Cubeless vs. cubeful
tc...@lsa.umich.edu
1. in a cubeless game, A is better than B both in terms of winning chances
and gammon chances, but
2. in a money game with the cube, B is better than A?
--
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
Neil Robins
<tc...@lsa.umich.edu> wrote in message
news:4993598a$0$306$b45e...@senator-bedfellow.mit.edu...
Yes such positions not only exist but are very common. Often, A involves
leaving your opponent some joker throw and B doesn't when you are very close
to a cube.
tc...@lsa.umich.edu
Neil Robins <neil.r...@ntlworld.com> wrote:
><tc...@lsa.umich.edu> wrote in message
>news:4993598a$0$306$b45e...@senator-bedfellow.mit.edu...
>> Do there exist positions with two candidate moves A and B such that
>>
>> 1. in a cubeless game, A is better than B both in terms of winning chances
>> and gammon chances, but
I should also have said that A's cubeless equity is better than B's.
>> 2. in a money game with the cube, B is better than A?
>
>Yes such positions not only exist but are very common. Often, A involves
>leaving your opponent some joker throw and B doesn't when you are very
>close to a cube.
Interesting...can you give an example that doesn't require computer
analysis to verify?
bob
Match ID : cAkHAAAAAAAA
+24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
| O O O O O | | | 0 points
| O O O O O | | |
| O O | | |
| O O | | |
| | | |
| |BAR| |v (Cube: 1)
| | | |
| | | X |
| | | X |
| X X X X | | X X | Rolled 61
| X X X X O X | | X X | 0 points
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: user
This will be an interesting postion for you. There is a lot to
consider here!
Bob Koca
tc...@lsa.umich.edu
bob <bob_...@hotmail.com> wrote:
> GNU Backgammon Position ID: 294DAAJrsz0AAA
> Match ID : cAkHAAAAAAAA
> +24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
> | O O O O O | | | 0 points
> | O O O O O | | |
> | O O | | |
> | O O | | |
> | | | |
> | |BAR| |v (Cube: 1)
> | | | |
> | | | X |
> | | | X |
> | X X X X | | X X | Rolled 61
> | X X X X O X | | X X | 0 points
> +-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: user
O.K., I'm stumped. The 6 should be played 8/2, and there are two plausible
candidates for the 1: the safe 8/7 and the bold 6/5*. The safe play leaves
the race more-or-less even. If O doesn't immediately disengage, then X has
the advantage, but I think O can take if X doubles.
The bold play wins on O's 16 rolls that dance, because O won't be able to
take the cube. But O has 20 rolls to enter and hit, after which O will
usually win. So the safe play seems right if there is a cube.
Is the point that in cubeless play, 6/5* creates more winning chances?
Even if O enters and hits, the game has to be played to its conclusion
if there is no cube.
David C. Ullrich
The position is too "interesting" for me to try to say what the right
play is in either case, but I suspect part of the point is that in a
cubeless game hitting risks X losing a gammon, while with the
cube in the middle (assuming Jacoby) hitting may be more
attractive since X can just drop if he's hit back and then bounces.
The idea that Jacoby protects one against losing a gammon has
led me into bogus conclusions in the past, because the threat of
a gammon nonetheless affects equities and cube strategy. But
come to think of it, if X is hit and then he bounces I think
X has a drop even if there's no such thing as a gammon, so
Jacoby really does make the possible gammon after 6/5*
irrelevant (while it's certainly relevant in a cubeless game).
I think, probably maybe.
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.)
tc...@lsa.umich.edu
<In article <8ae9d905-9314-4ec3...@l16g2000yqo.googlegroups.com>,
<bob <bob_...@hotmail.com> wrote:
<> GNU Backgammon Position ID: 294DAAJrsz0AAA
<> Match ID : cAkHAAAAAAAA
<> +24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
<> | O O O O O | | | 0 points
<> | O O O O O | | |
<> | O O | | |
<> | O O | | |
<> | | | |
<> | |BAR| |v (Cube: 1)
<> | | | |
<> | | | X |
<> | | | X |
<> | X X X X | | X X | Rolled 61
<> | X X X X O X | | X X | 0 points
<> +-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: user
<
<O.K., I'm stumped.
