A slightly awkward roll
tc...@lsa.umich.edu
GNU Backgammon Position ID: 0HNwEBbgc/AxAA
+24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
| O O | | O X X | 0 points
| O | | O X X |
| O | | O X |
| O | | X |
| | | X |
| |BAR| |v (Cube: 1)
| X | | |
| X | | |
| X | | X O |
| O X | | X O | Rolled 45
| O O X | | O X O | 0 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
Walt
> GNU Backgammon Position ID: 0HNwEBbgc/AxAA
> +24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
> | O O | | O X X | 0 points
> | O | | O X X |
> | O | | O X |
> | O | | X |
> | | | X |
> | |BAR| |v (Cube: 1)
> | X | | |
> | X | | |
> | X | | X O |
> | O X | | X O | Rolled 45
> | O O X | | O X O | 0 points
> +-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: tchow
Of course you hit. O has no board. O has a blot in his home board. You
have to leave a blot no matter what you do, so you might as well take
away half his roll by hitting.
Where to hit? Hit on the 7. Hitting on the 2 allows a direct shot and
then the other half of the opponent's roll can be used to cover the
blot on the 20. By hitting on the 7, any hit has to leave the blot on
the 20 exposed.
Ok, your rollout probably will show this to be wrong, because most of
the positions you post have a significant qf, but in the absence of qf,
that's my move.
//Walt
David C. Ullrich
>This is a money game. Do you hit? If so, how do you hit?
>
> GNU Backgammon Position ID: 0HNwEBbgc/AxAA
> +24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
> | O O | | O X X | 0 points
> | O | | O X X |
> | O | | O X |
> | O | | X |
> | | | X |
> | |BAR| |v (Cube: 1)
> | X | | |
> | X | | |
> | X | | X O |
> | O X | | X O | Rolled 45
> | O O X | | O X O | 0 points
> +-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: tchow
Hitting on the bar point seems clear - must be a trick question.
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.)
Philippe Michel
> This is a money game. Do you hit? If so, how do you hit?
>
> GNU Backgammon Position ID: 0HNwEBbgc/AxAA
> +24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
> | O O | | O X X | 0 points
> | O | | O X X |
> | O | | O X |
> | O | | X |
> | | | X |
> | |BAR| |v (Cube: 1)
> | X | | |
> | X | | |
> | X | | X O |
> | O X | | X O | Rolled 45
> | O O X | | O X O | 0 points
> +-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: tchow
I don't hit. 13/8 13/9.
16/7* seems very loose with its second blot and the loss of the 16 point.
Among hits, the safe-ish and ugly 13/8 6/2* is probably more reasonnable
but 13/8 13/9 should be easy to follow up whether hit or not and very
promising in the latter case.
With no board at all and a good racing lead, I don't really mind O
surrendering something in my inner board to make the bar point.
N Merrigan
The key to the position is tempo. X has to leave a shot but does he have to
relinquish the initiative as a result? If your answer is no, then, you've
found the correct play.
N.Merrigan
<tc...@lsa.umich.edu> wrote in message
news:4b075f5f$0$505$b45e...@senator-bedfellow.mit.edu...
tc...@lsa.umich.edu
>This is a money game. Do you hit? If so, how do you hit?
>
> GNU Backgammon Position ID: 0HNwEBbgc/AxAA
> +24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
> | O O | | O X X | 0 points
> | O | | O X X |
> | O | | O X |
> | O | | X |
> | | | X |
> | |BAR| |v (Cube: 1)
> | X | | |
> | X | | |
> | X | | X O |
> | O X | | X O | Rolled 45
> | O O X | | O X O | 0 points
> +-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: tchow
Some of my rollouts are still running, and I will eventually post them here
when they're done, but I thought I would post a followup based on what I've
found so far.
GNU Backgammon likes to hit 16/7*. Walt and David thought this was the
"obvious" move, and if so that's good, because I don't want to be posting
only positions where the "obvious" move is not the one GNU prefers. However,
I do not believe that the problem is that easy. For example, if we shift
O's anchor to the 4-point, then GNU seems to slightly prefer 13/8 6/2*,
although I haven't rolled it out enough to be sure yet. Move the anchor to
the 5-point and the preference for 13/8 6/2* increases. So far I have not
seen anybody post an analysis that gives different answers depending on
whether O's anchor is on the 3-point versus the 4-point or the 5-point.
