Middle game position
Philippe Michel
+-1--2--3--4--5--6--------7--8--9-10-11-12-+
| X X O O | | O O X X |
| X O O | | O O X |
| O | | O X |
| O | | |
| | | |
| | | |v [1]
| | | |
| X | | X |
| X | | X |
| O X | | X O |
| O X | | X O |
+24-23-22-21-20-19-------18-17-16-15-14-13-+
X to play 6 3
What should X plan be ?
Julian
In article <EELqG...@syseca.syseca.fr>, Philippe Michel
<mic...@syseca.fr> writes
The moved I considered were:
3/9 17/20
3/9 19/22
9/15 12/15
9/18
O has a pretty stripped position and needs either to attack your
stragglers (hence keep the anchor! Breaking it is just asking to be
blitzed and gammoned) or try running while you have no development to
speak of. The immediate priority for him is to move the backs, breaking
the midpoint is weaker. Hits are strong for O, hence 9/15 12/15 must be
better than 9/18. On the other hand I prefer 3/9 17/20 to 3/9 19/22,
because in this sort of position the man out of play is quite a
liability. My instincts are to put something in the way of the back men
and hope for a stronger anchor, so 9/15 12/15 is my bet.
---------------------------------------------------------------------------
Julian Hayward 'Booles' on FIBS jul...@ratbag.demon.co.uk
+44-1344-640656 http://www.ratbag.demon.co.uk/
---------------------------------------------------------------------------
Daddy, why doesn't this magnet pick up this floppy disk?
---------------------------------------------------------------------------
MelRae
Philippe Michel wrote:
> +-1--2--3--4--5--6--------7--8--9-10-11-12-+
> | X X O O | | O O X X |
> | X O O | | O O X |
> | O | | O X |
> | O | | |
> | | | |
> | | | |v [1]
> | | | |
> | X | | X |
> | X | | X |
> | O X | | X O |
> | O X | | X O |
> +24-23-22-21-20-19-------18-17-16-15-14-13-+
>
> X to play 6 3
>
> What should X plan be ?
X's plan should be to pass the cube which will surely be coming next!
Don Rae
Kit Woolsey
Philippe Michel (mic...@syseca.fr) wrote:
: +-1--2--3--4--5--6--------7--8--9-10-11-12-+
: | X X O O | | O O X X |
: | X O O | | O O X |
: | O | | O X |
: | O | | |
: | | | |
: | | | |v [1]
: | | | |
: | X | | X |
: | X | | X |
: | O X | | X O |
: | O X | | X O |
: +24-23-22-21-20-19-------18-17-16-15-14-13-+
: X to play 6 3
: What should X plan be ?
My inclination is to play 1/4 3/9. X's biggest danger right now is
getting primed, and this is the move to extricate his back men with
relatively little risk. The anchor on O's 9 point figures to be very
valuable for quite a while. The alternative of 9/15, 12/15 makes a good
blocking point, but it looks like O would likely be doomed in the priming
battle.
Kit
lee
In article <7MEupZAS...@ratbag.demon.co.uk>, Julian
<jul...@ratbag.demon.co.uk> writes
>> | X X O O | | O O X X |
>> | X O O | | O O X |
>> | O | | O X |
>> | O | | |
>> | | | |
>> | | | |v [1]
>> | | | |
>> | X | | X |
>> | X | | X |
>> | O X | | X O |
>> | O X | | X O |
>> +24-23-22-21-20-19-------18-17-16-15-14-13-+
>>
>> X to play 6 3
>>
>>What should X plan be ?
>
>
>3/9 17/20
>3/9 19/22
>9/15 12/15
>9/18
>
This gives O a blot to attack on the 4 pt rather than the 3 pt, but
still, it eliminates the risk of X being primed from the back.
IMHO, X should bite the bullet to either make the 4 pt or escape one man
to the 9pt, an excellent defensive point.
Lee
--
----------------------------------------------
l...@infoplus.demon.co.uk
Web site: http://www.ibmpcug.co.uk/~oak/info/
Email for links to/from this site
----------------------------------------------
Chuck Bower
>Philippe Michel wrote:
>
>> +24-23-22-21-20-19-------18-17-16-15-14-13-+
>> | X X O O | | O O X X |
>> | X O O | | O O X |
>> | O | | O X |
>> | O | | |
>> | | | |
>> | | | |v [1]
>> | | | |
>> | X | | X |
>> | X | | X |
>> | O X | | X O |
>> | O X | | X O |
>> NOTE: points renumbered CRB
>> X to play 6 3
>>
>> What should X plan be ?
