This is actually a question I've raised about counts in general, not specifically
Isight. However, I got absolutely zero feedback on it, and I do think it's an
important point so I'd like to press it a bit.

It is common for a position to be almost-a-race.
The classic situation in which this occurs is that the only contact is
that both players own their own midpoints.
Assume that situation. And assume that the action (with whatever count)
is D/P by a margin of 0.001.
Since there are usually rolls which can't be played with maximum efficiency,
because of blotting, the minimal contact will usually favour the trailer.
So D/P by 0.001 becomes D/T (and maybe even quite a clear take).

Now, on another thread, I remember Axel saying that his method doesn't
require adjustment. Well, in the sense of incorporating crossover counts or stacks, there's no reason to adjust because it should just be part of the
counting formula.

But how about this concept of adjusting-for-slight-contact? Is it really
unnecessary?

Paul

"peps...@gmail.com" <pepstein5@gmail.com> writes:

> the minimal contact will usually favour the trailer

Interesting topic!

> I remember Axel saying that his method doesn't require adjustment.

Without context, this is a strange quote. My method was
calibrated/tested for PURE races only. I agree that probably a pip or
two should be added to the leader's count, but did not check this. Tom
Keith's database contains only PURE races. So I KNOW of no good
adjustments for this case.

Otherwise, my method is based on an adjusted pipcount, so yes, it
requires a lot of adjustments in wasteful positions. However, I never
augment it further by any hand-waving or magic corrections. Even
cub-offs work reasonably well. Only in pure-roll positions that I know
analytically, I will of course abandon it.

> But how about this concept of adjusting-for-slight-contact? Is it
> really unnecessary?

As I said, probably this is a good idea, but requires further
research. One could try to have GNU Backgammon play against itself until
the contact has been broken, step one move back and check the position
for the small overlap of armies, quantify and then penalize it, again
minimizing the total equity loss over all these positions.

My gut feeling is that it is probably not worth the effort, because
these positions do not come up frequently enough. When on roll, I would
use Woolsey's rule: If it is a borderline take, many people will pass
due to lack of knowledge about racing formulae. If it is a borderline
double, probably you should hold and there are not too many market
losers.

I will keep this idea on my list, and, once I strongly feel the need to
update my article, this might go into it.

Best regards

Axel

On Thursday, May 6, 2021 at 7:20:08 PM UTC+1, Axel Reichert wrote:
> "peps...@gmail.com" <peps...@gmail.com> writes:
>
> > the minimal contact will usually favour the trailer
> Interesting topic!
> > I remember Axel saying that his method doesn't require adjustment.
> Without context, this is a strange quote. My method was
> calibrated/tested for PURE races only. I agree that probably a pip or
> two should be added to the leader's count, but did not check this. Tom
> Keith's database contains only PURE races. So I KNOW of no good
> adjustments for this case.
>
> Otherwise, my method is based on an adjusted pipcount, so yes, it
> requires a lot of adjustments in wasteful positions. However, I never
> augment it further by any hand-waving or magic corrections. Even
> cub-offs work reasonably well. Only in pure-roll positions that I know
> analytically, I will of course abandon it.
> > But how about this concept of adjusting-for-slight-contact? Is it
> > really unnecessary?
> As I said, probably this is a good idea, but requires further
> research. One could try to have GNU Backgammon play against itself until
> the contact has been broken, step one move back and check the position
> for the small overlap of armies, quantify and then penalize it, again
> minimizing the total equity loss over all these positions.
>
> My gut feeling is that it is probably not worth the effort, because
> these positions do not come up frequently enough. When on roll, I would
> use Woolsey's rule: If it is a borderline take, many people will pass
> due to lack of knowledge about racing formulae. If it is a borderline
> double, probably you should hold and there are not too many market
> losers.
>
> I will keep this idea on my list, and, once I strongly feel the need to
> update my article, this might go into it.
>
This theme is discussed clearly (if briefly) in Backgammon Boot Camp, so it might
be more of a mainstream topic than you suggest.
Thanks a lot for your thoughts.

Paul

On 5/6/2021 2:29 PM, peps...@gmail.com wrote:

> This theme is discussed clearly (if briefly) in Backgammon Boot Camp, so it might
> be more of a mainstream topic than you suggest.

