Game #8
Open Division Final
San Mateo, California
20 April 1997
11 Point Match
Michael Derylo (X) vs. Dan Epstein (O)
Score: 1 - 0
Analysis by Ron Karr
BGBB members Michael Derylo and Danny Epstein meet up in this month's finals.
Each of them brings his own distinctive playing style,
honed during years of chouette play,
to this instructive game from early in the match.
| 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 64
Candidate Plays Equities
24/18 13/9 +0.013
8/2 6/2 +0.012
24/14 +0.005
13/7 24/20 -0.037
24/18 24/20 -0.051
13/7 13/9 -0.051
13/3 -0.075
|
|
RK:
|
Most players either run with 24/14,
split and build with 24/18 13/9,
or,
since the advent of neural nets,
make the 2 point (which used to be considered way too impure).
These plays are very close;
the decision might depend on the match score or on one's mood at the time.
Bringing two checkers down with 13/7 13/9 is an ultra-offensive play,
considered weaker by humans and computers.
X risks getting hit on his side of the board,
which costs more in the race than getting hit on the opponent's side
(O hits with all 6s, plus 53 and 44).
O's non-hitting rolls play constructively by bringing builders down.
If not hit,
X is likely to end up with his bar point,
but O may make an equal or better point.
Since this play results in more backgames and deep anchor games
than the other plays,
and JellyFish doesn't play those types of games as well as other positions,
we should probably upgrade its equity a bit
(but not enough to make the difference).
Some might make this play if seeking complications,
such as when playing a weaker player,
or at certain match scores.
For example,
when your opponent is one point from victory,
having several checkers sent back isn't as bad as usual,
since gammons don't count.
And staying on the opponent's ace point is more advantageous than normal,
since you have chances until the end and can't be doubled out.
|
| |
X
|
O
|
|
1.
|
64: 13/7 13/9
|
|
|
| Play 1b |
+-------------+---+-------------+
| X O | | O X |
| X O | | O X |
| O | | O X |
| O | | | 167
| O | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | | O |
| X | | O | 157
| X | | X O |
| O X | | X O |
| O X | | X X X O |
+-------------+---+-------------+
|
|
O to play 32
Candidate Plays Equities
13/10 13/11 -0.132
13/10 6/4 -0.165
24/21 13/11 -0.171
13/10 24/22 -0.174
8/5 13/11 -0.188
13/8 -0.198
6/3 13/11 -0.199
24/21 24/22 -0.213
|
|
RK:
|
O can't hit but simply brings two builders down,
thus increasing his chances of making a new point next time.
These builders are safer than normal,
since if X hits,
the blots on his side of the board remain vulnerable.
|
| |
X
|
O
|
|
1.
|
...
|
32: 13/10 13/11
|
|
| Play 2a |
+-------------+---+-------------+
| X O | | O O O X |
| X O | | O X |
| O | | O X |
| O | | | 162
| O | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | | |
| X | | | 157
| X | | X O |
| O X | | X O |
| O X | | X X X O |
+-------------+---+-------------+
|
|
X to play 54
Candidate Plays Equities
24/15* +0.098
9/4 8/4 +0.060
8/3 7/3 +0.010
|
|
RK:
|
One of the few rolls that doesn't make X's bar point.
Making the 3 point would leave no direct shots,
but allows O freedom to make a better point and take the advantage.
Making the 4 point is better,
despite leaving direct 6s
(most 6s already play well for O).
However,
hitting is best,
despite the fact that most numbers hit back.
It grabs a definite racing advantage (29 pips),
removes one of O's builders,
and prevents O from making any offensive points
(except with doubles).
|
| |
X
|
O
|
|
2.
|
54: 24/15*
|
|
|
| Play 2b |
+-------------+---+-------------+
| X O | | O X O X |
| O | | O X |
| O | | O X |
| O | | | 177
| O | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | O | |
| X | | | 148
| X | | X O |
| O X | | X O |
| O X | | X X X O |
+-------------+---+-------------+
|
|
O to play 54
Candidate Plays Equities
Bar/16* -0.051
Bar/20 24/20 -0.157
|
|
RK:
|
O enters on the 20 point,
then must decide whether to button up by making the solid anchor,
or hit the blot on the 16 point.
