Cube Action in a Volatile Position
Peter Schneider
this position came up the other day.
(Note that O is on the bar.)
What would be your cube action?
GNU Backgammon Position ID: u9yACUBuboFgBA
Match ID : cAngAAAAIAAA
+13-14-15-16-17-18------19-20-21-22-23-24-+ O: opp
| X X | O | O O X O O O | 0 points
| X | | O O O O |
| | | O O |
| | | |
| | | |
v| |BAR| | 7 point match (Cube: 1)
| | | |
| | | |
| | | X X |
| O | | X X X X | On roll
| O O X | | X X X X | 4 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: juggler
Pip counts: O 104, X 116
Best,
Peter aka the juggler on FIBS
Michael Petch
On 14/08/09 3:00 PM, in article 7em1h9F...@mid.individual.net, "Peter
Schneider" <schneiderp...@gmx.net> wrote:
At this score X might want to consider holding onto the cube. I'm not sure
this is a cube (I wouldn't cube yet), but I am pretty sure at 3away-7away
this is an easy take for O. If X doesn't roll a 3 right away, and O comes on
reasonably fast there could be recube action with some luck.
The issue I have is that many players who play O might be inclined to drop
(Many weaker opps are timid to take while on the bar). I'd say if you think
your opponent has a tendency to drop - I'd say cash now.
Mike
tc...@lsa.umich.edu
Michael Petch <mpe...@capp-sysware.com> wrote:
>At this score X might want to consider holding onto the cube. I'm not sure
>this is a cube (I wouldn't cube yet), but I am pretty sure at 3away-7away
>this is an easy take for O. If X doesn't roll a 3 right away, and O comes on
>reasonably fast there could be recube action with some luck.
My guess is that the "correct" cube action is Double/Take. Eighteen rolls
put a second checker up and six more rolls make a fifth point in the table.
At 3 away/7 away there's no need to be excessively cautious. O probably
has a take, being so far behind.
--
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
tc...@lsa.umich.edu
muratk <mu...@compuplus.net> wrote:
>On Aug 14, 4:44�pm, tc...@lsa.umich.edu wrote:
>
>> My guess is that the "correct" cube action is Double/Take.
>>�Eighteen rolls put a second checker up and six more rolls
>> make a fifth point in the table. At 3 away/7 away there's
>> no need to be excessively cautious. O probably has a take,
>> being so far behind.
>
Sort of. I did mention before that risk-averse play might be somewhat
similar to (correct) play when one is far ahead in a match. It's not
exactly the same, though. The correct match-play move is the one that
maximizes one's probability of winning the match, while the risk-averse
play is the one that optimizes a somewhat mysterious function that describes
certain kinds of human behavior.
Both concepts are a little fuzzy, though. Maximizing one's chances of
winning a match requires estimating the probability that a randomly chosen
game will end in a gammon; this is a number we have only a vague handle on.
Neil Robins
"Peter Schneider" <schneiderp...@gmx.net> wrote in message
news:7em1h9F...@mid.individual.net...
should expect an immediate recube to four from the bar.
tc...@lsa.umich.edu
Neil Robins <neil.r...@ntlworld.com> wrote:
>"Peter Schneider" <schneiderp...@gmx.net> wrote in message
>news:7em1h9F...@mid.individual.net...
>>
>> Match ID : cAngAAAAIAAA
>> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: opp
>> | X X | O | O O X O O O | 0 points
>> | X | | O O O O |
>> | | | O O |
>> | | | |
>> | | | |
>>v| |BAR| | 7 point match (Cube: 1)
>> | | | |
>> | | | |
>> | | | X X |
>> | O | | X X X X | On roll
>> | O O X | | X X X X | 4 points
>> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: juggler
>> Pip counts: O 104, X 116
>>
>>
>should expect an immediate recube to four from the bar.
But there just aren't that many bad throws. 54 and 52 are bad, for sure,
but 64, 51, 42, and 22 at least let you clean up blots and make the bar.
A recube after anything but 54 or 52 would be pretty gutsy.
Peter Schneider
<tc...@lsa.umich.edu> wrote
> In article <IoZhm.287458$Sn5.1...@newsfe26.ams2>,
> Neil Robins <neil.r...@ntlworld.com> wrote:
>>"Peter Schneider" <schneiderp...@gmx.net> wrote in message
>>news:7em1h9F...@mid.individual.net...
