Where do you put your blots?
tc...@lsa.umich.edu
difference where I put my blots, but according to the rollout, there is
a standout play here. What is it?
Money game with Jacoby, as usual.
GNU Backgammon Position ID: 4PMxQwBsDvgRQA
+13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
| X O X O | | O | 0 points
| X O O | | O |
| X O | | O |
| X O | | O |
| 6 O | | O |
v| |BAR| | (Cube: 1)
| | | |
| | | |
| | | X |
| O | | X X X | Rolled 24
| O O | X | X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ 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
David C. Ullrich
>I have to play a 2-4 from the bar. I wasn't sure that it made a lot of
>difference where I put my blots, but according to the rollout, there is
>a standout play here. What is it?
I must be overlooking something because it seems too easy.
X should come in on the 23 point to make it as hard as
possible for O to play awkward numbers behind him -
that leaves bringing the man down from the midpoint
with the 4.
>Money game with Jacoby, as usual.
>
> GNU Backgammon Position ID: 4PMxQwBsDvgRQA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O X O | | O | 0 points
> | X O O | | O |
> | X O | | O |
> | X O | | O |
> | 6 O | | O |
>v| |BAR| | (Cube: 1)
> | | | |
> | | | |
> | | | X |
> | O | | X X X | Rolled 24
> | O O | X | X X X | 0 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: tchow
David C. Ullrich
"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
Walt
> I have to play a 2-4 from the bar. I wasn't sure that it made a lot of
> difference where I put my blots, but according to the rollout, there is
> a standout play here. What is it?
>
> Money game with Jacoby, as usual.
>
> GNU Backgammon Position ID: 4PMxQwBsDvgRQA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O X O | | O | 0 points
> | X O O | | O |
> | X O | | O |
> | X O | | O |
> | 6 O | | O |
> v| |BAR| | (Cube: 1)
> | | | |
> | | | |
> | | | X |
> | O | | X X X | Rolled 24
> | O O | X | X X X | 0 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: tchow
Over the board I would probably just play bar/21 6/4. It's not apparent
that leaving an unnecessary blot is advantageous.
QF makes me think that there's a better play: stripping the 6 can't be
strategic, an exchange of hits works to our advantage, and the stack on
the 13 is ugly. Still, regardless of which point we choose to enter 2s
4s and 6s are duplicated (including a 6 to safety the blot on the 8)
Moving a checker down from the 13 adds a 1 or a 3 to the rolls that hit.
If you're going to move a checker off the 13 then bar/21 puts the two
runners in communication while bar/23 roes not. That's probably worth
something. Also 13/11 is better at making the 5 point than 13/9. So, by
process of elimination bar/21 13/11 must be the move.
I'm still unconvinced that it's better than bar/21 6/4.
//Walt
Paul
>
> - Show quoted text -
I prefer Walt's play. In fact, I already decided mentally on this
play before seeing his posting.
To be brief, I agree with Walt that it's good to put the checkers on
the 21 point and the 16 point in communication with each other, an
aspect not present in your play.
I also like Walt's play for minimizing the opponent's shots. Moving
off the 6 is bad positionally, I admit, but I'm willing to pay that
price to minimise the shots.
Those are some brief reasons that I agree with Walt, but I am by no
means confident of my choice -- just giving a tentative opinion.
Paul Epstein
Paul
Sorry, I read Walt too hastily. What I meant is that Walt's over-the-
board play is my play -- bar/21 6/4.
Paul Epstein
Grunty
Once again, Holy Scriptures come to advice us on tough dilemmas like
this.
Excerpt from Backgammonius, X:22
"When your inner board's stronger than your opponent's, then play
boldly."
"When your inner board's weaker than your opponent's, then play
chickenly."
Here our board's much stronger than our opp's, so we've got to
maximize contact: b/21!
Entering b/23 we'd be relieving all pressure from our opp, because
that checker doesn't cover any outer space. This play'd leave him
plenty of comfort to hit our outer blot, constructively placing a
builder in the process.
As for the deuce, 6/4 serves no purpose other than put out of play a
potentially valued checker. That leaves us with 13/11 as the only
reasonable play - and a good play in its own right for the reasons
above.
