Double 2's
tc...@lsa.umich.edu
horribly wrong!
GNU Backgammon Position ID: s3mQAQN03sABAw
Match ID : cAkJAEAAEAAA
+24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
| O O O X O | | O X | 4 points
| O O O X O | | X |
| O | | X |
| O | | |
| | | |
| |BAR| |v (Cube: 1)
| | | |
| X | | |
| X X | | |
| X O X | | X O | Rolled 22
| X X O X | | X O | 2 points
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: tchow
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
Piranha
Hitting is out of the question and being behind in the race, I keep
the position as it is.
Only safe move that improves something is
13/7, 4/2
Paul
It's important for X to hit for the usual reasons, particularly since
X is behind in the race. A useful practical point is that, if X wants
to play fast and X has sub-excellent pip-counting skills (social
etiquette requires speed in non-clock situations, and in clock
situations the need for speed is obvious), O can be seen to have a
significant lead thus: If you remove O's checkers on O's 1 point and
X's checkers on X's 7 point, you get a near symmetrical position.
Therefore, including the non-corresponding checkers shows that O has a
significant lead.
Further argument for the hit: O does not have many builders in place
to shut X out. Note that the hit duplicate O's 2's. Given the hit,
minimising O's returns is clearly desirable. So my play is to hit and
then play 6/4. 6/4 is antipositional and undesirable. If it was
legal to just play 3 of the 2's, I would rather hit and then pick up
the dice. But I judge the anti-positional problems of 6/4 to be less
than the extra shots O gets from the alternative plays.
Paul Epstein
tc...@lsa.umich.edu
I'll give you a hint here...GNU 2-ply says that 20/14* 6/4 is 40th best!
Somewhat better is 20/14* 3/1, ranked 28th. We don't really need a bot
to tell us that hitting is wrong. Outboarded 4 to 2, with a blot in our
table and numerous other ways to get hit back, we are leading with the
chin if we give up our advanced anchor to hit. Yes, we are behind in the
race, but this is not the moment to panic. Our opponent is rather stripped
and is likely to give us future opportunities to hit. Better to wait until
our board is stronger before getting into a slugfest.
I did not hit, but still managed to pick the 8th best play according to
a rollout, which I will wait a bit before posting.
Piranha
> In article <4d601879-4580-4ea7-af53-def848983...@f12g2000yqn.googlegroups.com>,
Too lazy to set up the position, but I´m curious to know, where my
choice 13/7, 4/2 ranks?
Grunty
After this play the race will stand:
O: 120, X: 132 - 8 = 124
So this is a battle for timing -- he who gets forced to abandon their
anchor first, falls at disadvantage for the attacking threats.
My first choice is: 13/11(3) 4/2.
This play allows X to play sixes using the 11-point spare.
13/7 places a spare on the bar-point too, but it would be dumped onto
the ace-point on a subsequent six, and yet the other die has to be
played. A bit too straightforward for my taste.
Also, making the 11-point exerts direct pressure upon O's anchor,
looking forward to O running out of his mid-point timing.
My second choice is: 6/4/2 4/2 3/1.
This play preserves a distant spare on the mid-point, and makes an
inner point for the tough times to come. X will cheerfully make the
ace-point with a 5.
Regarding the hit 20/14* -- why going into a punching against a guy
whose fists double your own? X isn't desperate at all -- unless he
needs to make a demonstration to his girlfriend.
tc...@lsa.umich.edu
> GNU Backgammon Position ID: s3mQAQN03sABAw
> Match ID : cAkJAEAAEAAA
> +24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
> | O O O X O | | O X | 4 points
> | O O O X O | | X |
> | O | | X |
> | O | | |
> | | | |
> | |BAR| |v (Cube: 1)
> | | | |
> | X | | |
> | X X | | |
> | X O X | | X O | Rolled 22
> | X X O X | | X O | 2 points
> +-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: tchow
Below is the rollout of GNU's top 9 plays. Grunty's first choice is also
GNU's first choice. In this sort of position, X wants to keep up the
pressure on O's checkers and simultaneously build up a board, so that X
can hit and contain one of O's checkers. X can hit with this roll but
is not yet ready to do so, and thus must figure out how to keep up the
pressure.
