54 to play
tc...@lsa.umich.edu
environment was in transition. In particular, I acquired an old
Windows machine, which finally allowed me to purchase and run eXtreme
Gammon. Assuming this computer doesn't die on me (the hard drive is
starting to show signs of damage), I hope to be posting plenty of
XG rollouts from now on.
Without further ado, here is a problem to think about:
XGID=-BaB-aC-A---cFb--c-cb---A-:0:0:1:54:0:0:1:0:10
X:Player 1 O:Player 2
Score is X:0 O:0. Money session, Jacoby
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X |
| X O O | | O O |
| X O | | O |
| X | | |
| 6 | | |
| |BAR| |
| | | |
| | | |
| O | | X |
| O | | X X X |
| O X | | X O X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Cube : 1
X to play 54
--
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
Bradley K. Sherman
<tc...@lsa.umich.edu> wrote:
>Score is X:0 O:0. Money session, Jacoby
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X O O | | O O X |
> | X O O | | O O |
> | X O | | O |
> | X | | |
> | 6 | | |
> | |BAR| |
> | | | |
> | | | |
> | O | | X |
> | O | | X X X |
> | O X | | X O X O X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ Cube : 1 X to play 54
13/8,6/4*
I think you have to hit here, because O's position can get
a lot better fast if you don't. 13/8,13/9 is my
second choice.
--bks
Bradley K. Sherman
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X O O | | O O X |
> | X O O | | O O |
> | X O | | O |
> | X | | |
> | 6 | | |
> | |BAR| |
> | | | |
> | | | |
> | O | | X |
> | O | | X X X |
> | O X | | X O X O X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+ Cube : 1 X to play 54
13/8,6/2*
Richard Henry
> In article <4cebf27e$0$508$b45e6...@senator-bedfellow.mit.edu>,
A blot left on 2 is less likely to be hit than a blot on 9 on O's next
roll (31% vs 44%) and if O gets on (75%) without hitting 2, 2 is safe.
Walt
> I haven't posted any new positions in a while, because my computer
> environment was in transition. In particular, I acquired an old
> Windows machine, which finally allowed me to purchase and run eXtreme
> Gammon. Assuming this computer doesn't die on me (the hard drive is
> starting to show signs of damage), I hope to be posting plenty of
> XG rollouts from now on.
>
> Without further ado, here is a problem to think about:
>
> XGID=-BaB-aC-A---cFb--c-cb---A-:0:0:1:54:0:0:1:0:10
>
> X:Player 1 O:Player 2
> Score is X:0 O:0. Money session, Jacoby
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X O O | | O O X |
> | X O O | | O O |
> | X O | | O |
> | X | | |
> | 6 | | |
> | |BAR| |
> | | | |
> | | | |
> | O | | X |
> | O | | X X X |
> | O X | | X O X O X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Cube : 1
> X to play 54
I definitely bring one down from the bar. A stack of six is about three
checkers too many.
Then I try to decide whether to bring down a second stone, or to hit
loose on the two point. Hmmmm.... hitting strips the six point without
either the 5 or the 4 being made, and it slots a checker on a point
that's the third or fourth choice to make next. And seeing no builders
lurking other than our poor stripped 8 point, think that hitting loose
is not sound.
So I bring a second one down. 13/8 13/7.
I'll refrain from opining on how the Jacoby rule impacts this decision
because I always get it wrong anyway.
//Walt
badgolferman
Agreed.
> Then I try to decide whether to bring down a second stone, or to hit
> loose on the two point. Hmmmm.... hitting strips the six point
> without either the 5 or the 4 being made, and it slots a checker on a
> point that's the third or fourth choice to make next. And seeing no
> builders lurking other than our poor stripped 8 point, think that
> hitting loose is not sound.
>
> So I bring a second one down. 13/8 13/7.
I play the same thing. I am looking to build foundations and that
gives me the best chance. I'd rather have one of the men from 13
killed if that's going to happen than one from 6.
> I'll refrain from opining on how the Jacoby rule impacts this decision
> because I always get it wrong anyway.
>
I have no idea what the Jacoby rule means.
tc...@lsa.umich.edu
The Jacoby rule, which is widely used in money play, states that a gammon
or a backgammon counts as only a single point if the cube is still in the
center at the end of the game.
The Jacoby rule will occasionally affect correct cube action, most often by
forcing the leader to double more aggressively in highly volatile positions.
On very rare occasions the Jacoby rule may affect correct checker play, but
this hardly ever happens.
As far as I can tell, the Jacoby rule was introduced because it was perceived
to speed up money play. Many (very imperfect) human backgammon players are
reluctant to turn the cube. If their position is not overwhelming, they're
afraid to raise the stakes, and if their position *is* overwhelming, they'd
rather try for an undoubled gammon than end the game with a double/pass.
To prevent such players from playing out boring games to the bitter end,
hoping for an unlikely but not impossible gammon when they really should
just cash, the Jacoby rule was introduced.
Among expert players the Jacoby rule typically does not speed things up
because the expert will just turn the cube sooner in the few cases where
it makes a difference, and the game will still be played to completion,
but now with the cube turned.
Bradley K. Sherman
<tc...@lsa.umich.edu> wrote:
>
>Among expert players the Jacoby rule typically does not speed things up
>because the expert will just turn the cube sooner in the few cases where
>it makes a difference, and the game will still be played to completion,
>but now with the cube turned.
I don't think this is true, if we define "speed things up"
as playing more games per unit time. There are times
where there are two jokers in a row (a player throws the
perfect double and the opponent dances with two checkers
against a three point board, say) when the Jacoby rule
will shorten the game considerably.
Not a big deal. The rest of your explanation was good and
it is good of you to take the time to help people who could
just google "jacoby rule" and be enlightened.
--bks
tc...@lsa.umich.edu
Bradley K. Sherman <b...@panix.com> wrote:
>In article <4cec51a0$0$495$b45e...@senator-bedfellow.mit.edu>,
> <tc...@lsa.umich.edu> wrote:
>>
>>Among expert players the Jacoby rule typically does not speed things up
>>because the expert will just turn the cube sooner in the few cases where
>>it makes a difference, and the game will still be played to completion,
>>but now with the cube turned.
>
>I don't think this is true, if we define "speed things up"
>as playing more games per unit time. There are times
>where there are two jokers in a row (a player throws the
>perfect double and the opponent dances with two checkers
>against a three point board, say) when the Jacoby rule
>will shorten the game considerably.
That's true as far as it goes, but you have to weigh it against the times
when Jacoby causes the expert to double early and therefore force a game
to be played to completion, when without Jacoby he would just wait a turn
and then cash.
On the BGOnline forum, Daniel Murphy reported that he had GNU Backgammon
play tons of games against itself, with and without Jacoby, and timed the
results. There was very little difference. GNU is not perfect but it
certain qualifies as an expert player, so I think these results are
indicative.
tc...@lsa.umich.edu
>Score is X:0 O:0. Money session, Jacoby
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X O O | | O O X |
> | X O O | | O O |
> | X O | | O |
> | X | | |
> | 6 | | |
> | |BAR| |
> | | | |
> | | | |
> | O | | X |
> | O | | X X X |
> | O X | | X O X O X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
>Cube : 1
>X to play 54
Walt hit the nail on the head here. 13/8 is clear, and the only question
is whether to play 13/9 or 6/2*. Ahead in the race, X would prefer to
just come around safely. If a strong attacking opportunity materializes
then X will attack, but 6/2* does not initiate a strong attack because X
has little attacking material and O has decent defensive resources---the
5pt and 11pt made, and a potential anchor slotted. The main arguments in
favor of 6/2* are that it leaves slightly fewer immediate return shots
(11 versus 13) and that it takes away half of O's roll. However, 6/2*
strips the 6pt, which is a more serious concession than many players
realize. If we were to alter the position by moving one of X's checkers
down from the midpoint to another spare on the 6pt, then 6/2* would probably
be best. Here, though, if O dances then X's 2pt blot remains a liability
that is difficult to cover, and X's stripped 6pt cannot hit O's blot on
X's 5pt either. Though X would prefer not to allow O to use a full roll,
6/2* creates a fragile and strung-out position that is hard to put back
together. The flexible and pure 13/9 is better here, unstacking the heavy
midpoint and putting pressure on O to ward off X's threats to either escape
or attack next turn.
1. Rollout: 13/9 13/8 eq:-0.110
Player : 46.06% (G:14.72% B:0.35%)
Opponent: 53.94% (G:12.81% B:0.60%)
Confidence: (-0.128<E<-0.092)
2. Rollout: 13/8 6/2* eq:-0.206 (-0.096)
Player : 44.28% (G:15.93% B:0.40%)
Opponent: 55.72% (G:15.48% B:0.69%)
Confidence: (-0.227<E<-0.185)
1296 Games rolled with Variance Reduction.
Moves and cube decisions: 3 ply
eXtreme Gammon Version: 1.21