Trice devotes an entire chapter to End-contact positions, where contact
is on the verge of being broken. OK, it's only four positions and he's
circumspect about principles that might apply generally. So I'm not
seeing much to go on re applying race formulae to these kinds of positons.

The money quote is "Sometimes the equities and cube action can be
calculated toa high degree of accuracy, but more often they call for a
mix of calculation, judgment, and intuition."

Here's the position that sticks in my mind:

At 74 to 85 it's a fairly clear cash if you ignore contact and just use
your favorite race cube formula, but that little bit of contact pushes
it into take territory. I find this surprising.

XGID=-BBBBBC-----bB--a--cbcbb--:0:0:1:00:0:0:3:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+24-23-22-21-20-19------18-17-16-15-14-13-+
| O O O O O | | O X |
| O O O O O | | X |
| O O | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| X | | |
| X X X X X X | | O |
| X X X X X X | | O |
+-1--2--3--4--5--6-------7--8--9-10-11-12-+
Pip count X: 74 O: 85 X-O: 0-0
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 77.40% (G:0.02% B:0.00%)
Opponent Winning Chances: 22.60% (G:0.05% B:0.00%)
Double/Take
Player Winning Chances: 77.34% (G:0.02% B:0.00%)
Opponent Winning Chances: 22.66% (G:0.05% B:0.00%)

Cubeless Equities: No Double=+0.548, Double=+1.093

Cubeful Equities:
No double: +0.813 (-0.148)
Double/Take: +0.961
Double/Pass: +1.000 (+0.039)

Best Cube action: Double / Take

Rollout:
1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.005 (+0.807..+0.818)
Confidence Double: ± 0.007 (+0.954..+0.968)

Double Decision confidence: 100.0%
Take Decision confidence: 100.0%

Duration: 8.9 seconds

eXtreme Gammon Version: 2.10

--
Ah....Clem
The future is fun, the future is fair.

On 5/6/2021 2:29 PM, peps...@gmail.com wrote:
> This theme is discussed clearly (if briefly) in Backgammon Boot Camp, so it might
> be more of a mainstream topic than you suggest.

I kind of agree with Axel here. "Mainstream" or not, the topic
seems to be of limited practical value, unless you include contact
positions where the contact is more than "minimal." And then once
that Pandora's box is opened, I suspect that it will be hard to
come up with good formulas.

But, maybe I'm wrong.

In my database, I have about 250 positions with a non-contact
cube action (not including score-based race cubes, which are a
whole 'nother kettle of fish), and about 100 positions that I
decided to call "nearly race cubes." But that includes positions
like the one below, where the contact is not what I would call
"minimal." I'd guess that maybe only 10-20 of the positions
could reasonably be called "minimal contact."

XGID=-BC-CBD--a-----b-A-b-bce--:0:0:1:00:0:0:0:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| O X | | O O O O |
| O | | O O O O |
| | | O O |
| | | O |
| | | O |
| |BAR| |
| | | |
| | | X |
| | | X X X |
| | | X X X X X |
| O | | X X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 71 O: 75 X-O: 0-0
Cube: 1
X on roll, cube action

---
Tim Chow

On 2021-05-07, ah....Clem <ah_clem@ymail.com> wrote:

> At 74 to 85 it's a fairly clear cash if you ignore contact and just use
> your favorite race cube formula, but that little bit of contact pushes
> it into take territory. I find this surprising.

There is minimal contact, but it is very efficient against X. All his
aces either expose a blot or have a lot of wastage. If his spare was
further away, on the 10 or 11 point and O had 4 or 5 more pips as well,
the relative lead would be slightly lower but X position would be
stronger.

If fact, X position looks neat, reference-ish with the closed board and
spare on the 6, but a bit unlikely to happen in practice. What kind of
preceding pair of rolls could lead to this ?