Bob, are you going to post a full analysis of this position?
I would also like to see other examples where correct cubeful and cubeless
play differ dramatically.
tc...@lsa.umich.edu
it through gnubg.
In article <q3qfp4le02ikmgkg6...@4ax.com>,
David C. Ullrich <dull...@sprynet.com> wrote:
>On 14 Feb 2009 16:21:49 GMT, tc...@lsa.umich.edu wrote:
>>In article <8ae9d905-9314-4ec3...@l16g2000yqo.googlegroups.com>,
>>bob <bob_...@hotmail.com> wrote:
>>> GNU Backgammon Position ID: 294DAAJrsz0AAA
>>> Match ID : cAkHAAAAAAAA
>>> +24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
>>> | O O O O O | | | 0 points
>>> | O O O O O | | |
>>> | O O | | |
>>> | O O | | |
>>> | | | |
>>> | |BAR| |v (Cube: 1)
>>> | | | |
>>> | | | X |
>>> | | | X |
>>> | X X X X | | X X | Rolled 61
>>> | X X X X O X | | X X | 0 points
>>> +-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: user
[...]
>The position is too "interesting" for me to try to say what the right
>play is in either case, but I suspect part of the point is that in a
>cubeless game hitting risks X losing a gammon, while with the
>cube in the middle (assuming Jacoby) hitting may be more
>attractive since X can just drop if he's hit back and then bounces.
This is a plausible analysis, but I don't think it agrees with gnubg's
analysis (I'm assuming gnubg uses Jacoby by default). If it were double
match-point, then either 8/2 8/7 or 8/2 6/5* would win about 39-40% of
the time. The greater number of gammon losses therefore makes 8/2 6/5*
slightly worse in a cubeless game.
On the other hand, in a money game, gnubg deems 8/2 6/5* right by a mile.
After 8/2 6/5*, gnubg recommends an immediate double by O and a take by X,
after which it estimates O's equity as +0.138. If O enters immediately,
then O will almost certainly win, with about 16% of those wins being
gammons. But on O's 16 dancing rolls, X will redouble and O will drop.
In a cubeless game, O would still win about 20% of those games.
If instead X plays safe with 8/2 8/7, then gnubg estimates O's equity to
be +0.331.
The point seems to be that by hitting, X creates 16 bad rolls for O that
decide the game immediately in X's favor. The risk of getting hit back
is less than O's chances of winning after X's "safe" play, and O's gammon
chances aren't strong enough to swing the balance.
tc...@lsa.umich.edu
>On the other hand, in a money game, gnubg deems 8/2 6/5* right by a mile.
>After 8/2 6/5*, gnubg recommends an immediate double by O and a take by X,
>after which it estimates O's equity as +0.138. If O enters immediately,
>then O will almost certainly win, with about 16% of those wins being
>gammons.
Oops! This is wrong. Even if O enters immediately, hitting (say with 61),
X is not necessarily lost because X owns the cube and O has an open 6-point.
Thus O loses immediately with 16 dancing rolls and doesn't even win all the
remaining 20/36 games.
O could try to get around this situation by not doubling from the bar. But
then O still has to drop on the 16 dancing rolls, and if X drops O's double
on the other 20 rolls, then O's equity is only +4/36 or about +0.111---not
any better. (So this part of David Ullrich's analysis seems correct.)