The anchor gives O a secure position:
X won't be able to make a prime or a closed board.
However,
there are some drawbacks.
X is ahead in the race
and may simply be able to run home past O's anchor.
In addition,
X may start to build up his board,
and then it will be even more dangerous for O to hit outfield blots
from his anchor.
So he should avoid that situation and just hit now.
By hitting,
O regains ground in the race and sends another X checker back,
thus reducing X's offensive potential.
Also,
X has two other blots that can potentially be hit.
If O doesn't hit,
it will be easier for X to tidy up.
|
| |
X
|
O
|
|
2.
|
...
|
54: Bar/20 24/20
|
|
| Play 3a |
+-------------+---+-------------+
| X O | | O X O X |
| O | | O X |
| O | | O X |
| O | | | 168
| O | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | | |
| X | | | 148
| X | | X O |
| O X | | X O |
| O O X | | X X X O |
+-------------+---+-------------+
|
|
X to play 64
Candidate Plays Equities
Level 6
24/14* +0.095
15/9 7/3 +0.092
15/9 24/20 +0.088
13/7 13/9 +0.081
9/3 7/3 +0.070
15/9 13/9 +0.066
7/1* 13/9 +0.023
13/7 15/11 +0.017
Level 5
13/7 13/9 +0.127
24/14* +0.097
15/9 7/3 +0.096
15/9 13/9 +0.086
15/9 24/20 +0.083
9/3 7/3 +0.071
7/1* 13/9 +0.051
13/7 15/11 +0.043
|
|
RK:
|
An interesting decision.
Now that O has anchored,
what should X do with 64?
Hitting is certainly tempting
(as usual early in the game).
You gain in the race and remove one of O's builders,
plus partially escaping a back checker.
However,
the bold-vs-safe criteria
(see Paul Magriel's classic Backgammon)
appear to favor caution on X's part.
X is ahead in the race,
so he has less to gain from a blot-hitting contest.
O has an anchor,
so the upside of hitting is limited
(X can't hope to make a closed board or prime).
If X hits,
he leaves four blots,
and most numbers return hit somewhere.
My thought was to play something like 15/9 7/3,
which makes a valuable blocking point and minimizes return shots and blots.
Yet another alternative is simply to make the solid four-prime with 13/9 13/7,
despite leaving two outfield blots.
This increases the pressure on O's back checkers.
X is favored to get hit,
but X should be able to enter quickly and anchor
or keep challenging in the outfield while O's board is weak.
After seeing the rollouts
(JellyFish level 5 favoring the prime-making play),
I was curious as to whether a level 6 rollout would make a difference.
(We rolled out a few other plays later in the game on level 6 as well.
Keep in mind that the standard deviation on the level 6 rollouts is greater
-- around 2% -- so one can't draw firm conclusions from small differences.)
On level 6 JellyFish doesn't like the four-prime as much,
and it's close between hitting and making the 9 point.
In summary: Who knows?
Hitting may well be best,
and it certainly isn't an error.
|
| |
X
|
O
|
|
3.
|
64: 24/14*
|
|
|
| Play 3b |
+-------------+---+-------------+
| O | | O X X X |
| O | | O X |
| O | | O X |
| O | | | 182
| O | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | O | |
| X | | | 138
| X | | X O |
| O X | | X O |
| O O X | | X X X O |
+-------------+---+-------------+
|
|
O to play 31
Candidate Plays Equities
Bar/24 13/10* -0.190
|
|
RK:
|
O hits back, as expected.
|
| |
X
|
O
|
|
3.
|
...
|
31: Bar/24 13/10*
|
|
| Play 4a |
+-------------+---+-------------+
| O | | O O X X |
| O | | O X |
| O | | O X |
| O | | | 178
| O | X | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | | |
| X | | | 148
| X | | X |
| O O X | | X O |
| O O X | | X X X O |
+-------------+---+-------------+
|
|
X to play 31
Candidate Plays Equities
bar/22 8/7 +0.168
|
|
RK:
|
And X finds it hard to consolidate.
