Containment
tc...@lsa.umich.edu
most builders at the critical points also leave the most indirect shots.
In the (money-game) position below, O is on the bar and X has a 2-6 to
play. What's the right play here?
GNU Backgammon Position ID: uLs5AEB2NkYCDA
+13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
| X O O | O | O O O X | 0 points
| O O | | O O O X |
| O | | O O O |
| | | |
| | | |
v| |BAR| |
| | | |
| | | |
| | | X |
| X | | X X X X | Rolled 26
| X X | | X X X X | 0 points
+12-11-10--9--8--7-------6--5--4--3--2--1-+ X: tchow (Cube: 2)
--
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
Paul
I would avoid 9/7 -- the whopping 1/6 probability opponent hits a shot
is far too big a price for the extra builders. If I'm correct about
this (and I do feel fairly certain) then 14/8 seems forced.
I suppose 14/8 12/10 could also be considered. However again, this
gives opponent 1/18 more shots than my play and the extra benefits are
definitely not worth it.
Paul Epstein
Paul Epstein
Paul
Typo -- I meant to advocate 14/6.
Peter Schneider
<tc...@lsa.umich.edu> wrote
> When one is trying to contain a
> checker, often the plays that aim the
> most builders at the critical points
> also leave the most indirect shots.
>
> In the (money-game) position below,
> O is on the bar and X has a 2-6 to
> play. What's the right play here?
>
> GNU Backgammon Position ID: uLs5AEB2NkYCDA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O O | O | O O O X | 0 points
> | O O | | O O O X |
> | O | | O O O |
> | | | |
> | | | |
> v| |BAR| |
> | | | |
> | | | |
> | | | X |
> | X | | X X X X | Rolled 26
> | X X | | X X X X | 0 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: tchow (Cube: 2)
Ok, I'll bite. My first idea was 14/8 12/10, and Paul's post didn't
convince me of 14/6. The reason is that 12/10 activates that checker nicely
and breaks a super duplication of 5s we need everywhere after 14/6. I also
find it very satisfying to point on our 4 pt. (But to go all in and move
14/8 9/7 seems too extreme, especially since we still -- by far -- can't
recube after O dances. The 9pt is an asset not to be given up lightly.)
What about the risk involved in 14/8 12/10? Being hit would set us back in
the race -- one of the two winning plans from a 3pt holding game. On the
other hand we'll likely waste pip soon and open our board (which foils our
other winning plan) anyway, or else leave with a single checker and incur
the risk of being hit en passant, or even closed out. So the pip loss
affects mostly the outcomes that involve early big doubles (currently only
55) that bring us to a recube, or close to one. Having another checker back
would even have the slight benefit of improving our timing, provided we
roll a 5 soon in order to re-circulate that third checker.
I think that if my move is wrong it's because of this pip loss.--
The checker on the 8 is nicely positioned since only 44 hits it. (44 also
hits -- on the 12 -- after 14/6.)
The only additional shot incurred is 46 by 0 -- a good roll for O anyway
even if we don't go there.
Being hit again increases the chances to lose gammon, but moderately only
since we have the 3pt anchor. It should increase O's chances to lose
gammon as well! So the gammon risk seems not a strong enough reason to play
safer.
Now let's see how all my words stand up against the harsh reality ;-).
Best wishes for the holidays,
Peter aka the juggler
Peter Schneider
I'm just wondering -- after I enter the position ID from your post I still
have to manually set the cube, the roll and the match length (to zero,
here). I think it's because there is no match ID and hence no information
about it. My gnubg ( 0.90-mingw 20090721) exports a a money game position
as text with position ID plus match ID -- doesn't yours? It would be more
convenient and remove an error source if you could provide it.
But in any case thanks for the entertaining quizzes, and keep them coming.
Best
Peter aka the juggler
Piranha
X needs 5s everywhere, to escape from behind as well as to close his
4.
Suppose I´d move 14/6, and next I roll 52, could I afford to keep the
backmen behind, hoping for another 5 within the next 2 or 3 rolls?
On the other hand chances for O to escape are near infinite as long as
my point 4 is open and chances to close it are minimal as long as I
urgently need 5s elswhere.
I´d say on equity X isn´t even ahead, halfway even at best, therefore
I don´t care about an extra risk to get hit, if I can´t make the 4
soon, I lose and if I use all 5s I roll to make the 4, I still lose as
soon as my home board crushes.