What worries me a bit as far as trusting gnubg, though, is that even with a
rollout, gnubg reports O's equity in this situation as +0.088 rather than
+0.111. This suggests to me that gnubg is not turning the cube properly
during the rollout. Does anyone know how gnubg is obtaining the cubeful
equity in this kind of situation?
tc...@lsa.umich.edu
>What worries me a bit as far as trusting gnubg, though, is that even with a
>rollout, gnubg reports O's equity in this situation as +0.088 rather than
>+0.111. This suggests to me that gnubg is not turning the cube properly
>during the rollout. Does anyone know how gnubg is obtaining the cubeful
>equity in this kind of situation?
I think I can guess part of the answer. From the original position, suppose
X hits, O fails to double and then dances, and X then doubles. Gnubg's first
inclination is to evaluate this position as a take, but rolling out from this
position at the grandmaster (rather than expert) level indicates a drop. So
when I do an expert-level rollout it is probably assessing it as a take and
continuing to play out the game. Thus it is predicting slightly less equity
for O than if O had (correctly) dropped.
David C. Ullrich
>[...]
>
>What worries me a bit as far as trusting gnubg, though, is that even with a
>rollout, gnubg reports O's equity in this situation as +0.088 rather than
>+0.111. This suggests to me that gnubg is not turning the cube properly
>during the rollout. Does anyone know how gnubg is obtaining the cubeful
>equity in this kind of situation?
I was going to say ___ but I wasn't sure. I devised a test, which
seems to indicate that ___ actually _is_ what it does!
My impression has been that gnubg does a cubeless rollout and
then "adjusts" the numbers to allow for the cube. Evidence for
this: In the position
GNU Backgammon Position ID: CgAAUAAAAAAAAA
Match ID : cAkAAAAAAAAA
+13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
| | | O O | OOO 0 points
| | | | OOO
| | | | OOO
| | | | OO
| | | | OO
v| |BAR| | (Cube: 1)
| | | | XX
| | | | XX
| | | | XXX
| | | | XXX On roll
| | | X X | XXX 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: user
if you do a 0-ply rollout it says "double, pass".
(I imagine you're familiar with this, but for readers who
may not be: This is the classic example where it's a take
even though the probability of winning is less than 1/4;
if X rolls a 1 then O has a redouble (which is also a take)
and the extra equity from that makes it a take for O.)
tc...@lsa.umich.edu
>then "adjusts" the numbers to allow for the cube.
Interesting. I know that Kit Woolsey, in his "Backgammon Encyclopedia,"
says that he prefers to have Snowie do cubeless rollouts because they
are faster and because he doesn't trust Snowie to perform the correct
cube action during a rollout anyway. What he doesn't explain is how
to get a cubeful equity out of a cubeless rollout. In general, this
must be impossible (though I'm too lazy at the moment to construct two
positions with identical cubeless rollouts but distinct cubeful equities).
More generally, my guess would be that in positions like the one I posted,
where (with high probability) correct play will cause the cube to fly back
and forth a couple of times in quick succession, an "adjusted" cubeless
rollout could be way off.
David C. Ullrich
>In article <t96h4515mj89opevq...@4ax.com>,
>David C. Ullrich <dull...@sprynet.com> wrote:
>>My impression has been that gnubg does a cubeless rollout and
>>then "adjusts" the numbers to allow for the cube.
>
>Interesting. I know that Kit Woolsey, in his "Backgammon Encyclopedia,"
>says that he prefers to have Snowie do cubeless rollouts because they
>are faster and because he doesn't trust Snowie to perform the correct
>cube action during a rollout anyway. What he doesn't explain is how
>to get a cubeful equity out of a cubeless rollout. In general, this
>must be impossible (though I'm too lazy at the moment to construct two
>positions with identical cubeless rollouts but distinct cubeful equities).
Yes. You don't need an actual backgammon position to show that
this is impossible in general - a hypothetical position in which the
probability of winning the game is the same as in that classic
position from my last post but in which there is no redouble
suffices.
(Ok, for an actual _proof_ you need actual backgammon positions,
but...)