The only constructive play is to cover the bar point.
Now at least X has some additional blocking power
against O's back checkers.
|
| |
X
|
O
|
|
4.
|
31: Bar/22 8/7
|
|
|
| Play 4b |
+-------------+---+-------------+
| X O | | O O X X |
| O | | O X |
| O | | O X |
| O | | | 178
| O | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | | |
| X | | | 144
| X | | |
| O O X | | X X O |
| O O X | | X X X O |
+-------------+---+-------------+
|
|
O to play 52
Candidate Plays Equities
8/3* 13/11* -0.182
13/8 13/11* -0.247
10/5 13/11* -0.307
13/11*/6 -0.328
10/5 6/4 -0.356
|
|
RK:
|
The usual criteria favor a bold play by O .
X is ahead in the race,
has no anchor,
and has three blots.
Hitting with the 2 is clear,
but O should keep hitting with 8/3.
This immobilizes X,
prevents him from protecting the blot on his 9 point,
and leads to the possibility of a blitz.
Even if X hits back,
his board is weak;
O should be able to enter and resume hitting if necessary.
Playing 13/8 is more positionally "pure,"
not playing a checker too deep in O's board,
but it gives X too much freedom.
O may end up having to attack later anyway,
and conditions may not be as good for it as they are now.
|
| |
X
|
O
|
|
4.
|
...
|
52: 13/8 13/11*
|
|
| Play 5a |
+-------------+---+-------------+
| X O | | O O O X |
| O | | O X |
| O | | O X |
| O | | O | 171
| O | X | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | | |
| X | | | 155
| X | | |
| O O X | | X X |
| O O X | | X X X |
+-------------+---+-------------+
|
|
X to play 32
Candidate Plays Equities
Level 6
Bar/22 9/7 +0.190
Bar/22 6/4 +0.159
Bar/22 13/11 +0.114
Level 5
Bar/22 9/7 +0.168
Bar/22 13/11 +0.110
Bar/22 6/4 +0.109
|
|
RK:
|
With only one on the bar,
X is able to anchor and safety his remaining blot.
Since X is ahead in the race and has fewer checkers back,
playing safe is thematic.
Despite this,
I would have at least considered playing 6/4.
Why?
O has a bunch of builders poised to make new points
in front of X's anchor.
If X plays safe now he has very few numbers
to make a new point safely next time.
Most likely he'll either stack checkers on his existing points
or be forced to leave a shot somewhere.
By slotting two valuable points now,
X forces O to hit at a time when he only has a one-point board,
rather than later,
when he has improved his position.
Nonetheless,
a shot is a shot,
and JellyFish indicates the risk would not be justified.
X has spares on the midpoint to play with,
so he isn't desperate yet.
|
| |
X
|
O
|
|
5.
|
32: Bar/22 9/7
|
|
|
| Play 5b |
+-------------+---+-------------+
| X O | | O O O X |
| X O | | O X |
| O | | O X |
| O | | O | 171
| O | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | | |
| X | | | 150
| X | | X |
| O O X | | X X |
| O O X | | X X |
+-------------+---+-------------+
|
|
O to play 33
Candidate Plays Equities
24/21(2) 8/5(2) -0.010
24/21 11/5 8/5 -0.097
|
|
RK:
|
A fine roll, improving the anchor and making the 5 point.
|
| |
X
|
O
|
|
5.
|
...
|
33: 24/21(2) 8/5(2)
|
|
| Play 6a |
+-------------+---+-------------+
| X O O | | O O O X |
| X O O | | O X |
| O | | X |
| O | | | 159
| O | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | | |
| X | | | 150
| X | | X |
| O O X | | X X |
| O O X | | X X |
+-------------+---+-------------+
|
|
X to play 32
Candidate Plays Equities
13/8 -0.047
6/1 -0.111
6/3 13/11 -0.143
|
|
RK:
|
X correctly keeps his checkers in front of his opponent.