> XGID=-BBBBBC-----bB--a--cbcbb--:0:0:1:00:0:0:3:0:10
>
> X:Player 1 O:Player 2
> Score is X:0 O:0. Unlimited Game, Jacoby Beaver
> +24-23-22-21-20-19------18-17-16-15-14-13-+
> | O O O O O | | O X |
> | O O O O O | | X |
> | O O | | |
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | X | | |
> | X X X X X X | | O |
> | X X X X X X | | O |
> +-1--2--3--4--5--6-------7--8--9-10-11-12-+
> Pip count X: 74 O: 85 X-O: 0-0
> Cube: 1
> X on roll, cube action
>
> Analyzed in Rollout
> No double
> Player Winning Chances: 77.40% (G:0.02% B:0.00%)
> Opponent Winning Chances: 22.60% (G:0.05% B:0.00%)
> Double/Take
> Player Winning Chances: 77.34% (G:0.02% B:0.00%)
> Opponent Winning Chances: 22.66% (G:0.05% B:0.00%)
>
> Cubeless Equities: No Double=+0.548, Double=+1.093
>
> Cubeful Equities:
> No double: +0.813 (-0.148)
> Double/Take: +0.961
> Double/Pass: +1.000 (+0.039)
>
> Best Cube action: Double / Take
>
> Rollout:
> 1296 Games rolled with Variance Reduction.
> Moves: 3-ply, cube decisions: XG Roller
> Confidence No Double: ± 0.005 (+0.807..+0.818)
> Confidence Double: ± 0.007 (+0.954..+0.968)
>
> Double Decision confidence: 100.0%
> Take Decision confidence: 100.0%
>
> Duration: 8.9 seconds
>
> eXtreme Gammon Version: 2.10
>

On 5/7/2021 5:31 PM, Philippe Michel wrote:

> If fact, X position looks neat, reference-ish with the closed board and
> spare on the 6, but a bit unlikely to happen in practice. What kind of
> preceding pair of rolls could lead to this ?
>

I don't know, you'd have to ask Walter Trice. Do you have a ouija board
handy?

--
Ah....Clem
The future is fun, the future is fair.

On 5/6/2021 11:03 PM, Timothy Chow wrote:
> On 5/6/2021 2:29 PM, peps...@gmail.com wrote:

> I kind of agree with Axel here.  "Mainstream" or not, the topic
> seems to be of limited practical value, unless you include contact
> positions where the contact is more than "minimal."  And then once
> that Pandora's box is opened, I suspect that it will be hard to
> come up with good formulas.

Well, there's the "Rule of fours" which covers a lot of frequently
occurring positions, although they're not "minimal contact". But they do
leverage a race cube formula so I think are germane to this thread.

It goes something like this:

The RULE OF FOURS:
If you have escaped your checkers and have four or less on the midpoint
while your opponent has an advanced anchor (four, five, or bar point),
cube when the pipcount indicates it would be a pass without contact
using your favorite race cube formula (some say you need a 15% lead).
Take up to two times the “point of last take”.

Be wary of a “stinger” (i.e. a single opponent’s checker on the ace or
deuce) - it may be an asset or a liability for your opponent
invalidating the mechanical application of this rule

THE RULE OF THREE:
As in the rule of four, but with the anchor on the three point. Cube
when ahead by 3 pips. Take up to 30 pips behind.

--
Ah....Clem
The future is fun, the future is fair.

"ah....Clem" <ah_clem@ymail.com> writes:

> The RULE OF FOURS [...] Take up to two times the “point of last take”.

What does "Take up to two times the point of last take" mean here? Could
you please give a numerical example?

> THE RULE OF THREE:

Nice one, never heard of this before. Thanks.

Best regards

Axel

On 5/8/2021 4:02 AM, Axel Reichert wrote:
> "ah....Clem" <ah_clem@ymail.com> writes:
>
>> The RULE OF FOURS [...] Take up to two times the “point of last take”.
>
> What does "Take up to two times the point of last take" mean here? Could
> you please give a numerical example?

Let's say the pipcount is 120 to 140. To keep things simple, use Trice's
10% + 1 to determine the point of last take. That's 13 in this example;
for a no-contact position the trailer can take if she's within 13 pips
and should pass if behind by more than that.

With an anchor on the 4,5,or 7 points she can take up to twice that
amount, or up to 26 pips behind. So, if it were 120 to 147 it would be a
pass. Or another way to state is that the doubling window opens at 133
and closes at 147.

Forumulaicly, if P is the on-roll player's pipcount, the doubling window
for the opponent's pipcount is

[P + P/10 + 1, P + 2(P/10 + 1)]
>
>> THE RULE OF THREE:
>
> Nice one, never heard of this before. Thanks.

And none of this is perfect - it specifies the position of only six of
the 30 checkers on the board, so the placement of the other 24 will
change things. And it doesn't account for match score or cube position,
but it's a fairly good approximation for unlimited play.