In article <33EC1333...@netvigator.com>,
MelRae <mel...@netvigator.com> wrote:
>
> X's plan should be to pass the cube which will surely be coming next!
>
Me and my mindguard disagree. Here are JFv3.0 level-6 cubless
rollout results:
22/16, 8/5
total g+bg bg equiv. N = 4917
X wins 67.4 24.6 2.0 eq. = 0.553 std dev = 0.018
O wins 32.6 5.9 0.2 Double, TAKE (99% confidence level)
22/16, 24/21
total g+bg bg equiv. N = 5045
O wins 66.5 28.4 1.1 eq. = 0.554 std dev = 0.019
X wins 33.5 6.9 0.2 Double, TAKE (99% confidence level)
22/16, 6/3
total g+bg bg equiv. N = 5038
O wins 68.9 23.9 2.1 eq. = 0.576 std dev = 0.018
X wins 31.1 5.7 0.2 Double, TAKE (91% confidence level)
16/10, 13/10
total g+bg bg equiv. N = 4764
O wins 71.0 24.8 2.3 eq. = 0.594 std dev = 0.019
X wins 29.0 5.8 0.2 Double, PASS (95% confidence level)
Assuming money play at strength equivalent to JFv3.0 level-6,
"correct" play is a tossup between 22/16, 8/5 and 22/16, 24/21. X has
a TAKE after either play (and after 22/16, 6/3) BUT should PASS if s/he
made the 10 point. O has a clear double after ANY play by X. (See Kit's
post for logical "human" reasoning behind plays.)
Chuck
bo...@bigbang.astro.indiana.edu
c_ray on FIBS
Fredrik Dahl
Kit Woolsey wrote:
(snip)
>
> So, what should that certain point be? Analysis of many "known"
> positions has indicated that if we use .550 as the settlement point, then
> the results appear to be accurate. If we use a higher or lower number,
> the results appear to be distorted. This is just judgment, but many good
> players have analyzed this problem and everybody has pretty much come up
> with the same result. So, that is what we mean when we say that .550 is
> the settlement point for rollouts.
>
> Kit
Right. In races 0.55 is too low, however, particularly in short races.
The idea behind the settlement procedure is that sometimes the doubler
gets to cash takable positions, and other times he loses good chances to
double his opponent in. We choose the settlement point in the hope that
these effects will cancel out. For positions with gammon chances and
plenty of contact 0.55 appears right, but in short races the drop point
will often be below 0.55, so the doubler never gets the benefit of
cashing takes. I would use 0.5 in races. In bearoffs it should be even
lower, and for very short bearoffs the procedure of settlements is
probably too crude to give accurate results.
--
- Fredrik Dahl
MelRae
Chuck Bower wrote:
Thanks for the results, Chuck! I certainly agree with them, but
would have interpreted them as passes! Here I am no doubt going to
demonstrate my ignorance, but I had thought it was generally accepted
that any position where the opponent has an equity greater than 0.550
was a standard pass. For instance, it is standard practice to use 0.550
as the settlement number when performing rollouts with Jellyfish. I
would be grateful for a better understanding of this!
Regards,
Don Rae
Kit Woolsey
: Thanks for the results, Chuck! I certainly agree with them, but
: would have interpreted them as passes! Here I am no doubt going to
: demonstrate my ignorance, but I had thought it was generally accepted
: that any position where the opponent has an equity greater than 0.550
: was a standard pass. For instance, it is standard practice to use 0.550
: as the settlement number when performing rollouts with Jellyfish. I
: would be grateful for a better understanding of this!
: Regards,
: Don Rae
Here is what is going on:
If you were not allowed to redouble once you took the double, it would be
proper to pass if your equity were worse than -.500 (this can easily be
seen -- it just another way of expressing the 3 to 1 odds needed to take
a cube). However you do have recube equity, which means that on some of
the games you would have to lose if played to conclusion you would win by
use of the cube.
How much is this recube worth? If gammons didn't count and you could be
sure of recubing at the point where your opponent has a borderline
take/pass, it has been shown that you can take with equity of -.600 (this
is a neat exercise to prove this -- try it). However most of the time
you won't be able to make that perfect redouble, so it is logical that
your take point won't be quite so low. Each position type is different,
but as a good rule of thumb most experts agree that the minimum takepoint
for an "average" position is about -.570. Oddly enough, the more
gammonish the position, the more you can take with lower equity. This is
because if you are getting gammoned a lot you are also winning a lot (if
your equity is still in the take ballpark), which means that you will get
more recube use than usual.