I believe that the first thing to notice about the position is that X is
way ahead in the race. X has escaped both back checkers while O still has
three checkers back. Nobody has made any new home-board points yet. It
follows that O is eager to get into a blot-hitting contest, whereas X would
prefer to just bring his checkers quietly home. X's first instinct should
be to avoid the kind of slugfest that O is desperate to start.
For that reason, X should not reflexively play 16/7* without carefully
considering the alternatives. The trouble, of course, is that there is
no "safe" play. 13/8 13/9 allows O to hit with any direct 6 or 2, as
well as with 3-4. If X wants to take the path of minimizing contact,
then 13/8 6/2* leaves far fewer shots. And if X is not afraid of the
return shots but just wants to build good structure if X is not hit,
then 16/7* looks superior to 13/8 13/9. O's hitting 4's are duplicated
so 16/7* doesn't leave any more return shots and it knocks O off balance.
So I think the real choice is between 13/8 6/2* and 16/7*.
Over the board, I chose 13/8 6/2*, which as I said GNU doesn't like much.
While it is safer, it does not do much to repair X's inflexibility problems.
Even if O misses, X's next roll may very well be awkward again. On the
other hand, after 16/7*, if X does not get hit, then X has a good chance of
making a big structural improvement with a strong, flexible configuration.
Flexibility is very important when it comes to hanging on to a race lead.
Although I'm not completely sure yet, I think that flexibility is the key
to understanding why 13/8 6/2* becomes more attractive when O's anchor is
shifted forwards. If O has an advanced anchor, then X has more opportunities
to handle awkward rolls by dumping checkers behind the anchor. Though this
might look ugly, X is far enough ahead in the race that he will be happy to
do this if it means he can keep his big racing lead secure. However, in the
diagrammed position, X's inflexibility problems are severe enough that he is
better off paying now rather than paying later.
David C. Ullrich
Surely if O has the 5 point then the bar point is less useful to X and
less important to O; otoh if O is stuck back on the 3 point then O
would really like to make the bar point instead, and X would really
like the bar point for blocking O.
In particular, when O is back on the 3 point then if X has his bar
that makes outfield blots much safer, while the bar has little
effect on the safety of blots X may want to bring down if O has
the 5 point.
(Is that just a post hoc rationalization for a "reflexive" lucky
guess? Maybe yes, maybe no. We'll never know what I would
have said about the modified position where O has the 5 point
if you'd posed the question before saying what gnubg thought
about it. But in the original position it simply "seems" "clear"
that the bar point is very important, and in the modified
position it seems much less so - when O has an advanced
anchor it's "clearly" less plausible for X to try to build a
prime in front of him...)
>I believe that the first thing to notice about the position is that X is
>way ahead in the race. X has escaped both back checkers while O still has
>three checkers back. Nobody has made any new home-board points yet. It
>follows that O is eager to get into a blot-hitting contest, whereas X would
>prefer to just bring his checkers quietly home. X's first instinct should
>be to avoid the kind of slugfest that O is desperate to start.
>
>For that reason, X should not reflexively play 16/7* without carefully
>considering the alternatives. The trouble, of course, is that there is
>no "safe" play. 13/8 13/9 allows O to hit with any direct 6 or 2, as
>well as with 3-4. If X wants to take the path of minimizing contact,
>then 13/8 6/2* leaves far fewer shots. And if X is not afraid of the
>return shots but just wants to build good structure if X is not hit,
>then 16/7* looks superior to 13/8 13/9. O's hitting 4's are duplicated
>so 16/7* doesn't leave any more return shots and it knocks O off balance.
>So I think the real choice is between 13/8 6/2* and 16/7*.
>
>Over the board, I chose 13/8 6/2*, which as I said GNU doesn't like much.
>While it is safer, it does not do much to repair X's inflexibility problems.
>Even if O misses, X's next roll may very well be awkward again. On the
>other hand, after 16/7*, if X does not get hit, then X has a good chance of
>making a big structural improvement with a strong, flexible configuration.
>Flexibility is very important when it comes to hanging on to a race lead.
I think that's more or less equivalent to what I was going to say.
If X wants to just come home safely his biggest problem is clearing
the 16 point. Playing 13/8 6/2* doesn't do anything towards that
objective, while if X hits on the bar and gets away with it he has
a good chance to clean things up next time.