Therefore I´d play 14/8 and 12/10.
Furthermore I would think 12/6, 9/7 may still be better than 14/6.
tc...@lsa.umich.edu
Peter Schneider <schneiderp...@gmx.net> wrote:
>My gnubg ( 0.90-mingw 20090721) exports a a money game position
>as text with position ID plus match ID -- doesn't yours? It would be more
>convenient and remove an error source if you could provide it.
O.K., I can do that. The reason I've been omitting it is that I often
tinker with those parameters, and I can easily see myself forgetting to
reset the match ID appropriately before cutting and pasting. Then it
would be confusing because I would be saying something in the text that
contradicts the match ID. But if you want the match ID as well, I'll
try to do that in the future.
Peter Schneider
a minor correction:
[discussing to leave a blot at the 10 pt]
> Being hit again increases the chances to lose gammon, but moderately only
> since we have the 3pt anchor. It should increase O's chances to lose
> gammon as well!
"It" meant that the *checker* increases our gammon chances, but not when
hit but rather when not hit.
Best,
Peter
tc...@lsa.umich.edu
>In the (money-game) position below, O is on the bar and X has a 2-6 to
>play. What's the right play here?
>
> GNU Backgammon Position ID: uLs5AEB2NkYCDA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O O | O | O O O X | 0 points
> | O O | | O O O X |
> | O | | O O O |
> | | | |
> | | | |
>v| |BAR| |
> | | | |
> | | | |
> | | | X |
> | X | | X X X X | Rolled 26
> | X X | | X X X X | 0 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: tchow (Cube: 2)
Below are the rollout results. 14/8 12/10 comes out clearly on top.
I feel that I don't fully understand this position, but in addition to the
observations others have made, here are some of my thoughts. The fact
that X is behind in the race and still has a lot of escape work to do is
important. If X were fully escaped and the race were close, then X would
want to play more cautiously, trying to avoid shots and to creep up on an
opportunity to turn the cube. As things stand now, however, X has less to
lose by being hit. Therefore X is eager to aim more ammunition at the
4-point quickly, even at the risk of allowing indirect shots. If you
chose to play safe, you may be surprised that even if we strengthen O's
board by taking all four of O's spares and using them to make the remaining
two points in O's home board (giving O a five-point board), GNU 4-ply still
prefers 14/8 12/10 over 14/6 by 0.041.
The exact balance of safety and aggression is something I'm still trying
to understand, but my impression is that on the whole, most people play
more cautiously than the bots advise us to in these sorts of situations.
1. Rollout 14/8 12/10 Eq.: -0.123
0.396 0.062 0.001 - 0.604 0.112 0.004 CL -0.261 CF -0.123
[0.001 0.001 0.000 - 0.001 0.002 0.000 CL 0.003 CF 0.005]
2. Rollout 14/8 9/7 Eq.: -0.168 ( -0.045)
0.387 0.061 0.001 - 0.613 0.134 0.005 CL -0.302 CF -0.168
[0.001 0.001 0.000 - 0.001 0.002 0.001 CL 0.003 CF 0.005]
3. Rollout 14/6 Eq.: -0.170 ( -0.047)
0.374 0.055 0.001 - 0.626 0.097 0.004 CL -0.297 CF -0.170
[0.001 0.001 0.000 - 0.001 0.002 0.000 CL 0.003 CF 0.005]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 841755612 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]
Walt
> When one is trying to contain a checker, often the plays that aim the
> most builders at the critical points also leave the most indirect shots.
>
> In the (money-game) position below, O is on the bar and X has a 2-6 to
> play. What's the right play here?
>
> GNU Backgammon Position ID: uLs5AEB2NkYCDA
> +13-14-15-16-17-18------19-20-21-22-23-24-+ O: gnubg
> | X O O | O | O O O X | 0 points
> | O O | | O O O X |
> | O | | O O O |
> | | | |
> | | | |
> v| |BAR| |
> | | | |
> | | | |
> | | | X |
> | X | | X X X X | Rolled 26
> | X X | | X X X X | 0 points
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ X: tchow (Cube: 2)
I wouldn't move 14/8. I like the checker on the 14 to hit an escapee,
and a blot on the eight is vunerable to a 4-4 joker. 14-6 is playable,
but seems passive.