>>>
>>> GNU Backgammon Position ID: u9yACUBuboFgBA
>>> Match ID : cAngAAAAIAAA
>>> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: opp
>>> | X X | O | O O X O O O | 0 points
>>> | X | | O O O O |
>>> | | | O O |
>>> | | | |
>>> | | | |
>>>v| |BAR| | 7 point match (Cube: 1)
>>> | | | |
>>> | | | |
>>> | | | X X |
>>> | O | | X X X X | On roll
>>> | O O X | | X X X X | 4 points
>>> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: juggler
>>> Pip counts: O 104, X 116
>>>
>>>
>>A double here looks seriously wrong to me at this score. A bad throw and
>>you
>>should expect an immediate recube to four from the bar.
>
> But there just aren't that many bad throws. 54 and 52 are bad, for sure,
> but 64, 51, 42, and 22 at least let you clean up blots and make the bar.
> A recube after anything but 54 or 52 would be pretty gutsy.
I concur. Looked briefly at the position after 54 (after moving 18/14 18/13
which gnubg rates doubtful) and didn't see a recube there. The 4 point
board is simply too strong and you can "hide" the blots behind
duplications.
While O will have a sequence of indirect shots in the course of the game
after the posted position if X doesn't pick up the second checker, I don't
think that any of them justifies a recube. O needs a hit first, and then X
must not enter or even re-hit.
One of the reasons it's a cube, I guess ;-).
Peter Schneider
I wrote
I posted this position because gnubg's 2-ply idea about the cube action
differs a lot from the results of a rollout. Over the virtual board, I
cubed and my opp dropped, both rated wrong by gnubg when I analyzed the
game. The pass was considered a huge blunder:
Cube analysis
2-ply cubeless equity +0,839 (Money: +0,833)
0,741 0,421 0,018 - 0,259 0,087 0,002
Cubeful equities:
2-ply cubeful prune [world class]
1. No double +0,774
2. Double, pass +1,000 ( +0,226)
3. Double, take +0,688 ( -0,086)
Proper cube action: No double, take (27,6%)
I didn't buy that because I liked my cube and was glad that I wasn't on the
receiving side. I also thought that it's time to double before I lose my
market by picking up the second checker. I was curious what others think.
And while 9 out of 10 times a rollout confirms gnubg's initial estimate and
not mine, this time it was not so:
Rollout details:
Centered 1-cube:
0,770 0,416 0,018 - 0,230 0,070 0,003 CL +0,872 CF +0,911
[0,002 0,006 0,003 - 0,002 0,002 0,004 CL 0,007 CF 0,011]
Player APersson owns 2-cube:
0,772 0,417 0,035 - 0,228 0,058 0,004 CL +1,170 CF +1,072
[0,003 0,012 0,008 - 0,003 0,002 0,001 CL 0,023 CF 0,026]
Full cubeful rollout with var.redn.
335 games, Mersenne Twister dice gen. with seed 866742623 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]
(It's a cubeful rollout just because it's my standard setting; it just
ocurs to me that that may not be the best idea in a position which gnubg
misinterpretes.)
I can only guess what it is that 2-ply doesn't see here:
-- O is pretty inflexible and will continue to leave shots (if X stays in
the game); that's simply outside of 2-plys lookahead scope and isn't
predicted well enough by the static evaluation.
-- gnubg underestimates the long term damage of O's buried checker: it
makes it harder for O to cover plus it adds to the inflexibility.
-- X is ahead in the race which means that X can play it safe and get away
with it while O needs to incur risks in order to win.
Thanks for your comments.
tc...@lsa.umich.edu
In article <7esaplF...@mid.individual.net>,
Peter Schneider <schneiderp...@gmx.net> wrote:
>(It's a cubeful rollout just because it's my standard setting; it just
>ocurs to me that that may not be the best idea in a position which gnubg
>misinterpretes.)
Balanced against that, though, is that in a position where the possibility of
the cube flying back and forth rapidly is precisely what's at stake, it seems
that a cubeful rollout is mandatory, rather than an attempt to "adjust" a
cubeless rollout.
By the way, what cube action do 3-ply and 4-ply recommend?
Walt
At this match score, turning the cube should result in a recube fairly
shortly. It's volitile enough that I'd be hesitant to blow my four
point lead by losing and being tied at 4-4 or losing a gammon and the match.
Plus, there are good gammon chances. I'd sit on the cube and try for
gammon - Crawford at 6-0 looks pretty good.