>Although I'm not completely sure yet, I think that flexibility is the key
>to understanding why 13/8 6/2* becomes more attractive when O's anchor is
>shifted forwards. If O has an advanced anchor, then X has more opportunities
>to handle awkward rolls by dumping checkers behind the anchor. Though this
>might look ugly, X is far enough ahead in the race that he will be happy to
>do this if it means he can keep his big racing lead secure. However, in the
>diagrammed position, X's inflexibility problems are severe enough that he is
>better off paying now rather than paying later.
David C. Ullrich
tc...@lsa.umich.edu
David C. Ullrich <dull...@sprynet.com> wrote:
>Surely if O has the 5 point then the bar point is less useful to X and
>less important to O; otoh if O is stuck back on the 3 point then O
>would really like to make the bar point instead, and X would really
>like the bar point for blocking O.
Yes, I like your explanation.
One could describe the decision as a balancing act between
- starting to clear the back point, and fighting for the bar point
versus
- not getting hit back.
tc...@lsa.umich.edu
>In article <4b075f5f$0$505$b45e...@senator-bedfellow.mit.edu>, I wrote:
>>This is a money game. Do you hit? If so, how do you hit?
>>
>> GNU Backgammon Position ID: 0HNwEBbgc/AxAA
>> +24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
>> | O O | | O X X | 0 points
>> | O | | O X X |
>> | O | | O X |
>> | O | | X |
>> | | | X |
>> | |BAR| |v (Cube: 1)
>> | X | | |
>> | X | | |
>> | X | | X O |
>> | O X | | X O | Rolled 45
>> | O O X | | O X O | 0 points
>> +-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: tchow
>
>Some of my rollouts are still running, and I will eventually post them here
>when they're done
Here they are. First, the original position:
1. Rollout 16/7* Eq.: +0.320
0.573 0.171 0.009 - 0.427 0.106 0.004 CL +0.216 CF +0.320
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.003 CF 0.007]
2. Rollout 13/8 6/2* Eq.: +0.274 ( -0.046)
0.569 0.144 0.005 - 0.431 0.108 0.004 CL +0.175 CF +0.274
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.003 CF 0.006]
Full cubeful rollout with var.redn.
5184 games, Mersenne Twister dice gen. with seed 840986854 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]
Next, wth O's anchor moved to the 4-point instead of the 3-point:
1. Rollout 13/8 6/2* Eq.: +0.283
0.576 0.127 0.005 - 0.424 0.104 0.004 CL +0.175 CF +0.283
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.002 CF 0.006]
2. Rollout 16/7* Eq.: +0.274 ( -0.009)
0.563 0.163 0.008 - 0.437 0.108 0.004 CL +0.185 CF +0.274
[0.001 0.001 0.001 - 0.001 0.001 0.000 CL 0.003 CF 0.008]
3. Rollout 13/9 13/8 Eq.: +0.236 ( -0.046)
0.562 0.138 0.006 - 0.438 0.112 0.004 CL +0.152 CF +0.236
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.002 CF 0.006]
Full cubeful rollout with var.redn.
5184 games, Mersenne Twister dice gen. with seed 841620726 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]
Finally, with O's anchor moved to the 5-point instead of the 3-point:
1. Rollout 13/8 6/2* Eq.: +0.233
0.565 0.118 0.004 - 0.435 0.109 0.004 CL +0.139 CF +0.233
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.002 CF 0.006]
2. Rollout 16/7* Eq.: +0.212 ( -0.021)
0.552 0.144 0.006 - 0.448 0.113 0.004 CL +0.138 CF +0.212
[0.001 0.001 0.000 - 0.001 0.001 0.000 CL 0.003 CF 0.007]
Full cubeful rollout with var.redn.
5184 games, Mersenne Twister dice gen. with seed 841627206 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]
I would have rolled out 13/9 13/8 for all three cases except that I only
realized after the fact that I had included it only in one case. I'm pretty
sure it would not have made the top two. In the case of the 5-point anchor,
there's also 13/4 to consider; a 0-ply rollout suggests that it would not
have come out on top, but that it's not too far off.
Philippe Michel
> I would have rolled out 13/9 13/8 for all three cases except that I only
> realized after the fact that I had included it only in one case. I'm pretty
> sure it would not have made the top two.
I suppose it would do better in the original problem, where both 4 5 and 7
points are available and worse in the latter case where there is only the
bar. But not necessarily by the needed 0.04-0.05.
That was my idea : slotting the 9 point is a little worse than the bar (a
little only, it is 6 pips away from the anchor, a good place to make a
point) but the spares can be used, if not hit, to make better points all
the more easily that there is nothing left dangling on the 16 point.