# Chained pivot/loop notation: a proposal

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### Josh Purinton

Jan 4, 2009, 2:00:30 PM1/4/09
Some combinations of multiple pivots and loops occur frequently enough
in games to warrant their own notation. I propose extending the
existing pivot/loop notation [1] for this, for example:

After 16-, the position would be written as "16".
After 1(17)1[2-4] it would be"12L3".
After 5(18)5[6-11] it would be "6L5L3".
After 5(19)18[12-15] it would be "6+4P1L3".
After 16(20)19 it would be "6+4+3LPP1".
After 2(21)3 it would be "6+4+A3LPP1"

See attached diagram.

To denote whether a position is to be considered in normal or misere
play, I propose adding a "+" or "-" suffix, and enclosing the position
in parenthesis if it already contains a "+" symbol. For example:

16-
(3LPP1+4+6)+

Note that a chain of pivots and loops can be written in two ways
("forwards" and "backwards"). I propose starting with the end that has
the largest number. For example, "6L5L3" is to be preferred over
"3L5L6", and "A3LPP1" is to be preferred over "PP1LA3".

[1] Peltier, Jeff. (2008-06-08) "Playing Sprouts with Misere Grundy
Tables" <http://www.geocities.com/chessdp/SproutsMisereGrundy2007-4.htm>

cplnotationexample.png

### danny purvis

Jan 6, 2009, 12:44:52 AM1/6/09
Oddly, I have been thinking of similar notational devices recently. I have been somewhat inhibited, however, by the notion that we already had GLOP or other notations for starting positions.

From: Josh Purinton <josh.p...@gmail.com>
Sent: Sunday, January 4, 2009 2:00:30 PM
Subject: Chained pivot/loop notation: a proposal

### danny purvis

Jan 6, 2009, 1:22:45 AM1/6/09
I see now that the proposal is for notation supplementing the typology notation already in use. That seems to me an extremely useful project.

Less likely to be of value is the idea I had recently of elaborating conventions for specifying starting positions such that every live spot has an assigned spot number. I suspect existing notations would serve better, but, I must say, I have not much studied these resources.

From: danny purvis <wgosa_...@yahoo.com>
Sent: Tuesday, January 6, 2009 12:44:52 AM
Subject: Re: Chained pivot/loop notation: a proposal

### danny purvis

Jan 6, 2009, 1:56:37 AM1/6/09
After 16-, the position would be written as "16".

Simply "16" can often be ambiguous. How about something that stands out as more specialized for those ambiguous situations. I mean "16" is great in contexts such as "16+3P2". But if someone says, "I am now going to discuss 16," the meaning is not so clear. I suggest we say, "I am now going to discuss 16NC" in the latter case and "16+3P2" in the former.

After 1(17)1[2-4] it would be"12L3".
After 5(18)5[6-11] it would be "6L5L3".
After 5(19)18[12-15] it would be "6+4P1L3".
After 16(20)19 it would be "6+4+3LPP1".
After 2(21)3 it would be "6+4+A3LPP1"

The final four seem nicely natural extensions of existing conventions. I'm all for it.

(I would guess, though, that at some point a fundamental redesign encompassing those preliminary, somewhat ad hoc conventions might be desireable. For instance, we are calling a circle with one pivot a "P" and a circle with two pivots an "L". What if there are more than two pivots? Similarly, line segments with multiple pier spots call for a more generalized approach.)

From: Josh Purinton <josh.p...@gmail.com>
Sent: Sunday, January 4, 2009 2:00:30 PM
Subject: Chained pivot/loop notation: a proposal

### Josh Purinton

Jan 6, 2009, 2:26:06 AM1/6/09
On Tue, Jan 6, 2009 at 1:56 AM, danny purvis <wgosa_...@yahoo.com> wrote:
> (I would guess, though, that at some point a fundamental redesign
> encompassing those preliminary, somewhat ad hoc conventions might be
> desireable. For instance, we are calling a circle with one pivot a "P" and a
> circle with two pivots an "L". What if there are more than two pivots?
> Similarly, line segments with multiple pier spots call for a more
> generalized approach.)

I know what you mean, but a fundamental redesign seems to me
unwarranted. Pivot/loop notation was never intended to be
all-encompassing -- that's for AJS notation and derivatives. I believe
the a large fraction of the positions in modern tournament sprouts can
be represented in an extended pivot/loop notation, perhaps with a few
slight modifications not yet discussed here. Pivot/loop notation has
proven its usefulness in analysis and communication, even without
these extensions. Rather than fundamentally re-design it when we need
to discuss positions that it cannot describe, I think we should
instead describe those positions with an AJS-like notation such as
Glop notation.

### danny purvis

Jan 6, 2009, 2:52:22 AM1/6/09
I was thinking of the possibility of adding, say, curly brackets to pivot/loop notation. 3P4 and 3L4 could become 3P{1}4 and 3P{2}4, respectively. PP1 could become PP{1}1. A3 could become A{1}3. This use of curly brackets would only slightly increase presentational complexity but would automatically include ranges of positions currently undescribable by pivot/loop notation.

Well, I say "only slightly," but really this sort of thing could quickly become unreadable in building up more complex biospheres.

Sent: Tuesday, January 6, 2009 2:26:06 AM
Subject: Re: Chained pivot/loop notation: a proposal

### danny purvis

Jan 6, 2009, 3:03:13 AM1/6/09
Or here is another possibility. If my use of curly brackets were accepted, we could also say that "3P4" means "3P{1}4", that "3L4" means "3P{2}4," and so forth. We would still use the shorter notation but have the curly brackets in reserve for such positions as 3P{3}4, PP{2}1, and A{2}3.

From: danny purvis <wgosa_...@yahoo.com>
Sent: Tuesday, January 6, 2009 2:52:22 AM

### danny purvis

Jan 6, 2009, 3:16:40 AM1/6/09
A natural extension of this use of curly brackets could also apply to the idea I mentioned earlier, a notation for specifying certain simple positions where every live point gets a spot number. 2P0P0P1+5+0P3 could be specified 1-2{3}{4}{5}6|7-11|{12}13-15

Sent: Tuesday, January 6, 2009 3:03:13 AM

### Josh Purinton

Jan 6, 2009, 3:17:26 AM1/6/09
On Tue, Jan 6, 2009 at 3:03 AM, danny purvis <wgosa_...@yahoo.com> wrote:
> we could also say that "3P4" means "3P{1}4", that "3L4" means "3P{2}4," and
> so forth. We would still use the shorter notation but have the curly
> brackets in reserve for such positions as 3P{3}4, PP{2}1, and A{2}3.

I'd suggest angle braces again (because they look cleaner to me, the
necessity of escaping them in HTML notwithstanding). So I'd say 3P4
means 3<1>4 and 3L4 means 3<2>4 and then we'd have 3<3>3, 3<4>3, etc.
It's all quite logical, but in practice I rarely see a position like
x<3>y in tournament play, and we already have BL ("big loop") for
X<4>Y.

### danny purvis

Jan 6, 2009, 3:30:03 AM1/6/09
The reason I like curly brackets is precisely because they look less clean, suggesting porosity, accessibility, i.e. "pivotness".

Sent: Tuesday, January 6, 2009 3:17:26 AM

Subject: Re: Chained pivot/loop notation: a proposal

### danny purvis

Jan 6, 2009, 3:31:36 AM1/6/09
Or, as appropriate, "pierness".

From: danny purvis <wgosa_...@yahoo.com>
Sent: Tuesday, January 6, 2009 3:30:03 AM

Subject: Re: Chained pivot/loop notation: a proposal

### danny purvis

Jan 6, 2009, 3:37:26 AM1/6/09
The extension to PP2 and A3 would be somewhat less natural. Order would be significant. An A3 could be represented as A{1-3}4-6, with the understanding that spots #1 and #3 each have two liberties while spot #2 has one liberty. A PP2 could be represented as PP{2,3}4, with the understanding that spot #2 has one liberty and spot #3 has two liberties.

Sent: Tuesday, January 6, 2009 3:16:40 AM

### Jeff Peltier

Jan 6, 2009, 5:51:42 PM1/6/09
Thanks Josh and Danny for your nice insights.n

First, as the inventor of the P for Pivot and L for Loop, I'm ashamed that it is not easy to extend it naturally.
I was very pleased to see the nesting of those, but again it is not easy to extend when you have eg. two loops at the same level and then a pivot as after 10 : 1(11)1[2-9] 2(12)2[3] 4(13)4[5,6].
Despite these graph problems, I like it because I see Sprouts positions like this without any number to pollute the positions (so it is a sort of canonization of a position).

