.1%
White 60.4% G 1.7% BG 0.0%
Equity (White): +0.214
Equity (Black owns 2 cube)
Black 58.7% G 1.6% BG 0.1%
White 41.3% G 15.8% BG 0.4%
Equity (Black): +0.029
Equity (cubeless)
Black 46.2% G 10.0% BG 0.4%
White 53.8% G 17.5% BG 0.5%
Equity (White): +0.154
|
|
RK:
|
White's position does appear somewhat menacing:
he has a good three-point board, and Black has three vulnerable blots.
The problem is that White doesn't have any devastating threats
that would justify turning the cube.
If White enters and hits,
Black usually has plenty of time to enter and anchor somewhere,
or return hit.
If White doesn't hit,
Black is ahead in the race.
All of his checkers are in play and he can potentially form some sort
of blockade against White's two back checkers.
It's extremely unlikely that White will lose his market
(that is, find that Black has an easy drop on the next roll);
even White's best number
(probably 55)
is not necessarily deadly.
It's best to wait for a time when White has more threats
before handing over the cube.
Here's how to interpret the rollout data for cube decisions:
The cubeless figures assume all games are played to the end.
They are interesting,
but they don't always indicate for sure whether a position is a double
(because you need to take volatility into account)
or a take
(because you have to take the value of owning the cube into account).
The other figures attempt to show the value of the game
with the cube owned by one side,
or in the middle.
They use a "settlement limit" of .550.
In other words,
if one player gets to a position where his cubeless equity is .550 or greater,
and he has access to the cube,
he's counted as winning the game.
This hopefully gives a reasonable approximation of cube value.
It reflects the fact that some positions
with higher cubeless equities are correct takes,
and often correct doubles are made with a lower equity.
These figures cannot be considered perfect but should give some indication
of what is going on.
If you are deciding whether to take or pass,
the criterion is:
it's a take if your equity owning the cube is greater than -.50.
You'll lose less than half a point
times the doubled cube value,
which is better than dropping and giving up the full cube value.
If you are deciding whether to double,
the criterion is:
double if the equity with your opponent owning the cube is more than half
of your equity in the current cube position
(in the middle or owned by you).
When you double,
your raw equity almost always decreases,
but you're now playing for twice the stakes.
|
|
JF:
|
I would not have doubled (level 7 evaluation).
|
| |
Black
|
White
|
|
4.
|
...
|
Double -> 2
|
|
| Play 5a |
|
|
Black to play. Accept or drop?
Equity (center cube)
Black 39.6% G 1.1% BG 0.1%
White 60.4% G 1.7% BG 0.0%
Equity (Black): -0.214
Equity (Black owns 2 cube)
Black 58.7% G 1.6% BG 0.1%
White 41.3% G 15.8% BG 0.4%
Equity (Black): +0.029
Equity (cubeless)
Black 46.2% G 10.0% BG 0.4%
White 53.8% G 17.5% BG 0.5%
Equity (Black): -0.154
|
|
RK:
|
Easy take for Black.
The rollout data show that White is a cubeless favorite,
and a favorite with the cube in the center.
However, owning the cube,
Black is actually a slight favorite, so if this were a money game,
it would be a correct beaver.
|
|
JF:
|
I would have accepted (level 7 evaluation).
|
| |
Black
|
White
|
|
5.
|
Accept
|
|
|
| Play 5b |
|
|
White to play 64
Candidate Plays Equities
Bar/21 13/7 +0.013
Bar/15 -0.042
Bar/21 24/18 -0.056
|
|
RK:
|
White has no safe plays with his 6.
Therefore, he should play to his strength,
which is his strong home board,
and play 13/7.
This puts the greatest amount of pressure on Black's blots.
Even if Black hits with a 3,
he is still vulnerable to numerous return shots.
Playing 21/15 avoids exposing another blot,
but it allows Black to hit in his own outer board,
where the checkers are less exposed to return shots and can serve as builders.
|
| |
Black
|
White
|
|
5.
|
...
|
64: Bar/15
|
|
| Play 6a |
|
|
Black to play 63
Candidate Plays
17/11 13/10*
|
|
RK:
|
Black is able to hit while consolidating two of his blots.
|
| |
Black
|
White
|
|
6.