There are lots of market losers, so this may be the last chance to
double, but I'd still refrain from doubling.
//Walt
tc...@lsa.umich.edu
>By the way, what cube action do 3-ply and 4-ply recommend?
I decided to play with this position myself using gnubg, and the answer
was still no double at 4-ply. I did a 1296 expert-level rollout, and
got more-or-less the same results as your rollout, namely double/pass.
The difference is quite striking, and I'm now not completely sure what
to believe. In addition to the usual caveats about bots, there's another
gotcha in match-play evaluations, which is that one needs to estimate
dubious quantities such as the probability of a gammon (starting from the
initial position). When the decision is a delicate one, small changes
in such estimates can have a large effect.
As far as what practical lessons can be extracted from this position, though,
I think that in such a volatile position it's important to go through all
the rolls, rather than just making a general assessment of the position
based on how it looks. Here you have several indirect shots, and your
hitting numbers and point-making numbers are nicely diversified (except
for 31). I can imagine a similar-looking position being actually much
worse for you because you have fewer good rolls. The only way to tell the
difference is to count them explicitly.
Peter Schneider
<tc...@lsa.umich.edu> wrote
> Fascinating analysis...great posting.
:-)) Too much honor...
> By the way, what cube action do 3-ply and 4-ply recommend?
They still think it's a huge take:
Match ID u9yACUBuboFgBA:cBHgAAAAIAAA
(gnubg developers: This would be nice to have in the result box
to make sure one is talking about the proper position).
Cube analysis
3-ply cubeless equity +0,859 (Money: +0,856)
0,755 0,420 0,009 - 0,245 0,080 0,003
Cubeful equities:
3-ply cubeful prune [grandmaster]
1. No double +0,813
2. Double, pass +1,000 ( +0,187)
3. Double, take +0,810 ( -0,003)
Proper cube action: No double, take (1,5%)
Cube analysis
4-ply cubeless equity +0,848 (Money: +0,842)
0,745 0,418 0,017 - 0,255 0,082 0,002
Cubeful equities:
4-ply cubeful prune
1. No double +0,794
2. Double, pass +1,000 ( +0,206)
3. Double, take +0,745 ( -0,049)
Proper cube action: No double, take (19,1%)
Peter Schneider
<tc...@lsa.umich.edu> wrote
> there's another
> gotcha in match-play evaluations, which is that one needs to estimate
> dubious quantities such as the probability of a gammon (starting from the
> initial position). When the decision is a delicate one, small changes
> in such estimates can have a large effect.
Well, 70 and 90 mp (errors for not cubing/taking) are not so delicate,
are they? It's an error I'd find excusable for myself in a cube action
but most better players would consider it pretty large.
Besides, assumed gammon ratios influence a cube recommendation based
on a static evaluation as well. (Apart from the fact that 4-ply
is not really static and hopefully played "according to score".)
> The difference is quite striking, and I'm now not completely sure what
> to believe.
I tend to believe the rollout. You'd have to have really strong arguments
to make a case for the opposite.
> As far as what practical lessons can be
> extracted from this position, though,
> I think that in such a volatile position
> it's important to go through all the rolls.[...]
> I can imagine a similar-looking position being actually much
> worse for you because you have fewer good rolls.
Good point.
It can not explain the rollout/n-ply discrepancy though because
bots go through all the rolls all the time and never tire.
(Which is an indication of their stupidity. This thought
makes me feel better.)
tc...@lsa.umich.edu
Peter Schneider <schneiderp...@gmx.net> wrote:
>Well, 70 and 90 mp (errors for not cubing/taking) are not so delicate,
>are they? It's an error I'd find excusable for myself in a cube action
>but most better players would consider it pretty large.
By delicate, I meant that you get a wild swing in the answer when switching
from 4-ply evaluation to 2-ply rollout (from no double to double/pass).
>I tend to believe the rollout. You'd have to have really strong arguments
>to make a case for the opposite.
Well, given the choice, I would certainly opt for the rollout over the
evaluation, but the discrepancy between the two means that I'm no longer
sure I trust the rollout. The rollout is, after all, ultimately based on
the evaluation function. You hinted at this problem yourself when you
expressed doubts about doing a cubeful rollout.
A relevant question, for instance, is whether there really is a recube after
the weak rolls, and if so, which rolls. Do rollouts agree with evaluations
on this question? If not, then this discrepancy could cause problems for the
rollout from the initial position.