Occupying the points that are six away from O's rear points is often the
best way to do this. Suppose we alter the position by moving O's blot
to O's 4-point and X's spare from X's midpoint to X's barpoint. Then by
far the best way to play 2-2 would be 20/18(2) 13/11(2), occupying both
six-away points. But 20/18(2) 13/11(2) is no good in the actual position
because it leaves a blot on the midpoint. Also, X wants to keep some
pressure on O's blot, and stepping up the back checkers releases some of
that pressure.
Unable to seize both six-away points, X's correct play is to seize one
of them, with 13/11(3), and then play the remaining 2 inside his home
table. It is fairly clear that 4/2 is the best 2, given X's goal of
building a strong board quickly.
My choice was to seize the other six-away point with 20/18(2) 6/2. But
there are several reasons this is the wrong choice. One is that O is
less likely to want to run from the midpoint anyway, so it's more important
to put pressure on O's rear point. Another reason is that after 13/11(3),
the spare on the 11-point is more flexibly positioned than on the midpoint.
Finally, as a general principle it's better to stay back on the 5-point
anchor rather than the barpoint anchor when behind in the race and
outboarded, since the 5-point anchor provides superior defense.
1. Rollout 13/11(3) 4/2 Eq.: +0.070
0.517 0.074 0.002 - 0.483 0.078 0.002 CL +0.030 CF +0.070
[0.001 0.001 0.000 - 0.001 0.002 0.000 CL 0.003 CF 0.006]
2. Rollout 13/11(3) 6/4 Eq.: +0.045 ( -0.025)
0.511 0.074 0.002 - 0.489 0.081 0.002 CL +0.015 CF +0.045
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.003 CF 0.006]
3. Rollout 13/11(3) 3/1 Eq.: +0.003 ( -0.067)
0.498 0.068 0.002 - 0.502 0.084 0.002 CL -0.021 CF +0.003
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.003 CF 0.006]
4. Rollout 13/7 4/2 Eq.: -0.046 ( -0.116)
0.482 0.085 0.002 - 0.518 0.088 0.002 CL -0.039 CF -0.046
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.003 CF 0.006]
5. Rollout 13/7 6/4 Eq.: -0.072 ( -0.142)
0.475 0.081 0.002 - 0.525 0.085 0.002 CL -0.054 CF -0.072
[0.001 0.001 0.000 - 0.001 0.002 0.000 CL 0.003 CF 0.006]
6. Rollout 6/2(2) Eq.: -0.074 ( -0.144)
0.476 0.085 0.002 - 0.524 0.093 0.002 CL -0.055 CF -0.074
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.003 CF 0.006]
7. Rollout 6/2 4/2 3/1 Eq.: -0.078 ( -0.148)
0.473 0.086 0.002 - 0.527 0.099 0.003 CL -0.068 CF -0.078
[0.001 0.001 0.000 - 0.001 0.002 0.000 CL 0.003 CF 0.006]
8. Rollout 20/18(2) 6/2 Eq.: -0.078 ( -0.148)
0.472 0.077 0.002 - 0.528 0.093 0.002 CL -0.071 CF -0.078
[0.001 0.002 0.000 - 0.001 0.002 0.000 CL 0.003 CF 0.006]
9. Rollout 13/7 3/1 Eq.: -0.102 ( -0.172)
0.465 0.077 0.001 - 0.535 0.087 0.002 CL -0.080 CF -0.102
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.003 CF 0.006]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 846563796 and
quasi-random dice
Play: supremo 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 16 more moves within equity 0.32
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
Grunty
play, I recommend, as an introductory reading, this article published
on this newsgroup:
"Playing doublets," 2008, Jan 5.
Then find a revised, examples-and-graphics-enriched version of that
article and a sequel of it in:
http://www.backgammon-biba.co.uk/GruntyPlayingDoublets.htm
http://www.backgammon-biba.co.uk/GruntyPlayingDoubles02.htm
Before writing all that stuff, I'd have probably opted for 20/14*
4/2.
;-))