So, what does this .550 settlement point we have all heard about mean?
Actually, it has nothing to do with a take point. What is happening is
that we are attempting to have Jellyfish roll out a position using the
cube, which can be of quite a bit of value to our understanding of the
position. One way to do this would be just to let JF let the cube fly as
it may. The problem is that if the cube gets up to 32 or 64 in the
rollout a couple of times it could badly distort the rollout, so this
isn't a good idea.
In the days before Jellyfish, players would roll out positions by hand.
They faced the same problem. The generally accepted procedure was to not
let the cube go to the moon, but to do as follows:
If the position is considered a borderline redouble, then don't redouble.
If the position is considered a close take, then score it as redouble - pass.
This way the cube never gets any higher, and the results are a reasonable
representation of what would happen if the cube were in full play.
For the rollouts, Jellyfish is programmed the same way. The position is
considered as no double (even though in fact it might be a double) until
the equity reaches a certain point. Once that point is reached, the
position is scored as double and pass (even though it might be a take).
Robert-Jan Veldhuizen
On 11-aug-97 04:42:47, lee wrote:
> In article <7MEupZAS...@ratbag.demon.co.uk>, Julian
> <jul...@ratbag.demon.co.uk> writes
>>In article <EELqG...@syseca.syseca.fr>, Philippe Michel
>><mic...@syseca.fr> writes
>>> +-1--2--3--4--5--6--------7--8--9-10-11-12-+
>>> | X X O O | | O O X X |
>>> | X O O | | O O X |
>>> | O | | O X |
>>> | O | | |
>>> | | | |
>>> | | | |v [1]
>>> | | | |
>>> | X | | X |
>>> | X | | X |
>>> | O X | | X O |
>>> | O X | | X O |
>>> +24-23-22-21-20-19-------18-17-16-15-14-13-+
>>>
>>> X to play 6 3
>>>
>>>What should X plan be ?
>>
>>The moved I considered were:
>>
>>3/9 17/20
>>3/9 19/22
>>9/15 12/15
>>9/18
>>
> What's wrong with 1-4, 3-9?
> This gives O a blot to attack on the 4 pt rather than the 3 pt, but
> still, it eliminates the risk of X being primed from the back.
Hmm, if I were O the first thing I'd like to do here is extend the 4pt
prime by slotting or hitting loose (or pointing of course, if that's
possible). Extending it with the 4pt seems more threatening to me than
the 9pt. X has no board him/herself, and O's back points are stripped,
so I think moving up to the 4pt is not a very good move here, you just
make O's gameplan even more attractive that way.
--
Zorba/Robert-Jan
Daniel Murphy
On Wed, 13 Aug 1997 15:06:32 -0700, Fredrik Dahl <fre...@sn.no>
wrote:
>Kit Woolsey wrote:
>(snip)
>>
>> So, what should that certain point be? Analysis of many "known"
>> positions has indicated that if we use .550 as the settlement point, then
>> the results appear to be accurate. If we use a higher or lower number,
>> the results appear to be distorted. This is just judgment, but many good
>> players have analyzed this problem and everybody has pretty much come up
>> with the same result. So, that is what we mean when we say that .550 is
>> the settlement point for rollouts.
>>
>> Kit
>
>Right. In races 0.55 is too low, however, particularly in short races.
>The idea behind the settlement procedure is that sometimes the doubler
>gets to cash takable positions, and other times he loses good chances to
>double his opponent in. We choose the settlement point in the hope that
>these effects will cancel out. For positions with gammon chances and
>plenty of contact 0.55 appears right, but in short races the drop point
>will often be below 0.55, so the doubler never gets the benefit of
>cashing takes. I would use 0.5 in races. In bearoffs it should be even
>lower, and for very short bearoffs the procedure of settlements is
>probably too crude to give accurate results.
What's the best settlement limit for rolling out a bearoff position
like this one?
Rephrased (since the equity for this position can be calculated
precisely for all cube states), which settlement level makes the
rollout agree most closely with the real values?
