Blitz versus prime
tc...@lsa.umich.edu
and prime-versus-prime cube problems, but what about blitz-versus-prime
problems? I haven't encountered too many of these, and my intuition for
them is still not very good. How would you assess the position below?
Ignore the score; this is a money game.
GNU Backgammon Position ID: 2OaGAWCxvQkBMA
Match ID : cAkAAEAAGAAA
+13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
| X O O | O | O O O X | 4 points
| O O | O | O O O X |
| O | | |
| | | |
| | | |
v| |BAR| | (Cube: 1)
| | | |
| | | X |
| | | X |
| O X | | X X X | On roll
| O X X | | X X X X | 3 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
Walt
> If you've studied backgammon then you've probably seen blitz cube problems
> and prime-versus-prime cube problems, but what about blitz-versus-prime
> problems? I haven't encountered too many of these, and my intuition for
> them is still not very good. How would you assess the position below?
> Ignore the score; this is a money game.
>
> GNU Backgammon Position ID: 2OaGAWCxvQkBMA
> Match ID : cAkAAEAAGAAA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O O | O | O O O X | 4 points
> | O O | O | O O O X |
> | O | | |
> | | | |
> | | | |
> v| |BAR| | (Cube: 1)
> | | | |
> | | | X |
> | | | X |
> | O X | | X X X | On roll
> | O X X | | X X X X | 3 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: tchow
>
If O anchors on the 2 or 3 then X is in a lot of trouble. That makes me
a bit timid about cubing. Also, with X sitting on the ace point hitting
loose to continue the blitz theme is somewhat iffy. And the immediate
threat of sending a third checker back behind the broken prime looms large.
Put these together, and I don't see a cube for X here from a strategic
perspective.
But, when I think about the possible rolls, all 6's 5's and 4's play
really well. And except for 3-1, 3's are good. So tactically, it looks
good.
So let's look at the take proposition and apply Woosley's law. O has
good winning chances, but also faces significant gammon threats. He'll
likely be looking at two checkers on the roof against a four point
board. That's hard to take. I'd be inclined to pass, but I'm not sure.
So, Woolsey's law says double, and I'll go with that.
//Walt
Neil Robins
<tc...@lsa.umich.edu> wrote in message
news:4b84a090$0$514$b45e...@senator-bedfellow.mit.edu...
> If you've studied backgammon then you've probably seen blitz cube problems
> and prime-versus-prime cube problems, but what about blitz-versus-prime
> problems? I haven't encountered too many of these, and my intuition for
> them is still not very good. How would you assess the position below?
> Ignore the score; this is a money game.
>
> GNU Backgammon Position ID: 2OaGAWCxvQkBMA
> Match ID : cAkAAEAAGAAA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O O | O | O O O X | 4 points
> | O O | O | O O O X |
> | O | | |
> | | | |
> | | | |
> v| |BAR| | (Cube: 1)
> | | | |
> | | | X |
> | | | X |
> | O X | | X X X | On roll
> | O X X | | X X X X | 3 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: tchow
>
checkkers back on the 24 point gives a lot more flexibility to get them out
than if they were both on the 22 point., and we're certainly hoping
opponent doesn't get a chance to interfere. I'd just see this as a strong
blitz with the opponent having the ever dangerous best three point board
and another useful point. Double/Take looks right to me.
David C. Ullrich
tc...@lsa.umich.edu wrote:
> If you've studied backgammon then you've probably seen blitz cube problems
> and prime-versus-prime cube problems, but what about blitz-versus-prime
> problems? I haven't encountered too many of these, and my intuition for
> them is still not very good. How would you assess the position below?
> Ignore the score; this is a money game.
I'd say O is in huge trouble. And I agree that I might not
call it blitz versus _prime_. In both cases that's because
O's bar point is open - move the men from the 16 point to the
18 point and it becomes much more interesting, seems to me.
>
> GNU Backgammon Position ID: 2OaGAWCxvQkBMA
> Match ID : cAkAAEAAGAAA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O O | O | O O O X | 4 points
> | O O | O | O O O X |
> | O | | |
> | | | |
> | | | |
> v| |BAR| | (Cube: 1)
> | | | |
> | | | X |
> | | | X |
> | O X | | X X X | On roll
> | O X X | | X X X X | 3 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: tchow
--
David C. Ullrich
N Merrigan
In fact, X has a lot to do here in such a short spell of time. Not even
close to a cube for me.
In money your looking for the most efficient cube, especially with Jacoby.
If X were already split say to O's 3-pt then I would guessimate this is the
closest to an efficient cube, with X on O's Bar-pt being a Pass and with X
on O's 2-pt being No Double.
As it is, X has yet to split.
Ciow
N.Merrigan
"David C. Ullrich" <dull...@sprynet.com> wrote in message
news:dullrich-DFD5EB...@text.giganews.com...
tc...@lsa.umich.edu
> GNU Backgammon Position ID: 2OaGAWCxvQkBMA
> Match ID : cAkAAEAAGAAA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O O | O | O O O X | 4 points
> | O O | O | O O O X |
> | O | | |
> | | | |
> | | | |
> v| |BAR| | (Cube: 1)
> | | | |
> | | | X |
> | | | X |
> | O X | | X X X | On roll
> | O X X | | X X X X | 3 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: tchow
O.K., so several have objected to my calling this a "blitz versus prime"
position. It's true that O's 5-out-of-6 prime has a gap in the middle.