>More generally, my guess would be that in positions like the one I posted,
>where (with high probability) correct play will cause the cube to fly back
>and forth a couple of times in quick succession, an "adjusted" cubeless
>rollout could be way off.
David C. Ullrich
Michael Petch
On 29/06/09 4:44 AM, in article t96h4515mj89opevq...@4ax.com,
"David C. Ullrich" <dull...@sprynet.com> wrote:
> GNU Backgammon Position ID: CgAAUAAAAAAAAA
> Match ID : cAkAAAAAAAAA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | | | O O | OOO 0 points
> | | | | OOO
> | | | | OOO
> | | | | OO
> | | | | OO
> v| |BAR| | (Cube: 1)
> | | | | XX
> | | | | XX
> | | | | XXX
> | | | | XXX On roll
> | | | X X | XXX 0 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: user
>
>
> if you do a 0-ply rollout it says "double, pass".
Tim brought this to the Gnubg mailing list. David can you tell us what
rollout settings you used? When I do a 0 ply rollout I get double, take.
Cube analysis
Cubeful rollout equity: +0.576
0.788 0.000 0.000 - 0.212 0.000 0.000
Cubeful equities:
1. Double, take +0.914
2. Double, pass +1.000 ( +0.086)
3. No double +0.457 ( -0.457)
Proper cube action: Double, take
Rollout details:
Centered 1-cube:
0.788 0.000 0.000 - 0.212 0.000 0.000 CL +0.576 CF +0.457
[0.000 0.000 0.000 - 0.000 0.000 0.000 CL 0.000 CF 0.000]
Player BIG_SirLancelot owns 2-cube:
0.788 0.000 0.000 - 0.212 0.000 0.000 CL +1.151 CF +0.914
[0.000 0.000 0.000 - 0.000 0.000 0.000 CL 0.000 CF 0.000]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 866716458 and quasi-random
dice
Play: 0-ply cubeful prune [expert]
Cube: 0-ply cubeful prune [expert]
David C. Ullrich
<mpe...@capp-sysware.com> wrote:
>
>On 29/06/09 4:44 AM, in article t96h4515mj89opevq...@4ax.com,
>"David C. Ullrich" <dull...@sprynet.com> wrote:
>
>> GNU Backgammon Position ID: CgAAUAAAAAAAAA
>> Match ID : cAkAAAAAAAAA
>> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
>> | | | O O | OOO 0 points
>> | | | | OOO
>> | | | | OOO
>> | | | | OO
>> | | | | OO
>> v| |BAR| | (Cube: 1)
>> | | | | XX
>> | | | | XX
>> | | | | XXX
>> | | | | XXX On roll
>> | | | X X | XXX 0 points
>> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: user
>>
>>
>> if you do a 0-ply rollout it says "double, pass".
>
>Tim brought this to the Gnubg mailing list. David can you tell us what
>rollout settings you used? When I do a 0 ply rollout I get double, take.
What I get looks almost the same as yours:
Cube analysis
Rollout cubeless equity +0.576
Cubeful equities:
1. Double, pass +1.000
2. Double, take +1.151 ( +0.151)
3. No double +0.457 ( -0.543)
Proper cube action: Double, pass
Rollout details:
Centered 1-cube:
0.788 0.000 0.000 - 0.212 0.000 0.000 CL +0.576 CF +0.457
[0.000 0.000 0.000 - 0.000 0.000 0.000 CL 0.000 CF 0.002]
Player gnubg owns 2-cube:
0.788 0.000 0.000 - 0.212 0.000 0.000 CL +1.151 CF +1.151
[0.000 0.000 0.000 - 0.000 0.000 0.000 CL 0.000 CF 0.005]
Truncated cubeful rollout (depth 11) with var.redn.