+24-23-22-21-20-19-+---+18-17-16-15-14-13-+
| O O O O O | | |
| O O O | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| X | | |
| X X X | | | 4
| X X X X | | |
+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
X on roll, holds cube at 4 (in the event, X redoubled and was punished
by eventually winning 16 points)
_______________________________________________
Daniel Murphy http://www.cityraccoon.com
backgammon on-line: http://www.fibs.com
in San Francisco: http://www.backgammon.org
in Denmark: http://www.cityraccoon.com/hbk.html
Alexander Nitschke
I think there is no such thing as a general settlement limit for bear
off positions, the recube possibilities vary too much from position to
position.
Nevertheless, I found the idea of an empirically derived settlement
limit appealing, so I sought for an answer to this question.
First, the exact equities for this position:
Cubeless play.
Equity: 0.415 (70.77%)
Cube in center.
Equity (no double): 0.643
Equity (double accepted): 0.698
Equity (double declined): 1.000
Cube with player 1.
Equity (no double): 0.682
Equity (double accepted): 0.698
Equity (double declined): 1.000
Cube with player 2. (Player 1 cannot double.)
Equity: 0.349
Player 1 has a redouble, which player 2 should take.
Now, I had to try with JF level 5 rollouts to find the settlement limit,
which gives equities nearest to the exact equities above.
Settlement level 0.400:
Cubeless play: 0.414
Cube in center: 0.672
Cube with player on roll: 0.713
Cube with player not on roll: 0.355
Settlement level 0.450:
Cubeless play: 0.414
Cube in center: 0.639
Cube with player on roll: 0.680
Cube with player not on roll: 0.361
Settlement level 0.500:
Cubeless play: 0.414
Cube in center: 0.610
Cube with player on roll: 0.648
Cube with player not on roll: 0.366
Settlement level 0.550:
Cubeless play: 0.414
Cube in center: 0.577
Cube with player on roll: 0.612
Cube with player not on roll: 0.373
Summary:
For centered cube and cube with the player on roll a settlement limit of
0.450 seems about right. The results diverge only very little from the
exact results.
For cube with player not on roll the settlement limit in this position
must be lower than 0.400 to give correct results. I assume this is only
partly due to the settlement but also due to the perfect checker play
from the underdog which is required to obtain maximum equity. The
optimal checker play regarding to the cube location in such positions
can quite differ from optimal cubeless checker play (which is applied in
JF rollouts). And my observations are that the underdog must differ more
than the favorite.
In general the correct settlement limit for this position seems to be
0.450. I'd like to test some more reference positions though to make
some more experiments to get deeper insight into this topic. The
positions may not have more than roughly 9 checkers / 35 pips on each
side to determine the exact equities.
--
Alexander
Chuck Bower
In article <34996C64...@ww.tu-berlin.de>,
Alexander Nitschke <alexander...@ww.tu-berlin.de> wrote:
>Daniel Murphy wrote:
(snip)
>> What's the best settlement limit for rolling out a bearoff position
>> like this one?
>>
>> Rephrased (since the equity for this position can be calculated
>> precisely for all cube states), which settlement level makes the
>> rollout agree most closely with the real values?
>>
>> +24-23-22-21-20-19-+---+18-17-16-15-14-13-+
>> | O O O O O | | |
>> | O O O | | |
>> | | | |
>> | | | |
>> | | | |
>> | | | |
>> | | | |
>> | | | |
>> | | | |
>> | X | | |
>> | X X X | | | 4
>> | X X X X | | |
>> +-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
>>
>> X on roll, holds cube at 4 (in the event, X redoubled and was punished
>> by eventually winning 16 points)
(snip a whole bunch of strong evidence leading to the conclusion:)
>In general the correct settlement limit for this position seems to be
>0.450. I'd like to test some more reference positions though to make
>some more experiments to get deeper insight into this topic. The
>positions may not have more than roughly 9 checkers / 35 pips on each
>side to determine the exact equities.
Wow, who but those second-guessing, hindsight is 20-20, armchair
BG experts who respond to r.g.bg posts flippantly would have
anticipated THIS??? (Not me!) Brilliant, groundbreaking work,
IMHO, Alexander. Now my whole confidence in level-5 limited cube
rollouts has just been flushed. But at least I can stand on my
high-horse soapbox and say that I've been warning in this newsgroup
for many months that the generic settlement limit of 0.55 was not
as trustworthy as many analysts assume. Now I am even MORE impatient
in anticipation of a commercially available BOT which does FULL cube
rollouts. Please, Fredrik; please, Olivier; please, Harald; please
Gerry;... Would one of you please put such a diskette in my Christmas
stocking????????