On 5/7/2021 5:31 PM, Philippe Michel wrote:
> If fact, X position looks neat, reference-ish with the closed board and
> spare on the 6, but a bit unlikely to happen in practice. What kind of
> preceding pair of rolls could lead to this ?
>
>> XGID=-BBBBBC-----bB--a--cbcbb--:0:0:1:00:0:0:3:0:10
>>
>> X:Player 1 O:Player 2
>> Score is X:0 O:0. Unlimited Game, Jacoby Beaver
>> +24-23-22-21-20-19------18-17-16-15-14-13-+
>> | O O O O O | | O X |
>> | O O O O O | | X |
>> | O O | | |
>> | | | |
>> | | | |
>> | |BAR| |
>> | | | |
>> | | | |
>> | X | | |
>> | X X X X X X | | O |
>> | X X X X X X | | O |
>> +-1--2--3--4--5--6-------7--8--9-10-11-12-+
>> Pip count X: 74 O: 85 X-O: 0-0
>> Cube: 1
>> X on roll, cube action

On X's previous roll, the position might have been the one
diagrammed below. X rolls 66, which he plays 17/5(2). Then
O rolls 21, which she plays 7/6 7/5. These cube actions and
checkers plays are in accordance with XG's recommendations.

No Ouija boards were harmed in the making of this position.

XGID=-BBBB-C-----bB--aBbbacbb--:0:0:1:66:0:0:3:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+24-23-22-21-20-19------18-17-16-15-14-13-+
| O O O O O | | O X O X |
| O O O O | | O X X |
| O | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| X | | |
| X X X X X | | O |
| X X X X X | | O |
+-1--2--3--4--5--6-------7--8--9-10-11-12-+
Pip count X: 98 O: 88 X-O: 0-0
Cube: 1
X to play 66

1. 4-ply 17/5(2) eq:+0.639
Player: 69.53% (G:0.05% B:0.00%)
Opponent: 30.47% (G:0.03% B:0.00%)

2. 4-ply 17/11(2) 13/7(2) eq:+0.610 (-0.029)
Player: 68.74% (G:0.00% B:0.00%)
Opponent: 31.26% (G:0.00% B:0.00%)

eXtreme Gammon Version: 2.19.207.pre-release

---
Tim Chow

On 5/8/2021 11:12 AM, I wrote:

> XGID=-BBBB-C-----bB--aBbbacbb--:0:0:1:66:0:0:3:0:10
>
> X:Player 1   O:Player 2
> Score is X:0 O:0. Unlimited Game, Jacoby Beaver
>  +24-23-22-21-20-19------18-17-16-15-14-13-+
>  |    O  O  O  O  O |   | O  X  O        X |
>  |    O  O  O     O |   | O  X           X |
>  |          O       |   |                  |
>  |                  |   |                  |
>  |                  |   |                  |
>  |                  |BAR|                  |
>  |                  |   |                  |
>  |                  |   |                  |
>  |                X |   |                  |
>  | X  X  X  X     X |   |                O |
>  | X  X  X  X     X |   |                O |
>  +-1--2--3--4--5--6-------7--8--9-10-11-12-+
> Pip count  X: 98  O: 88 X-O: 0-0
> Cube: 1
> X to play 66

Retracting further, we might have the position below,
where X rolls 61 and plays 7/6 7/1, after which O rolls
65 and plays 20/9.

XGID=-ABBBaBB----bB---Bbbacbb--:0:0:1:61:0:0:3:0:10

X:Player 1 O:Player 2
Score is X:0 O:0. Unlimited Game, Jacoby Beaver
+24-23-22-21-20-19------18-17-16-15-14-13-+
| O O O O O | | O X X |
| O O O O | | O X X |
| O | | |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | |
| X X X X | | X O |
| X X X X O X | | X O |
+-1--2--3--4--5--6-------7--8--9-10-11-12-+
Pip count X: 105 O: 99 X-O: 0-0
Cube: 1
X to play 61

---
Tim Chow

"ah...Clem" <ah_clem@ymail.com> writes:

> Let's say the pipcount is 120 to 140. To keep things simple, use
> Trice's 10% + 1 to determine the point of last take. That's 13 in this
> example; for a no-contact position the trailer can take if she's
> within 13 pips and should pass if behind by more than that.
>
> With an anchor on the 4,5,or 7 points she can take up to twice that
> amount, or up to 26 pips behind.

Got it. Many thanks for the explanation!

Axel