Bots will mark both plays so differently because one is a winning play
whereas the other is a losing play - don't care about the actual
equities, that's for the bots.
tc...@lsa.umich.edu
> GNU Backgammon Position ID: 4PMxQwBsDvgRQA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O X O | | O | 0 points
> | X O O | | O |
> | X O | | O |
> | X O | | O |
> | 6 O | | O |
>v| |BAR| | (Cube: 1)
> | | | |
> | | | |
> | | | X |
> | O | | X X X | Rolled 24
> | O O | X | X X X | 0 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: tchow
Grunty is right that safe-versus-bold is the right way to think about this
position. X is well behind in the race, with more checkers back and a
stronger board. Thus X wants to maximize contact.
What are the options? X has to enter from the bar, and then play the other
die using either the spare on the 6-point or the spare on the midpoint.
Let's look at the 6-point versus midpoint decision first. Playing from
the midpoint is clearly better positionally; it unstacks X's tallest point,
helps build a better forward position, and puts extra pressure on O to do
something about O's blot. The 6-point spare is valuable as a builder for
the 5-point, and moving it past the 5-point is a serious concession. The
sole disadvantage of playing from the midpoint is that it leaves another
blot. However, since X wants to maximize contact and has a stronger board,
leaving another blot is not much of a liability. All these considerations
point towards playing from the midpoint. We might have to take a second
look after we figure out the entire play to see if O really does have too
many good rolls after we play from the midpoint, but playing from the
midpoint really is the thematic choice here.
Now, where should we enter from the bar? The answer is that entering on
the 23-point maximizes contact. It might seem that keeping the checkers
connected by entering on the 21-point will give X more return shots if O
hits X's outfield blot loose. That is true as far as it goes, but the
thing is that O is unlikely to hit X's outfield blot loose. O has other
ways of playing 2's and 4's more safely; notably, if X enters with bar/21
then O will probably prefer 6/2 to 13/9* if O has to play a 4. O has a
very stacked and inflexible position, and one of O's few tools for playing
safely is to play behind X. Bar/21 gives O too many ways to do this. The
other thing to note is that X is not limited to trying to contain O's rear
checker. If that were the case then bar/21 might indeed be just as good
as if not better than bar/23. But since O is so inflexible, X has good
chances of getting a shot even if O manages to safety his rear checker,
simply because O will almost surely have to leave another blot soon. If
we assess the position as a whole rather than just focusing on O's rear
checker, we see that bar/23 maintains better contact.
This reasoning leads us to bar/23 13/9 as our top candidate. If we now
take a second look at bar/23 6/2, we see that bar/23 13/9 certainly makes
O's 1's play better, but not dramatically so. Since O has only a 1-point
board, X has almost the same number of return shots regardless of whether
O happens to hit on the 9-point. Bar/23 13/9 gives O some new double-hit
numbers, but they're not very good because they saddle O with a lot of
blots that will not be easy to clean up. There is no compelling reason
to play the anti-thematic 6/2. Thus bar/23 13/9 it is.
Over the board I suffered a moment of inattentiveness to the clear
safe-versus-bold indicators in this position and played the "safe"
bar/21 6/4. This is very much the wrong idea, as the rollout confirms.
1. Rollout bar/23 13/9 Eq.: -0.516
0.363 0.079 0.002 - 0.637 0.116 0.004 CL -0.314 CF -0.516
[0.001 0.001 0.000 - 0.001 0.002 0.000 CL 0.004 CF 0.009]
2. Rollout bar/23 6/2 Eq.: -0.603 ( -0.088)
0.339 0.067 0.002 - 0.661 0.132 0.005 CL -0.390 CF -0.603
[0.001 0.001 0.000 - 0.001 0.002 0.000 CL 0.003 CF 0.014]
3. Rollout bar/21 6/4 Eq.: -0.625 ( -0.109)
0.327 0.046 0.001 - 0.673 0.085 0.003 CL -0.389 CF -0.625
[0.001 0.001 0.000 - 0.001 0.002 0.000 CL 0.003 CF 0.006]
4. Rollout bar/21 13/11 Eq.: -0.626 ( -0.110)
0.331 0.049 0.002 - 0.669 0.097 0.003 CL -0.387 CF -0.626
[0.001 0.001 0.000 - 0.001 0.002 0.000 CL 0.003 CF 0.008]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 839217450 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]
Paul
Very good analysis, Tim. I see the case against my own choice (the
same as your play over the board) but I still don't see the case
against 6/2 (other than saying "It must be wrong because the rollout
says it is."). Why is 6/2 so anti-thematic? Leaving a blot is
clearly not a good thing. (We can see this by asking "If O has the
choice of hitting on the next roll, will O hit?" The answer is
generally, yes). More importantly, 6/2 helps to prepare a four point
board. It's not clear (to me) that X's checker on the 6 is better
placed than the checker on the 2 since X is not well placed to make
the 5 point.