However, I still feel that thinking of O's defensive structure as a prime
is a good way to analyze the position, as I'll explain in a moment.
On the blitz side of the board, it is clear that O faces serious
danger of being closed out and gammoned. If O's defense were any
weaker---for example, if the two checkers on O's 9-point were back
on the midpoint---then O would certainly have a big pass. But, at
the moment X has only a three-point board and a blot on the ace point.
O has reasonable chances of anchoring, and some chances of hitting, and
then we have to assess what O's chances of turning the game around are.
A large part of O's equity comes from X's two rear checkers, which are
in some danger of getting trapped. Here is where I think it is useful
to think of O's defensive structure as a prime. In many positions, an
ace-point anchor is worse than a deuce-point anchor, which in turn is
weaker than a 3-point anchor. But here, it is the opposite. If X had
a deuce-point or a 3-point anchor, then X's back checkers would have an
even harder job escaping than they do in the diagrammed position.
The rollout indicates that it's a small double and a big take, at least
with the Jacoby rule in force. I haven't rolled it out without Jacoby,
but my guess is that the double/no double decision would then be close
to a toss-up. Most of X's wins will be gammon wins, and doubling
activates those gammons. Move X's anchor up a pip or two and it becomes
a clear no double, even with Jacoby.
Over the board, I doubled, and was surprised when GNU 2-ply evaluation
dinged me for doing so. My decision was vindicated by the rollout, but
not by as much as I thought. Despite X's twelve checkers in the zone
and O's two checkers on the bar, O has more than enough defensive
resources to take. Note that X has a non-trivial chance of getting
gammoned himself if the game turns around.
Rollout details:
Centered 1-cube:
0.588 0.411 0.007 - 0.412 0.113 0.006 CL +0.474 CF +0.715
[0.002 0.002 0.001 - 0.002 0.001 0.000 CL 0.005 CF 0.012]
Player gnubg owns 2-cube:
0.604 0.437 0.004 - 0.396 0.111 0.007 CL +1.061 CF +0.764
[0.002 0.002 0.001 - 0.002 0.002 0.001 CL 0.011 CF 0.016]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 850353415 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]
Bradley K. Sherman
<tc...@lsa.umich.edu> wrote:
>
>
>Rollout details:
>Centered 1-cube:
> 0.588 0.411 0.007 - 0.412 0.113 0.006 CL +0.474 CF +0.715
> [0.002 0.002 0.001 - 0.002 0.001 0.000 CL 0.005 CF 0.012]
>Player gnubg owns 2-cube:
> 0.604 0.437 0.004 - 0.396 0.111 0.007 CL +1.061 CF +0.764
> [0.002 0.002 0.001 - 0.002 0.002 0.001 CL 0.011 CF 0.016]
Would someone be kind enough to point me to an explanation
of how to interpret these records?
--bks
tc...@lsa.umich.edu
The two most important numbers are the top right numbers in each table,
which in this case are +0.715 and +0.764. The number +0.715 is the
equity of "no double" and the number +0.764 is the equity of "double,
take." Since +0.764 < +1.000, it is correct to take if the double
is offered. Then since +0.764 > +0.715, it is correct to double, since
doing so raises one's equity.
"CF" stands for "cubeful" and "CL" stands for "cubeless." I don't find
the cubeless equity to be that useful, but some people do. The six
numbers preceding "CL" are the cubeless probabilities of winning, winning
a gammon, winning a backgammon, losing, losing a gammon, and losing a
backgammon respectively. In many positions, these cubeless numbers are
decent approximations to the *actual* probabilities of winning, losing,
etc., though in some positions the cube makes a big difference and you
can't just naively equate cubeless probabilities with actual probabilities.
The second row of each table, in brackets, indicates the estimated standard
deviations of the quantities in the first row. Again the most important
number is the one at the end. This is a measure of the uncertainty in the
cubeful equity estimate. If these numbers are too large relative to the
difference between +0.764 and +0.715 then you should not be surprised if
a longer rollout reverses the verdict.
Bradley K. Sherman
<tc...@lsa.umich.edu> wrote:
>In article <hmghjr$9dl$1...@reader1.panix.com>,
>Bradley K. Sherman <b...@panix.com> wrote:
>>In article <4b874116$0$514$b45e...@senator-bedfellow.mit.edu>,
>> <tc...@lsa.umich.edu> wrote:
>>> 0.604 0.437 0.004 - 0.396 0.111 0.007 CL +1.061 CF +0.764
>take." Since +0.764 < +1.000, it is correct to take if the double
Thanks, Tim. I understood everything you wrote except why
+0.764 < +1.000
implies a take.
I really appreciate the help.
--bks
Bradley K. Sherman
Bradley K. Sherman <b...@panix.com> wrote:
>
>Thanks, Tim. I understood everything you wrote except why
> +0.764 < +1.000
>implies a take.
>
Oh, wait, never mind. I get it. (Dropping == 1.)
Sorry.
--bks