WIth a four point board and an advanced anchor, taking some chances is
in order - spread the builders around and try to make another homeboard
point. 12/6 9/7 does this. So that's my move.
//Walt
tc...@lsa.umich.edu
Walt <walt_...@yahoo.com> wrote:
>I wouldn't move 14/8. I like the checker on the 14 to hit an escapee,
>and a blot on the eight is vunerable to a 4-4 joker. 14-6 is playable,
>but seems passive.
>
>WIth a four point board and an advanced anchor, taking some chances is
>in order - spread the builders around and try to make another homeboard
>point. 12/6 9/7 does this. So that's my move.
I didn't roll out your move, but at least on evaluation it came out clearly
worse than the three moves I did roll out. One thing I can definitely say
is that the reasoning about the 4-4 joker is misguided. If you have to
leave a blot, it's safest to leave it on the 8-point, precisely because it
duplicates 4's and can *only* be hit with a 4-4 joker.
I might try rolling out your move.
Paul
> In article <n3K_m.473241$Jp1.348...@en-nntp-02.dc1.easynews.com>,
Paul
> In article <n3K_m.473241$Jp1.348...@en-nntp-02.dc1.easynews.com>,
>
> >I wouldn't move 14/8. I like the checker on the 14 to hit an escapee,
> >and a blot on the eight is vunerable to a 4-4 joker. 14-6 is playable,
> >but seems passive.
>
> >WIth a four point board and an advanced anchor, taking some chances is
> >in order - spread the builders around and try to make another homeboard
> >point. 12/6 9/7 does this. So that's my move.
>
> I didn't roll out your move, but at least on evaluation it came out clearly
> worse than the three moves I did roll out. One thing I can definitely say
> is that the reasoning about the 4-4 joker is misguided. If you have to
> leave a blot, it's safest to leave it on the 8-point, precisely because it
> duplicates 4's and can *only* be hit with a 4-4 joker.
>
> I might try rolling out your move.
> --
> Tim Chow tchow-at-alum-dot-mit-dot-edu
I don't think there was anything wrong with Walt's reasoning although
obviously bots are far more likely to be correct. In the comment you
object to, Walt was simply comparing the checker on the 14 with that
same checker transferred to the 8 point. His point is that the 14
point checker is vulnerable to 0 shots whereas a checker on the 8 is
vulnerable to 1.
Paul Epstein
Paul
> I might try rolling out your move.
> --
> Tim Chow
But please remember to also roll out the case where the board is a
Klein bottle.
tc...@lsa.umich.edu
>I might try rolling out your move.
Here are the results. I only rolled out your move and GNU's top choice
this time.
1. Rollout 14/8 12/10 Eq.: -0.118
0.396 0.062 0.001 - 0.604 0.109 0.004 CL -0.258 CF -0.118
[0.001 0.001 0.000 - 0.001 0.002 0.000 CL 0.003 CF 0.005]
2. Rollout 12/6 9/7 Eq.: -0.185 ( -0.068)
0.374 0.058 0.001 - 0.626 0.120 0.006 CL -0.318 CF -0.185
[0.001 0.001 0.000 - 0.001 0.002 0.001 CL 0.003 CF 0.005]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 840115061 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]
Walt
> In article <4b3b8909$0$506$b45e...@senator-bedfellow.mit.edu>, I wrote:
>> I might try rolling out your move.
>
> Here are the results. I only rolled out your move and GNU's top choice
> this time.
>
> 1. Rollout 14/8 12/10 Eq.: -0.118
> 0.396 0.062 0.001 - 0.604 0.109 0.004 CL -0.258 CF -0.118
> [0.001 0.001 0.000 - 0.001 0.002 0.000 CL 0.003 CF 0.005]
> 2. Rollout 12/6 9/7 Eq.: -0.185 ( -0.068)
> 0.374 0.058 0.001 - 0.626 0.120 0.006 CL -0.318 CF -0.185
> [0.001 0.001 0.000 - 0.001 0.002 0.001 CL 0.003 CF 0.005]
>
> Full cubeful rollout with var.redn.
> 1296 games, Mersenne Twister dice gen. with seed 840115061 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]
fair enough.
If I could keep all my errors to .068 I'd be very happy. (c: