Game #3
Open Division Final
San Mateo, California
17 November 1996
11 Point Match
Kevin Mansfield (X) vs. Nick Ballard (O)
Score: 2 - 0
Analysis by Steve Clark
We revisited the November 17th finals,
because the participants packed more excitement per roll
into their games than was easily conveyed in a single example.
Where volatility happens, informative analysis ensues.
This is the second game of the Open Division finals,
between Kevin Mansfield and Nick Ballard.
| Play 1a |
+-------------+---+-------------+
| O X | | X O |
| O X | | X O |
| X | | X O |
| X | | O | 167
| X | | O |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| O | | X |
| O | | X | 167
| O | | O X |
| X O | | O X |
| X O | | O X |
+-------------+---+-------------+
|
|
X to play 54
Candidate Plays Equities
13/8 24/20 +0.020
13/8 13/9 +0.019
24/15 -0.007
13/4 -0.033
|
|
SC:
|
In the modern age where JellyFish dominates the known universe,
splitting comes out ahead.
Actually the plays are so close to a toss-up
that personal preference is the true deciding factor.
|
| |
X
|
O
|
|
1.
|
54: 13/8 13/9
|
42: 8/4 6/4
|
|
2.
|
52: 9/4 6/4
|
|
|
| Play 2b |
+-------------+---+-------------+
| O X X | | X O |
| O X X | | X O |
| X | | X O |
| X | | X O | 151
| | | O |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| O | | | 161
| O | | X |
| X O O | | O X |
| X O O | | O X |
+-------------+---+-------------+
|
|
O to play 52
Candidate Plays Equities
13/8 13/11 -0.048
13/8 6/4 -0.105
13/8 24/22 -0.114
|
|
SC:
|
Just when you have decided you should always split,
along comes a rollout result like this one.
Here bringing two checkers down wins because:
-
O has five checkers on the 13 point,
so that bringing two down does not strip the 13 point;
-
O has rolled no 5's, so that he does not need to create extra
ways to play this awkward number; and
-
X is slightly cramped and therefore is well placed (and eager)
to attack if O splits.
|
| |
X
|
O
|
|
2.
|
...
|
52: 13/8 13/11
|
|
| Play 3a |
+-------------+---+-------------+
| O X X | | X O |
| O X X | | X O |
| X | | X O |
| X | | X | 151
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| O | | | 154
| O | | O X |
| X O O | | O X |
| X O O | | O O X |
+-------------+---+-------------+
|
|
X to play 51
Candidate Plays Equities
24/18 -0.088
13/8 24/23 -0.089
13/8 6/5 -0.153
13/7 -0.155
8/2 -0.163
8/3 24/23 -0.181
|
|
SC:
|
Back to the merits of splitting.
Although coming out to O's bar point is usually somewhat inferior
to splitting to the 23 point,
here it comes out even.
The reason is that the 5 played elsewhere
further cramps X's slightly awkward position.
Moving 24/18 leaves a balanced position
which is so important to winning backgammon.
At the table I am sure I would make this play,
even though 13/8 24/23 comes out even in the rollouts.
The slotting plays (13/8 6/5 and 13/7) come out well behind.
The reason is that so many of X's next rolls will force him
to abandon the midpoint.
Slotting plays usually show up as slightly inferior in the rollouts.
In this position both slotting plays involve stripping the midpoint
so they are worse than usual.
If you can get all these split-or-slot plays right,
you can win significant money in any tournament in the world.
|
| |
X
|
O
|
|
3.
|
51: 13/7
|
|
|
| Play 3b |
+-------------+---+-------------+
| O X X | | X X O |
| O X X | | X O |
| X | | X O |
| X | | X | 145
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| O | | | 154
| O | | O |
| X O O | | O X |
| X O O | | O O X |
+-------------+---+-------------+
|
|
O to play 55
Candidate Plays Equities
13/3 11/6 8/3 -0.079
13/3(2) -0.089
13/3 8/3(2) -0.110
|
|
SC:
|
13/3 11/6 8/3 seems to be the obvious play.
While it stacks too many checkers on the 6 point,
it has the merit of preserving the mid point
while avoiding pushing an extra to the 3 point.
An extra checker on the 3 point here is not diversification,
it is a misplaced checker.
I am surprised that 13/3(2) was so close.
|
| |
X
|
O
|
|
3.
|
...
|
55: 13/3 8/3(2)
|
|
| Play 4a |
+-------------+---+-------------+
| O X X | | X X O |
| O X X | | X O |
| X | | X |
| X | | X | 145
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| O | | | 134
| O O | | |
| X O O O | | X |
| X O O O | | O O X |
+-------------+---+-------------+
|
|
X to play 41
Candidate Plays Equities
8/4 8/7 +0.099
13/9 8/7 +0.055
6/2 8/7 -0.007
|
|
SC:
|
X has gotten away with his slot and grabs the advantage.
Did you look at 24/20 with the 4?
In many similar positions it would be correct.
Here, however, white would be too happy to attack,
and X correctly rejects the split.
|
| |
X
|
O
|
|
4.
|
41: 8/4 8/7
|
|
|
| Play 4b |
+-------------+---+-------------+
| O X X | | X X O |
| O X X | | X X O |
| X X | | |
| X | | | 140
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| O | | | 134
| O O | | |
| X O O O | | X |
| X O O O | | O O X |
+-------------+---+-------------+
|
|
O to play 11
Candidate Plays Equities
24/23(2) 6/5(2) +0.202
24/22 6/5(2) +0.100
8/5 6/5 +0.100
|
|
SC:
|
6/5(2) is clear.
The results of the rollouts show how important it is
to get the random ace plays right.
Here making the 23 point is clear.
X will find that many 4's and 6's play awkwardly.
|
| |
X
|
O
|
|
4.
|
...
|
11: 24/23(2) 6/5(2)
|
|
5.
|
65: 24/13
|
|
|
| Play 5b |
+-------------+---+-------------+
| O X X | | X X O |
| O X X | | X X O |
| X X | | |
| X | | | 129
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| | | | 130
| O | | X |
| O O O O | | X |
| X O O O O | | O O X |
+-------------+---+-------------+
|
|
O to play 51
Candidate Plays Equities
11/5 -0.048
11/6 8/7 -0.055
11/6 3/2 -0.066
11/6 23/22 -0.076
13/8 3/2 -0.146
13/8 11/10 -0.148
|
|
SC:
|
How desperate are you?
You have to be pretty desperate to leave a direct shot
when slotting the back of a prime.
O could really use his bar point in this position so he goes for it.
The rear slot would be a clear winner if O had more cover rolls
on his next turn.
Even so his play is a toss-up with the safer 11/5.
|
| |
X
|
O
|
|
5.
|
...
|
51: 11/6 8/7
|
|
6.
|
42: 13/7
|
|
|
| Play 6b |
+-------------+---+-------------+
| O X X | | X X O |
| O X X | | X X O |
| X X | | X |
| X | | | 123
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| | | | 124
| O O | | |
| O O O O | | X |
| X O O O O | | O X |
+-------------+---+-------------+
|
|
O to play 11
Candidate Plays Equities
23/22(2) 3/1* +0.231
23/22 7/6 3/1* +0.150
7/5 3/1* +0.141
|
|
SC:
|
X will have a much tougher time getting away if he is on the bar.
23/22(2) with the other aces gives O a better chance
of escaping in the next few rolls.
|
| |
X
|
O
|
|
6.
|
...
|
11: 23/22(2) 3/1*
|
|
7.
|
42: Bar/23 6/2
|
|
|
| Play 7b |
+-------------+---+-------------+
| X O X X | | X X O |
| O X X | | X X O |
| X X | | X |
| | | | 118
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| | | | 120
| O | | |
| O O O O | | X |
| O X O O O O | | O X |
+-------------+---+-------------+
|
|
O to play 42
Candidate Plays Equities
6/2* 7/5 +0.169
6/2* 13/11 +0.118
6/2* 22/20 +0.113
13/7 +0.071
7/1 +0.047
|
|
SC:
|
This is a killer position.