1296 games, Mersenne Twister dice gen. with seed 866286418 and
quasi-random dice
Play: 0-ply cubeful prune [expert]
Cube: 0-ply cubeful prune [expert]
>Cube analysis
>Cubeful rollout equity: +0.576
> 0.788 0.000 0.000 - 0.212 0.000 0.000
>Cubeful equities:
>1. Double, take +0.914
>2. Double, pass +1.000 ( +0.086)
>3. No double +0.457 ( -0.457)
>Proper cube action: Double, take
>
>Rollout details:
>Centered 1-cube:
> 0.788 0.000 0.000 - 0.212 0.000 0.000 CL +0.576 CF +0.457
> [0.000 0.000 0.000 - 0.000 0.000 0.000 CL 0.000 CF 0.000]
>Player BIG_SirLancelot owns 2-cube:
> 0.788 0.000 0.000 - 0.212 0.000 0.000 CL +1.151 CF +0.914
> [0.000 0.000 0.000 - 0.000 0.000 0.000 CL 0.000 CF 0.000]
>Full cubeful rollout with var.redn.
>1296 games, Mersenne Twister dice gen. with seed 866716458 and quasi-random
>dice
>Play: 0-ply cubeful prune [expert]
>Cube: 0-ply cubeful prune [expert]
David C. Ullrich
Michael Petch
On 16/08/09 9:25 AM, in article 309g855c07frc81ci...@4ax.com,
"David C. Ullrich" <dull...@sprynet.com> wrote:
> What I get looks almost the same as yours:
>
> Cube analysis
> Rollout cubeless equity +0.576
>
> Cubeful equities:
> 1. Double, pass +1.000
> 2. Double, take +1.151 ( +0.151)
> 3. No double +0.457 ( -0.543)
> Proper cube action: Double, pass
> Rollout details:
> Centered 1-cube:
> 0.788 0.000 0.000 - 0.212 0.000 0.000 CL +0.576 CF +0.457
> [0.000 0.000 0.000 - 0.000 0.000 0.000 CL 0.000 CF 0.002]
> Player gnubg owns 2-cube:
> 0.788 0.000 0.000 - 0.212 0.000 0.000 CL +1.151 CF +1.151
> [0.000 0.000 0.000 - 0.000 0.000 0.000 CL 0.000 CF 0.005]
> Truncated cubeful rollout (depth 11) with var.redn.
> 1296 games, Mersenne Twister dice gen. with seed 866286418 and
> quasi-random dice
> Play: 0-ply cubeful prune [expert]
> Cube: 0-ply cubeful prune [expert]
>
Hi David,
I can't for the life of me reproduce this. If I use a Truncated Cubeful
rollout (depth 11) with variance reduction, same seed and 0 ply. I still
get double take and the same output.
Can you tell me what version (in the buildinfo page of the about box) of
GnuBG you are using and Platform (Windows/Linux/Mac etc) as well can you
email me a copy of this:
Go to your rollout setting, click the "save as" button. Save it to a .rol
file and send me a copy of that file. That will allow me to get all the
rollout settings you are using.
Thanks,
Michael
David C. Ullrich
Probably you've already been informed of this by Petch,
but just for the record: This doesn't prove what I said
it proves. It's not the way gnubg is designed to work,
it's a bug in the old version I was using that's been fixed
long ago.
Michael Petch
On 18/08/09 7:05 AM, in article 4m9l855390metdtj7...@4ax.com,
"David C. Ullrich" <dull...@sprynet.com> wrote:
>> if you do a 0-ply rollout it says "double, pass".
>
> Probably you've already been informed of this by Petch,
> but just for the record: This doesn't prove what I said
> it proves. It's not the way gnubg is designed to work,
> it's a bug in the old version I was using that's been fixed
> long ago.
I hadn't informed anyone so thanks!
David was using a version of 0.14.3 which has a number of issues in it when.
I was able to install a 0.14.3 release and could reproduce David's erroneous
results. The result is correct on the current release.
Thanks Tim for bringing the concern to the attention of the GnuBG mailing
list.
Michael