I don't like any sort of parenthesis which I can't read as I always need to check first for right nesting and closure.
Another possibility once used by Yper was to use letters for English numbers : T for three pier Spots, F for Four, Fi for Five, S for Six, Se for Seven, E for Eight, N for Nine, Te for Ten... this again has some limitations but as Josh pointed they are more and more rare as number grows (but I think in latest tournament, some F and even E loops were played !).

--
Jean-François

### Josh Purinton

Jan 6, 2009, 7:29:30 PM1/6/09
On Tue, Jan 6, 2009 at 5:51 PM, Jeff Peltier <jfpe...@gmail.com> wrote:
> First, as the inventor of the P for Pivot and L for Loop, I'm ashamed that
> it is not easy to extend it naturally.
> I was very pleased to see the nesting of those, but again it is not easy to
> extend when you have eg. two loops at the same level and then a pivot as
> after 10 : 1(11)1[2-9] 2(12)2[3] 4(13)4[5,6].

I propose that this position be written as 1L3(L1)(L2).

> I don't like any sort of parenthesis which I can't read as I always need to
> check first for right nesting and closure.

When writing down positions like the one above, I don't know of a way
to remain elegant and compact way without the use of some kind of
nesting parenthesis.

> Another possibility once used by Yper was to use letters for English numbers
> : T for three pier Spots, F for Four, Fi for Five, S for Six, Se for Seven,
> E for Eight, N for Nine, Te for Ten...

Arguments about notation can be endless, but I can't resist speaking
out against this particular idea. To go beyond P and L, Danny's way is
better. I think Roman uses something similar to Danny's approach in
his own analysis, so it can't be all bad.

### danny purvis

Jan 7, 2009, 9:35:49 AM1/7/09
Despite these graph problems, I like it because I see Sprouts positions like this without any number to pollute the positions (so it is a sort of canonization of a position).

I'm not sure what you mean by numbers polluting the position. Your notation already has cardinal numbers. My proposal is just to use additional cardinal numbers (in curly brackets) to specify additional pivots or pier spots. If Josh is correct that these positions will be rare, then I think my suggestion is all the more compelling because it is very easy to remember, and rarely rehearsed expedients are better if easily remembered.

I agree with you about parentheses, except, it is arguably better to have an available method than to have no method at all. If the notation is to accomodate your example, then it suddenly becomes powerful enough to specify quite complex positions. But to my mind, that's a good thing. And, at least for the given example, Josh's suggested 1L3(L1)(L2) is elegant.

My second proposal was for an entirely different type of notation. I much admire your idea "it is a sort of canonization of a position". Yes, that is an important purpose, and I suggest that we might call your notation "canonization notation". The other notation that I am proposing is less needed, but it would be nice to have a simple way to specify starting positions, positions that we wish to analyze, without having to run through a sequence of moves. Instead of "10 1(11)1[2-9] 2(12)2[3] 4(13)4[5,6]" we can say "1{2,3}4-6({7,8}9)({10,11}12,13)", though now I am wondering if that is really any more convenient.

Sadly, it seems impossible to extend canonization notation enough for any possible position to be specified by it. But here is a sprouts variant that occurs to me. "Canonizable sprouts" is played just like ordinary sprouts except that moves creating positions not specifiable by canonization notation are prohibited.

Danny

From: Jeff Peltier <jfpe...@gmail.com>
Sent: Tuesday, January 6, 2009 5:51:42 PM

Subject: Re: Chained pivot/loop notation: a proposal

### Josh Purinton

Jan 7, 2009, 9:49:00 AM1/7/09
On Wed, Jan 7, 2009 at 9:35 AM, danny purvis <wgosa_...@yahoo.com> wrote:
> "Canonizable sprouts" is played just like ordinary sprouts
> except that moves creating positions not specifiable by canonization
> notation are prohibited.

I think Roman *already* plays his moves this way, except perhaps at
the very end of the game. Furthermore, his moves are such that the
only replies available to his opponent are also specifiable by the
canonization notation!

I expect this greatly simplifies analysis.

### DannyPurvis

Jan 7, 2009, 11:22:11 AM1/7/09
to sprouts-theory
> I think Roman *already* plays his moves this way, except perhaps at
> the very end of the game. Furthermore, his moves are such that the
> only replies available to his opponent are also specifiable by the
> canonization notation!
>
> I expect this greatly simplifies analysis.

Interesting. Then perhaps playing canonizable sprouts would be a
useful training exercise for the rest of us!