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63: 17/11 13/10*
|
|
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| Play 6b |
|
|
White to play 54
Candidate Plays
Bar/20 24/20
|
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RK:
|
White forms a valuable anchor and hopes to be able to hit somewhere next time.
|
| |
Black
|
White
|
|
6.
|
...
|
54: Bar/20 24/20
|
|
| Play 7a |
|
|
Black to play 61
Candidate Plays Equities
10/3 -0.040
10/4 8/7 -0.080
|
|
RK:
|
10/3 is the only play which leaves only one checker subject to attack.
|
| |
Black
|
White
|
|
7.
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61: 10/3
|
|
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| Play 7b |
|
|
White to play 33
Candidate Plays
13/4* 13/10 +0.265
13/10(4) +0.121
13/7(2) -0.006
|
|
RK:
|
With the stronger board and with Black having an additional checker exposed,
it is clear to hit,
rather than play safely by making the bar or 10 point.
|
| |
Black
|
White
|
|
7.
|
...
|
33: 13/4* 13/10
|
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| Play 8a |
|
|
Black to play 64
Candidate Plays
Bar/21*/15*
|
| |
Black
|
White
|
|
8.
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64: Bar/21*/15*
|
52: Bar/20 Bar/23
|
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| Play 9a |
|
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Black to play 55
Candidate Plays Equities
15/10 8/3 6/1(2) +0.346
15/10 13/3 13/8 +0.281
8/3(2) 6/1(2) +0.276
13/3(2) +0.257
|
|
RK:
|
Black covers the 3 point,
then has to decide on the remaining 5s.
Normally, when far ahead in the race,
the straightforward plan is to clear your points from the rear
(in this case, the midpoint)
and just try to bring the checkers home.
In this case, the plan has some drawbacks:
-
Black can't safety the checker on the 15 point.
If White hits it,
it will be somewhat easier for him to contain that checker
after Black has given up his midpoint.
-
Even if White misses,
the resulting position is a bit awkward for Black to bring home.
By playing 15/10 6/1(2),
Black makes a third home board point and keeps the midpoint.
If White hits,
Black will be in better shape to escape or counterattack.
If not hit,
Black's improved board may make it easier for him to get home
since he will be threatening to attack White's blot if it's left there.
|
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Black
|
White
|
|
9.
|
55: 15/10 8/3 6/1(2)
|
32: 20/15*
|
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| Play 10a |
|
|
Black to play 41
Candidate Plays Equities
Bar/21 11/10* +0.247
Bar/24 6/2* +0.090
|
|
RK:
|
Even after being hit,
Black is well ahead in the race.
He doesn't necessarily want to hit and expose additional blots,
but there are no safe plays available.
Bar/24 6/2* leaves only one new blot and keeps the 11 point,
but leaves a direct shot on the 2 point,
which may be difficult to cover even if missed.
Bar/21 11/10* leaves ten indirect shots and two new blots,
but puts the back checker in a better place for escaping.
Thus Black is in better shape if not hit.
|
| |
Black
|
White
|
|
10.
|
41: Bar/21 11/10*
|
65: Bar/14*
|
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| Play 11a |
|
|
Black to play 64
Candidate Plays Equities
Bar/21 10/4 +0.066
Bar/21 8/2* +0.040
Level 6:
Candidate Plays Equities
Bar/21 8/2* +0.040
Bar/21 10/4 +0.030
|
|
RK:
|
After anchoring, Black must leave a shot somewhere.
He can attack 8/2* or play more positionally with 10/4.
How to decide?
Both sides have advanced anchors and three-point boards.
The timing appears to favor a hitting play.
Black's timing is worse,
since he's ahead in the race
(and his home board is a bit further advanced).
If both sides play passively,
Black is likely to be the first one to have to break something valuable;
White may even be able to make new points in front of Black's anchor.
By hitting,
Black may be able to get his back checkers moving
while White is trying to enter.
He also may be able to pick up White's other blot.
On the other hand,
playing 10/4 puts the checker in a better place if it's missed,
and doesn't expose an additional blot.
White probably won't safety both blots,
so if Black can make the 4 point and THEN attack,
he'll be in better shape.
The original rollouts imply that patience is best.
Subsequently,
we rolled out the position on Level 6
(which incorporates 1-ply lookahead,
thus playing at a higher level of skill)
and the hitting play came out slightly better.
A close decision.
|
| |
Black
|
White
|
|
11.
|
64: Bar/21 10/4
|
|
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| Play 11b |
|
|
White to play 22
Candidate Plays Equities
23/21* 13/11(3) +0.072
23/21* 20/18(2) 13/11 +0.065
23/21* 13/9 13/11 +0.054
23/21* 20/14 +0.048
23/21* 13/7 +0.015
|
|
RK:
|
White hits, and must play three more 2's.
There are several close plays here,
some of which are unlikely to be found by humans.
The obvious approach would seem to be:
-
Stay on the opponent's 5 point,
since it's the best defensive point,
and White's timing is OK so he has no urgency to get off it.
-
Keep the midpoint.
Therefore the play is 13/11 13/9.
This doesn't seem too dangerous since Black is on the bar.
The problem with this approach is that it leaves four blots around the board,
so if Black does hit somewhere,
White could end up with several checkers on the bar.
JellyFish prefers 13/11(3),
which leaves only three blots.
This makes the 11 point a kind of substitute midpoint.
20/18(2) 13/11 also leaves three blots.
The odd-looking 20/14 only leaves two blots,
despite giving up the anchor
(at least temporarily).
|
| |
Black
|
White
|
|
11.
|
...
|
22: 23/21* 13/9 13/11
|
|
| Play 12a |
|
|
Black to play 21
Candidate Plays Equities
Bar/24 6/4* -0.035
Bar/24 13/11* -0.059
Level 6:
Candidate Plays Equities
Bar/24 6/4* -0.032
Bar/24 13/11* -0.066
|
|
RK:
|
Black enters on the 24 point.
Given White's 4 blots,
hitting is clear
(as opposed to playing safe with 8/6);
if White fails to enter,
Black will be in great shape.
Hitting 13/11 has the advantage of sending an additional checker back
and leaving no direct return shots,
but it risks letting White make a second anchor,
as well as giving up the midpoint.
6/4 leaves just a few more shots and keeps a more solid position.
|
| |
Black
|
White
|
|
12.
|
21: Bar/24 6/4*
|
|
|
| Play 12b |
|
|
White to play 43
Candidate Plays Equities
Bar/21* 14/11 +0.356
Bar/21* 9/6 +0.327
Bar/21* 11/8 +0.249
|
|
RK:
|
An excellent roll,
hitting and consolidating.
This play seems clear and I was surprised that 9/6 came out as close as it did.
Why bring in another checker to the 6 point?
This probably means that JellyFish tends to attack in White's home board
rather than building additional outside blocking points,
so it wants as much ammunition in place as possible.
I believe this is a known bias of JellyFish,
and not necessarily correct strategy.
Even so, the rollouts still favor 14/11.
|
| |
Black
|
White
|
|
12.
|
...
|
43: Bar/21* 14/11
|
|
13.
|
31: Bar/21
|
|
|
| Play 13b |
|
|
White to play 31
Candidate Plays Equities
9/6 21/20 +0.311
9/5 +0.304
11/8 9/8 +0.299
13/9 +0.269
21/18 9/8 +0.199
|
|
RK:
|
The 8 point is quite useful as a blocking and landing point.
Is it worth the risk of leaving a few shots and 2 blots?
I would think so,
but the rollouts slightly prefer tidying up with 21/20 9/6,
or compromising with 9/5.
Again, this may reflect JellyFish's preference for attacking in the home board.
|
| |
Black
|
White
|
|
13.
|
...
|
31: 11/8 9/8
|
|
14.
|
64: 24/14*
|
|
|
| Play 14b |
|
|
White to play 52
Candidate Plays
Bar/20 13/11*
|
|
RK:
|
The hitting continues.
|
| |
Black
|
White
|
|
14.
|
...
|
52: Bar/20 13/11*
|
|
| Play 15a |
|
|
Black to play 11
Candidate Plays Equities
Bar/23 13/12(2)* -0.121
Bar/24 13/12* 8/6 -0.133
Level 6:
Candidate Plays Equities
Bar/23 13/12(2)* -0.089
Bar/24 13/12* 8/6 -0.111
|
|
RK:
|
Black enters and hits,
and needs to play two more 1s.
Playing 8/6 gives the most diversified position
for attacking and covering the outfield.
I would have thought it was worth the risk,
since the outfield blots aren't in any danger (yet).
But the rollouts slightly favor buttoning up the blots with 13/12 24/23.
Black already has good outfield control,
and his next priority is usually to get his spare checkers
in White's home board moving;
when he does that,
he doesn't want too many other blots around for White to hit.
|
| |
Black
|
White
|
|
15.
|
11: Bar/24 13/12* 8/6
|
63: Cannot move
|
|
| Play 16a |
|
|
Black to play 33
Candidate Plays Equities
21/18 13/4* +0.105
24/18 21/18(2) +0.089
24/12 +0.070
24/18 21/18 13/10 +0.048
24/18 21/18 12/9 +0.021
|
|
RK:
|
The most aggressive play is 21/18 13/4*,
battling for the valuable four point,
and directly threatening the other blot.
If White fails to hit,
Black is in great shape;
if White hits,
he becomes the favorite.
The rollouts show this as a slight favorite.
The best alternate play brings three checkers to the opponent's bar point
and provides excellent outfield control.
|
| |
Black
|
White
|
|
16.
|
33: 21/18 13/4*
|
31: Cannot move
|
|
| Play 17a |
|
|
Black to play. Double or roll?
Equity (Black owns 2 cube)
Black 88.8% G 4.7% BG 0.3%
White 11.2% G 4.6% BG 0.3%
Equity (Black): +0.775
Equity (White owns 4 cube)
Black 56.0% G 36.7% BG 1.3%
White 44.0% G 1.5% BG 0.2%
Equity (Black): +0.482
Equity (cubeless)
Black 65.1% G 38.9% BG 1.4%
White 34.9% G 9.7_% BG 0.6%
Equity (Black): +0.600
|
|
RK:
|
Black's last play paid off big-time.
Black is shooting at another blot
and has excellent chances to close the 4 point.
A clear double,
and the rollouts agree.
|
|
JF:
|
I would have doubled (level 7 evaluation).
|
| |
Black
|
White
|
|
17.
|
Double -> 4
|
|
|
| Play 17b |
|
|
White to play. Accept or drop?
Equity (Black owns 2 cube)
Black 88.8% G 4.7% BG 0.3%
White 11.2% G 4.6% BG 0.3%
Equity (White): -0.775
Equity (White owns 4 cube)
Black 56.0% G 36.7% BG 1.3%
White 44.0% G 1.5% BG 0.2%
Equity (White): -0.482
Equity (cubeless)
Black 65.1% G 38.9% BG 1.4%
White 34.9% G 9.7_% BG 0.6%
Equity (White): -0.600
|
|
RK:
|
With two checkers on the bar against a 3.5 point board,
another vulnerable blot,
and already 29 pips down in the race,
White is not in good shape.
However,
it appears he has just enough going for him to make this a marginal take.
White owns the defensive 5 point,
and has a good board and no checkers out of play.
If he can manage to enter his all his checkers from the bar
before Black brings everybody around,
he'll have chances to hit Black and contain him.
Black is favored but not guaranteed to make the 4 point.
If White makes it,
or hits there,
it's anyone's game.
If not,
White has chances to make another anchor on the 2 point,
or enter everyone quickly on the 5 point.
White's equity of -.482 indicates it's a close take.
The cubeless equity of -.600 would not be enough to take in most positions,
but it appears that the value of owning the cube to White is quite high.
The fact that it's a tournament match shouldn't make a big difference.
White can use the full 8 points from a redouble,
and his opponent would then get virtually no value from the cube,
so if anything this might give White more incentive to take here.
|
|
JF:
|
I would have accepted (level 7 evaluation).
|
| |
Black
|
White
|
|
17.
|
...
|
Pass
|
|
| Play 18a |
|
|
White lost the next game to fall behind 0-6,
but went on to win the match 11-9.
|
The game was recorded on tape by Richard McIntosh
and transcribed by Ron Karr.
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.
Except as noted below,
parameter values for rollouts on moves were:
- level 5
- 7776 games (36x216)
- horizon 7
- seed 1215
Standard deviations of equity estimates were between 0.004 and 0.007.
Moves for plays
11a,
12a,
and
15a
were rolled out at level 6,
with parameter values:
- level 6
- 1296 games (36x36)
- seed 1215
Standard deviations of equity estimates were between 0.008 and 0.009.
Parameter values for rollouts on cube decisions were:
- level 5
- 23328 games (36x648)
- full game
- seed 1215
- settlement limit 0.550
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