The extra builder on the 8 point can come in handy.
Slotting home board points can wait.
|
| |
X
|
O
|
|
6.
|
32: 13/8
|
|
|
| Play 6b |
+-------------+---+-------------+
| X O O | | O O O X |
| X O O | | O X |
| O | | |
| O | | | 159
| O | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | | |
| X | | | 145
| X | | X X |
| O O X | | X X |
| O O X | | X X |
+-------------+---+-------------+
|
|
O to play 22
Candidate Plays Equities
10/8 6/4(3) +0.141
10/4 6/4 +0.127
11/7 6/4(2) +0.113
6/2 6/4(2) +0.090
11/9 10/8 6/4(2) +0.075
|
|
RK:
|
A good roll, making the 4 point and avoiding direct shots.
|
| |
X
|
O
|
|
6.
|
...
|
22: 10/8 6/4(3)
|
|
| Play 7a |
+-------------+---+-------------+
| X O O O | | O O X |
| X O O O | | O X |
| O | | O |
| | | | 151
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| X | | |
| X | | | 145
| X | | X X |
| O O X | | X X |
| O O X | | X X |
+-------------+---+-------------+
|
|
X to play 32
Candidate Plays Equities
6/1 -0.193
8/3 -0.199
13/8 -0.298
|
|
RK:
|
Now playing 13/8 would be too risky,
leaving nine shots when O has a superior board.
Since X has a surplus on the 6 point,
he simply starts a new inner board point,
which can easily be covered later.
Even though the 3 point is a more desirable point to make than the 1 point,
6/1 seems slightly preferable to 8/3 because it leaves a spare on the 8 point,
useful for building or attacking if O leaves one of the anchors.
|
| |
X
|
O
|
|
7.
|
32: 6/1
|
|
|
| Play 7b |
+-------------+---+-------------+
| X O O O | | O O X |
| X O O O | | O X |
| O | | O |
| | | | 151
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| X | | | 140
| X | | X X |
| O O X | | X X |
| X O O X | | X X |
+-------------+---+-------------+
|
|
O to play 43
Candidate Plays Equities
Level 6
11/7 8/5 +0.106
8/1 +0.101
20/16 11/8 +0.086
11/4 +0.070
20/16 8/5 +0.068
20/13 +0.068
Level 5
20/16 8/5 +0.104
20/13 +0.108
11/4 +0.096
20/16 11/8 +0.095
8/1 +0.086
11/7 8/5 +0.084
|
|
RK:
|
An interesting decision.
It's important not to play on automatic pilot in positions like this.
(Many times I've made an "obvious" play,
realizing a few seconds later that I missed a great opportunity.)
By playing 11/4,
O sits on his position and leaves no shots.
The problem is,
what happens next time?
X's three-point prime may not seem all that imposing,
but it does block nine numbers,
causing O's front position to weaken.
And even though O is favored to be able to escape a back checker next time,
X is likely to have made an additional home board point,
making it more dangerous for O to run.
With X having a blot on his 1 point,
now is a good time to leap into the outfield.
This may seem risky,
but the greater risk is having the back checkers stuck in X's home board.
X may hit,
but O will have numerous return shots,
which may be deadly because of O's better board.
That said,
I was surprised the running play did not come out significantly better
than the safe play.
It appears X's gain in the cases when he makes the 5 point on O's head
(ten numbers),
despite the blot on the ace point,
just about offsets O's increased flexibility from running.
And the level 6 results are interesting.
All the plays are still close
(considering the margin of error),
but JellyFish's favorite is now 11/7 8/5!
This is certainly not a play I would have found.
The blot is pretty safe,
since O has return shots and a better board,
but since O can't cover it,
what's the advantage over 11/4?