There are three reasonable approaches and each leads
to a different type of position.
But the resulting positions are not very familiar
and the relative equities of each are not clear.
13/7 builds a 5-point prime but leaves O's game cut in half.
It also leaves a weak blot on the ace.
7/1 builds a 5-point board and makes use of that checker on the ace point.
If O makes this play,
he probably will have some good hitting rolls next turn,
but most of his missing rolls will be quite weak.
Of the various hitting plays,
it is clear that the mini-banzai of 6/2 7/5 is better
that the all-out kamikaze plays of 6/2 13/11 or 6/2 22/20.
O probably will be hit and he may as well make sure
that he can stay in the game when it happens.
The kamikaze plays do not provide that assurance.
The hitting play has some clear advantages.
It puts X on the bar against a 4-point board.
If X hits,
O will have a blot on the 2 point to shoot at (at least some of the time).
These extraneous blots are very important in this type of position.
Even if X hits back,
he will be deep in O's territory and will be struggling to escape.
This position is like many in Kit Woolsey's and Hal Heinrich's new book.
The correct play might be clear in retrospect
(particularly if you are looking at the rollout results),
but finding it at the table is as tough as nails.
|
| |
X
|
O
|
|
7.
|
...
|
42: 7/1
|
|
| Play 8a |
+-------------+---+-------------+
| X O X X | | X X O |
| O X X | | X X O |
| X X | | X |
| | | | 118
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| | | | 114
| O | | |
| O O O O O | | X |
| O X O O O O | | X |
+-------------+---+-------------+
|
|
X to play 52
Candidate Plays Equities
23/18 4/2 -0.083
23/16 -0.152
7/2 4/2 -0.253
7/2 6/4 -0.272
23/18 6/4 -0.322
13/8 13/11 -0.409
|
|
SC:
|
X does not find the best play here.
4/2 builds his board as best he can,
while 23/18 starts the escape of his back checker.
13/8 13/11 exposes another blot while abandoning the rear checker.
But surely this just looks like a minor misplay.
Right? Well, not exactly.
It turns out to be quite important that the back checker move up.
It is exposed in either place.
However, if he comes up to the 18 point,
he is half way to safety.
If he stays back,
he is just stuck back there for another turn.
Surely the correct play just jumped out at you, didn't it?
|
| |
X
|
O
|
|
8.
|
52: 13/8 13/11
|
|
|
| Play 8b |
+-------------+---+-------------+
| X O X X | | X X X O |
| O X X | | X X O |
| X X | | X X |
| | | | 111
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| | | | 114
| O | | |
| O O O O O | | |
| O X O O O O | | |
+-------------+---+-------------+
|
|
O to play. Double or roll?
Equity (center cube)
O 70.8% G 8.7% BG 0.2%
X 29.2% G 2.4% BG 0.2%
Equity (O): +0.479
Equity (X owns 2 cube)
O 52.6% G 28.2% BG 0.5%
X 47.4% G 3.3% BG 0.3%
Equity (X): -0.304
Equity (cubeless)
O 61.8% G 29.3% BG 0.6%
X 38.2% G 10.5% BG 0.6%
Equity (O): +0.425
|
|
SC:
|
The rollout shows this to be a minimum light double.
At the table it is tough to do, however.
O will have to attack in a situation where, if X comes in,
he will apparently have the advantage.