I'd be interested to see what gnu-non-rollout says (I am not
authorised to download gnubg onto this computer so I can't do this
myself) since that (although not the theoretical truth) is close to
the best we can expect from human reasoning.
Thanks again, Tim.
Great post as always.
Paul Epstein
tc...@lsa.umich.edu
Paul <paulde...@yahoo.com> wrote:
>I'd be interested to see what gnu-non-rollout says (I am not
>authorised to download gnubg onto this computer so I can't do this
>myself) since that (although not the theoretical truth) is close to
>the best we can expect from human reasoning.
Here are GNU 2-ply and 4-ply evaluations.
1. Cubeful 2-ply bar/23 13/9 Eq.: -0.443
0.374 0.081 0.001 - 0.626 0.132 0.005
2-ply cubeful prune [world class]
2. Cubeful 2-ply bar/21 13/11 Eq.: -0.493 ( -0.050)
0.358 0.061 0.001 - 0.642 0.117 0.004
2-ply cubeful prune [world class]
3. Cubeful 2-ply bar/21 6/4 Eq.: -0.522 ( -0.079)
0.351 0.057 0.001 - 0.649 0.110 0.003
2-ply cubeful prune [world class]
4. Cubeful 2-ply bar/23 6/2 Eq.: -0.523 ( -0.080)
0.355 0.073 0.001 - 0.645 0.141 0.005
2-ply cubeful prune [world class]
1. Cubeful 4-ply bar/23 13/9 Eq.: -0.460
0.373 0.084 0.002 - 0.627 0.130 0.005
4-ply cubeful prune
2. Cubeful 4-ply bar/21 13/11 Eq.: -0.522 ( -0.062)
0.353 0.058 0.001 - 0.647 0.113 0.004
4-ply cubeful prune
3. Cubeful 4-ply bar/23 6/2 Eq.: -0.551 ( -0.090)
0.352 0.074 0.002 - 0.648 0.143 0.005
4-ply cubeful prune
4. Cubeful 4-ply bar/21 6/4 Eq.: -0.558 ( -0.097)
0.345 0.054 0.001 - 0.655 0.108 0.003
4-ply cubeful prune
>Why is 6/2 so anti-thematic? Leaving a blot is clearly not a good thing.
>(We can see this by asking "If O has the choice of hitting on the next
>roll, will O hit?" The answer is generally, yes). More importantly,
>6/2 helps to prepare a four point board. It's not clear (to me) that
>X's checker on the 6 is better placed than the checker on the 2 since
>X is not well placed to make the 5 point.
It's certainly true that leaving a blot is not good, so the question is
why 6/2 is even worse. It is true that X is not currently well placed
to make the 5-point, but X is not well-placed to make the 2-point either,
even after slotting it. It's a good general rule of thumb that a spare on
the 6-point is very valuable, because it can be used to build any missing
home-board point and also to hit loose on any open home-board point.
If X does hit O on his very next turn, then X will almost certainly prefer
having an attacker poised on the 6-point rather than a blot on the 2-point
(since X is almost certainly not going to be able to hit O *and* cover
the 2-point blot on the next turn).
By the way, the story changes if we modify the position by moving a
checker from X's midpoint to X's 6-point. In this modified position,
X is not so far behind in the race any more (so the safe/bold balance
is a closer call) and now he has *two* spares on the 6-point. So if
he plays one of them 6/4 or 6/2 then he still has a flexible position.
In fact, in this new position, GNU 4-ply thinks the top three plays are
almost too close to call.
1. Cubeful 4-ply bar/21 6/4 Eq.: -0.325
0.402 0.063 0.001 - 0.598 0.082 0.003
4-ply cubeful prune
2. Cubeful 4-ply bar/23 6/2 Eq.: -0.328 ( -0.002)
0.403 0.091 0.002 - 0.597 0.109 0.004
4-ply cubeful prune
3. Cubeful 4-ply bar/23 13/9 Eq.: -0.333 ( -0.008)
0.401 0.093 0.002 - 0.599 0.109 0.004
4-ply cubeful prune
4. Cubeful 4-ply bar/21 13/11 Eq.: -0.375 ( -0.049)
0.391 0.071 0.002 - 0.609 0.100 0.004
4-ply cubeful prune