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# How bad is this hit?

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### Dan Scoones

Jan 19, 1997, 3:00:00 AM1/19/97
to

Hi all,

Last night on FIBS I played my first-ever match with TD_one. After
splitting my back men and getting pounded by a quick 55, I managed to
struggle my way to this 2-5 backgame:

+-24-23-22-21-20-19-+---+-18-17-16-15-14-13-+
| O X O O X O | | O |
| O X O O X O | | O |
| O O X O | | O |
| | | |
| | | |
| | | |
| | | | [1]
| | | |
| | | |
| | | |
| X | | |
| X X X | | X |
| X X X X | | X O |
+--1--2--3--4--5--6-+---+--7--8--9-10-11-12-+

1-point match
O: TD_one
X: rook
X to play 65

The bot has just left an indirect shot, i.e., 23/12*. I'm 99.99%
certain that my decision NOT to hit was correct at DMP. I played 20/9
instead, and managed to cover my 5-point just before TD_one was forced
to break into a double shot. I hit the shot and went on to win a
close race.

Question: if, in the diagram, we move X's spare checker on the 4-point
back one pip to cover the 5-point, does that make the hitting play
23/12* correct? What if X has rolled 53 and could hit with the spare
on the 20-point?

Putting it another way, what is the probability that a properly-timed
2-5 backgame will yield a direct shot? I've heard pretty convincing
evidence that it's one of the weakest two-point backgames of all.

Many thanks,
Dan Scoones
rook (FIBS)
xfactor (Games Grid)

### Kit Woolsey

Jan 19, 1997, 3:00:00 AM1/19/97
to

Dan Scoones (ro...@IslandNet.com) wrote:
: Hi all,

If the five point were covered, the hit seems right. Now you are in
position to win with the hit. If you could hit with the spare from the
20 point, why not? It's a free-roll -- you might win frontwards, and if
that doesn't work you have the same 2-5 backgame. In the actual position
I agree that you give up too much by hitting now.

: Putting it another way, what is the probability that a properly-timed

: 2-5 backgame will yield a direct shot? I've heard pretty convincing
: evidence that it's one of the weakest two-point backgames of all.

Well, it's still a two-point game, with some additional chances of geting
a double shot. How bad can that be?

Kit

### Chuck Bower

Jan 21, 1997, 3:00:00 AM1/21/97
to

In article <32e17e17...@News.IslandNet.com>,
Dan Scoones <ro...@IslandNet.com> wrote:

>Last night on FIBS I played my first-ever match with TD_one. After
>splitting my back men and getting pounded by a quick 55, I managed to
>struggle my way to this 2-5 backgame:
>
> +-24-23-22-21-20-19-+---+-18-17-16-15-14-13-+
> | O X O O X O | | O |
> | O X O O X O | | O |
> | O O X O | | O |
> | | | |
> | | | |
> | | | |
> | | | | [1]
> | | | |
> | | | |
> | | | |
> | X | | |
> | X X X | | X |
> | X X X X | | X O |
> +--1--2--3--4--5--6-+---+--7--8--9-10-11-12-+
>
>1-point match
>O: TD_one
>X: rook
>X to play 65
>

(snip)
>
>I played 20/9..., and managed to cover my 5-point just before TD_one

>was forced to break into a double shot. I hit the shot and went on to
>win a close race.

some "quantitative" results. I ran JF level-6 cubeless (money play)
rollouts and it gave the following results:

play X's % winning chances (std. dev.) money cubeless equity

20/9 33.6(1.4) -0.548(0.038)
20/15,8/2 29.3(1.8) -0.730(0.050)
20/14,8/3 27.9(1.3) -0.729(0.034)
23/12* 28.5(1.6) -0.850(0.048)

Thus JF agrees with your play, both for money and at DMP. (Note
that JF is really playing with gammons ("money play") so the
percentage wins will probably be differenent at DMP. Still, we
can probably accept the RELATIVE values (winning chances) of these
plays.

(snip)
>
>...what is the probability that a properly-timed

>2-5 backgame will yield a direct shot? I've heard pretty convincing
>evidence that it's one of the weakest two-point backgames of all.

I can't answer this question, but I find your last comment surprising.
Robertie's "Advanced Backgammon" doesn't agree with this "2-5... is one
of the weakest two-point backgames of all." (WARNING: I am speaking
from memory, since I don't have his book in front of me.) BTW, here I
am assuming that by "two-point backgames" you mean "games where backgamer
has exactly two of his/her opponent's inner board points". One way to
divide these up is to look at the number of points between the two you
actually hold:

No points between: 12, 23, 34, 45

One point between: 13, 24, 35

Two points between: 14, 25

Three points between: 15

(I realize that backgames with the opponent's 6-point do occur, but they
are so rare that I don't feel the least bit confident to even comment.)
My distorted view of recent backgammon history (1970 to present) recalls
that originally the 12 and 13 were the backgames that were talked about.
Players quickly found that the 12 is EXTREMELY difficult to time. Then
the 13 and 23 were considered the best.

As time progressed, there arose a feeling (maybe just mine;
history has a way of getting fuzzy) that IN GENERAL the value of a
two-point backgame decreased with the number of points between. (NOTE
that I said "IN GENERAL".)

In "Advanced Backgammon", I seem to recall that Robertie calls the
2-5 backgame quite playable, which surprised me when I first read it.
Since then my limited experience with the 2-5 has been positive (probably
not "positive equity", unfortunately).

As far as I know, no one has performed a systematic study of the
relative merits of the different backgames using the new robots. Does
anyone out there want to take on this task?? You may go down in history
as the first person to really understand the relative strengths and
weaknesses of the different two-point backgames! (Or maybe not...)

Chuck
bo...@bigbang.astro.indiana.edu
c_ray on FIBS

### Brian Sheppard

Jan 22, 1997, 3:00:00 AM1/22/97
to

Chuck Bower <bo...@bigbang.astro.indiana.edu> wrote in article
<5c34a9\$4...@dismay.ucs.indiana.edu>...

Whatever points you have are the best ones! :-)

Knowing which points have which chances is only marginally useful
information. I say this because my experience indicates that one
rarely has a choice of which anchors to keep.

However, if you really want to know the answer, you can get a pretty
good idea from some of Hugh Sconyers' CD-ROMs. I recall that he has
an exhaustive database of backgame positions where the defender holds
two points or fewer.

Brian

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