Also scary is that O has two checkers partially trapped on X's 3 point.
|
|
JF:
|
I would have doubled (level 7 evaluation).
|
| |
X
|
O
|
|
8.
|
...
|
Roll
|
|
| Play 8b2 |
+-------------+---+-------------+
| X O X X | | X X X O |
| O X X | | X X O |
| X X | | X X |
| | | | 111
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| | | | 114
| O | | |
| O O O O O | | |
| O X O O O O | | |
+-------------+---+-------------+
|
|
O to play 63
Candidate Plays Equities
22/13 +0.188
22/16 5/2* +0.152
13/7 5/2* +0.113
22/16 6/3 +0.110
13/4 +0.056
|
|
SC:
|
Another in a series of nutcracker problems.
It seems crazy for O to run when he isn't ahead.
Furthermore, banana split plays such as 22/16 5/2 or 13/7 5/2 are only right
when O is desperate
(Kent Goulding named these plays "banana splits"
because you have to be bananas to make such splits).
13/4 seems to be a nice sane play which everyone would make.
It brings in another pounder while keeping everything together.
Clearly nothing else is really worth considering.
The only trouble with the logic in the preceding paragraph is
that the answer is totally wrong.
In retrospect it is clear why the bananas play shows well.
The alternatives are awkward,
while the hit tries to take advantage of the blots X has spread around.
This is a tough play to see at the table
because everyone filters this type of play out of their thinking,
but it has real logic to it.
Well, ok, that makes sense so far but what about the running play of 22/13?
After all, it is the clear winner in the rollouts.
It gets a checker free at a time when O can not attack very effectively.
It makes X's 6,5 roll bad.
But so what?
Is there any chance that I would find this play at the table?
No way.
|
| |
X
|
O
|
|
8.
|
...
|
63: 13/4
|
|
| Play 9a |
+-------------+---+-------------+
| X O X X | | X X X O |
| O X X | | X X |
| X X | | X X |
| | | | 111
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | | |
| | | | 105
| O O | | |
| O O O O O | | |
| O X O O O O | | |
+-------------+---+-------------+
|
|
X to play 11
Candidate Plays Equities
8/5 6/5 -0.007
11/10 7/5 6/5 -0.044
7/5 6/5 2/1 -0.045
|
| |
X
|
O
|
|
9.
|
11: 8/5 6/5
|
64: 22/16 6/2*
|
|
10.
|
43: Cannot move
|
|
|
| Play 10b |
+-------------+---+-------------+
| X O X X X | | X X O X O |
| X X X | | X X |
| X | | X |
| | | | 109
| | | |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| | X | |
| | | | 95
| O | | |
| O O O O O | | |
| O O O O O O | | |
+-------------+---+-------------+
|
|
O to play. Double or roll?
Equity (center cube)
O 80.2% G 20.5% BG 0.3%
X 19.8% G 1.3% BG 0.1%
Equity (O): +0.799
Equity (X owns 2 cube)
O 69.3% G 31.9% BG 0.5%
X 30.7% G 1.4% BG 0.1%
Equity (X): -0.694
Equity (cubeless)
O 74.0% G 32.6% BG 0.5%
X 26.0% G 3.8% BG 0.2%
Equity (O): +0.771
|
|
SC:
|
Should O play on here?
At the equity shown,
virtually everyone agrees you should cash.
But no real work has been done to determine what equity O needs to play on.
This actually might be a play-on position,
but I doubt it.
|
| |
X
|
O
|
|
10.
|
...
|
Double -> 2
|
|
11.
|
Pass
|
|
|
| Play 11a |
+-------------+---+-------------+
| O X | | X O |
| O X | | X O |
| X | | X O |
| X | | O | 167
| X | | O |
| | | | +---+
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | |
| | | | +---+
| O | | X |
| O | | X | 167
| O | | O X |
| X O | | O X |
| X O | | O X |
+-------------+---+-------------+
|
|
SC:
|
This relatively short game has a wonderful variety
of tough and interesting positions.
A number of these are worth looking at again and again.
|
|
O went on to win a long match (11-6).
|
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 6788
Standard deviations of equity estimates were between 0.002 and 0.009.
Parameter values for rollouts on cube decisions were:
- level 5
- 23328 games (36x648)
- full game
- seed 6788
- settlement limit 0.570
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