It makes it more dangerous for X to run with a 6,
but I wouldn't expect him to be doing that soon anyway.
|
| |
X
|
O
|
|
7.
|
...
|
43: 11/4
|
|
| Play 8a |
+-------------+---+-------------+
| X O O O | | O X |
| X O O O | | O X |
| O | | O |
| O | | | 144
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| X | | | 140
| X | | X X |
| O O X | | X X |
| X O O X | | X X |
+-------------+---+-------------+
|
|
X to play 61
Candidate Plays Equities
8/1 -0.141
8/2 7/6 -0.223
|
|
RK:
|
X strengthens his board, which will help if O runs next time.
|
| |
X
|
O
|
|
8.
|
61: 8/1
|
|
|
| Play 8b |
+-------------+---+-------------+
| X O O O | | O X |
| X O O O | | O X |
| O | | O |
| O | | | 144
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| X | | | 133
| X | | X |
| X O O X | | X X |
| X O O X | | X X |
+-------------+---+-------------+
|
|
O to play 43
Candidate Plays Equities
Level 6
20/16 8/5 +0.051
8/1 +0.041
20/13 +0.027
20/16 4/1 -0.024
Level 6
8/1 +0.053
20/16 8/5 +0.051
20/13 +0.039
20/16 4/1 -0.007
|
|
RK:
|
O has a similar dilemma to the last time.
X has turned his blot into a point,
so running is a bit more dangerous.
And O would have preferred to break his back anchor with a 5 or 6.
Still,
I would be very tempted to run
while O still has the better board and blockade.
If O plays 8/1,
he's almost out of spare checkers to play with.
Again,
though,
JellyFish has the plays pretty close.
|
| |
X
|
O
|
|
8.
|
...
|
43: 8/1
|
|
| Play 9a |
+-------------+---+-------------+
| O X O O O | | O X |
| X O O O | | O X |
| O | | |
| O | | | 137
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| X | | | 133
| X | | X |
| X O O X | | X X |
| X O O X | | X X |
+-------------+---+-------------+
|
|
X to play 65
Candidate Plays Equities
13/7 13/8 -0.126
22/16 7/2 -0.187
22/16 6/1 -0.190
8/2 8/3 -0.196
13/2 -0.200
|
|
RK:
|
Bringing two checkers down is safe and sound.
However,
it does run the risk that O will be able to jump out
with one or two checkers and take control of the outfield,
which is important in positions like this.
Since X is ahead in the race,
and O has a blot on his 1 point and not the greatest attacking chances,
there's something to be said for a play like 22/16 7/2.
However, O does have the better board,
so this play is a bit too loose.
If O runs with a single back checker next time,
rather than both,
X will have chances to attack.
Then it may be safer for him to escape his back checkers.
|
| |
X
|
O
|
|
9.
|
65: 13/7 13/8
|
|
|
| Play 9b |
+-------------+---+-------------+
| O X O O O | | O |
| X O O O | | O |
| O | | |
| O | | | 137
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| X | | X | 122
| X | | X X |
| X O O X | | X X |
| X O O X | | X X |
+-------------+---+-------------+
|
|
O to play 41
Candidate Plays Equities
21/16 +0.061
20/15 +0.052
|
|
RK:
|
Finally, O is forced to go,
rather than break his board.
He keeps the most forward anchor for better outfield control.
|
| |
X
|
O
|
|
9.
|
...
|
41: 21/16
|
|
| Play 10a |
+-------------+---+-------------+
| O X O O O | | O |
| X O O O | | O |
| O | | |
| O | | | 132
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| X | | X | 122
| X | | X X |
| X O X | | X X |
| X O O X | | X X O |
+-------------+---+-------------+
|
|
X to play 64
Candidate Plays Equities
Level 6
22/16 22/18 -0.010
22/16 8/4* -0.190
8/2 6/2 -0.208
22/16 7/3 -0.219
8/2 7/3 -0.222
22/16 6/2 -0.227
22/12 -0.261
7/1 7/3 -0.270
7/1 6/2 -0.289
Level 5
22/16 22/18 +0.005
22/16 7/3 -0.197
22/16 8/4* -0.182
8/2 6/2 -0.187
8/2 7/3 -0.213
22/16 6/2 -0.238
22/12 -0.257
7/1 7/3 -0.263
7/1 6/2 -0.285
|
|
RK:
|
X hoped to point on the blot on the 4 point,
but no such luck.
Making the 2 point is a natural play when on auto-pilot.
The problem is:
How is X going to win this game?
He's ahead in the race
(20 pips after the roll)
and sooner or later he's going to have to escape his back checkers.
Breaking the anchor now may look risky,
but are things going to get better or worse if he waits?
O has a blot on his 1 point,
which is a liability,
but it may soon be covered.
The longer X waits,
the more he will have to pray for 66 or 44 (or possibly hit a fly shot)
in order to cash in on his racing advantage.
If X runs with 22/16,
how does he play the 4?
16/12 would expose him to a direct 4 as well as 5s and 1s.
Sometimes a hit and run play like 8/4* is called for,
but in this case it is bad news if O hits back.
Simply running the other checker with 22/18 is far superior to any other play,
according to the rollouts.
Sixteen numbers miss the blots altogether,
and in those cases X will have good chances to race home.
If X gets hit,
he isn't losing too much ground in the race,
and he is likely to get return shots;
O often has to break the 8 point to hit.
O doesn't have quite enough ammunition in place
to do serious damage yet.
In the worst case,
X should have a couple of rolls to enter
before O is in position to win with the cube.
|
| |
X
|
O
|
|
10.
|
64: 8/2 6/2
|
|
|
| Play 10b |
+-------------+---+-------------+
| O X O O O | | O |
| X O O O | | O |
| O | | |
| O | | | 132
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| | | X | 112
| X | | X |
| X X O X | | X X |
| X X O O X | | X X O |
+-------------+---+-------------+
|
|
O to play 63
Candidate Plays Equities
21/15 4/1 +0.260
21/15 16/13 +0.199
|
|
RK:
|
A good roll for O,
freeing his other back checker and increasing his outfield coverage,
and making a fourth home board point to boot.
Now it's too dangerous for X to run his back checkers
unless he hits a shot or rolls 44 or 66.
|
| |
X
|
O
|
|
10.
|
...
|
63: 21/15 4/1
|
|
| Play 11a |
+-------------+---+-------------+
| O X O O O | | O |
| O X O O O | | O |
| O | | |
| | | | 123
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| | | X | 112
| X | | X |
| X X O X | | X X |
| X X O X | | X X O O |
+-------------+---+-------------+
|
|
X to play 53
Candidate Plays Equities
7/2 7/4 -0.344
6/1 7/4 -0.370
7/2 6/3 -0.384
8/3 7/4 -0.401
8/3 6/3 -0.421
|
|
RK:
|
X must continue to make plays while waiting for something good to happen.
The good news is that he has six checkers on the 7 and 8 points,
plus a spare on the 6 point,
that he can play with before he's forced to break his anchor.
That should give him a reasonable chance to roll a double or hit a shot.
He should simply preserve his racing advantage by playing 7/2 7/4.
It may be tempting to make an additional home board point
rather than leaving an inner blot,
but it simply isn't worth leaving eleven shots
to get hit and blow the racing lead.
(Even if missed,
how would you like to roll one of your key doubles and not be able
to advance all the way because you have to safety your blot?)
|
| |
X
|
O
|
|
11.
|
53: 8/3 6/3
|
|
|
| Play 11b |
+-------------+---+-------------+
| O X O O O | | O |
| O X O O O | | O |
| O | | |
| | | | 123
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| | | X | 104
| | | X |
| X X X O X | | X |
| X X X O X | | X X O O |
+-------------+---+-------------+
|
|
O to play. Double or roll?
Equity (centered)
O 80.0% G 2.0% BG 0.1%
X 20.0% G 1.1% BG 0.0%
Equity (O): +0.610
Equity (X owns cube )
O 61.4% G 12.2% BG 0.4%
X 38.6% G 1.6% BG 0.0%
Equity (X): -0.338
Equity (cubeless)
O 67.4% G 12.6% BG 0.4%
X 32.6% G 4.7% BG 0.1%
Equity (O): +0.431
|
|
RK:
|
O has a positional advantage,
with a better anchor and blockade.
He has eleven numbers to hit and take a big lead.
He also has more freedom to play,
while X will be wasting pips with many of his rolls.
On the other hand,
X is ahead nineteen pips,
with several rolls to get a key double or hit a shot.
The big question is:
If O hits and X fans,
by how much will O "lose his market,"
i.e.,
will X then have a big pass?
If it's only a small market loser,
then O is technically better off to wait before doubling.
Rollouts showed that after hitting with a 3,
and X dancing,
O's equity would be between +0.714 and +0.761.
These are significant but not overwhelming market losers.
Therefore,
there is an incentive to double,
but it is likely to be somewhat close.
JellyFish's rollouts with settlements confirm this.
The way these rollouts work is:
If a player with access to the cube gets to a point
where his cubeless equity is greater than +0.550,
he's given credit for a win.
(See
Game #4
for a more detailed discussion of this.)
The rollouts show that O's equity after turning the cube is +0.338,
and doubling that gives +0.676.
This is higher than his equity of +0.610 with the cube in the middle,
so if you trust the figures,
a cube is warranted.
And of course,
regardless of the odds,
doubling can certainly be correct if you think your opponent may pass.
|
JF:
|
I would not have doubled (level 7 evaluation).
|
| |
X
|
O
|
|
11.
|
...
|
Double -> 2
|
|
| Play 12a |
+-------------+---+-------------+
| O X O O O | | O |
| O X O O O | | O |
| O | | |
| | | | 123
| | | |
| | | |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
| | | |
| | | |
| | | X | 104
| | | X |
| X X X O X | | X | +---+
| X X X O X | | X X O O | | 2 |
+-------------+---+-------------+ +---+
|
|
X to play. Accept or pass?
Equity (centered)
O 80.0% G 2.0% BG 0.1%
X 20.0% G 1.1% BG 0.0%
Equity (O): +0.610
Equity (X owns cube )
O 61.4% G 12.2 BG 0.4%
X 38.6% G 1.6 BG 0.0%
Equity (X): -0.338
Equity (cubeless)
O 67.4% G 12.6 BG 0.4%
X 32.6% G 4.7 BG 0.1%
Equity (O): +0.431
|
|
RK:
|
For the reasons stated above,
this is a fairly easy take.
Even though X left an unnecessary shot,
he still has plenty of chance to win,
and his chances of being gammoned are not high.
If he's hit,
he can recirculate the checker while maintaining the anchor.
If missed,
there's a chance to roll a double or hit a shot,
or even to escape safely after being forced off the anchor.
|
|
JF:
|
I would have accepted (level 7 evaluation).
|
| |
X
|
O
|
|
12.
|
Pass
|
|
|
| |
+-------------+---+-------------+
| O X O O O | | O |
| O X O O O | | O |
| O | | |
| | | | 123
| | | |
| | | |
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 |
| | | |
| | | |
| | | X | 104
| | | X |
| X X X O X | | X | +---+
| X X X O X | | X X O O | | 2 |
+-------------+---+-------------+ +---+
|
|
|
|
O went on to win the match 8-11.
|
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.
Parameter values for rollouts on moves were:
- level 5
- 7776 games (36x216)
- horizon 7
- seed 420
Standard deviations of equity estimates were between 0.003 and 0.006.
For plays 3a, 5a, 7b, 8b, and 10a,
parameter values for additional rollouts on moves were:
- level 6
- 216 games (36x6)
- seed 420
Standard deviations of level 6 equity estimates were between 0.018 and 0.022.
Parameter values for rollouts on cube decisions were:
- level 5
- 23328 games (36x648)
- full game
- seed 420
- settlement limit 0.550
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