And in backgammon, 2A 1A Crawford is the same score as 3A 1A post-Crawford.
With my interest (and relative strength) in backgammon, it's surprising
I've never come across that fact or heard it anywhere else.
It suddenly dawned on me and appears true.

Paul

On 2/8/2024 1:13 PM, peps...@gmail.com wrote:
> And in backgammon, 2A 1A Crawford is the same score as 3A 1A post-Crawford.
> With my interest (and relative strength) in backgammon, it's surprising
> I've never come across that fact or heard it anywhere else.
> It suddenly dawned on me and appears true.

It's mentioned here for example:

https://www.bkgm.com/gloss/lookup.cgi?gammon+go

Technically, the two scores aren't exactly the same, because at
3-away post-Crawford, you can try "the trick."

https://www.bkgm.com/rgb/rgb.cgi?view+437

---
Tim Chow

Timothy Chow <tchow12000@yahoo.com> wrote:
> ...
>Technically, the two scores aren't exactly the same, because at
>3-away post-Crawford, you can try "the trick."
>
>https://www.bkgm.com/rgb/rgb.cgi?view+437

But what if you get a lucky roll and the position turns *very*
gammonish? Then the waiting to double trick backfires.

--bks

On Thursday, February 8, 2024 at 1:13:41 PM UTC-5, peps...@gmail.com wrote:
> And in backgammon, 2A 1A Crawford is the same score as 3A 1A post-Crawford.
> With my interest (and relative strength) in backgammon, it's surprising
> I've never come across that fact or heard it anywhere else.
> It suddenly dawned on me and appears true.
>
> Paul

Neither is the same be it tennis or backgammon.

Stick

On 2/9/2024 9:31 AM, Bradley K. Sherman wrote:
> Timothy Chow <tchow12000@yahoo.com> wrote:
>> ...
>> Technically, the two scores aren't exactly the same, because at
>> 3-away post-Crawford, you can try "the trick."
>>
>> https://www.bkgm.com/rgb/rgb.cgi?view+437
>
> But what if you get a lucky roll and the position turns *very*
> gammonish? Then the waiting to double trick backfires.

Yes. Here's an example from Gus Hansen versus Bob Koca.

https://vimeo.com/10287279#t=2471

The commentators (one of whom I think was Sander Lyllof) thought
that Bob Koca's pass was a blunder, but XG says the pass was correct.

XGID=aaBBc-B-C---aD--AAcdb-----:0:0:1:00:10:12:0:13:10

Score is X:10 O:12 13 pt.(s) match.
+24-23-22-21-20-19------18-17-16-15-14-13-+
| O O | | O X X X |
| O O | | O X |
| O | | O X |
| O | | X |
| | | |
| |BAR| |
| | O | |
| | | |
| O | | X |
| X X O X | | X |
| O X X O X | | X O |
+-1--2--3--4--5--6-------7--8--9-10-11-12-+
Pip count X: 131 O: 180 X-O: 10-12/13
Cube: 1
X on roll, cube action

Analyzed in XG Roller++
Player Winning Chances: 66.08% (G:36.87% B:2.18%)
Opponent Winning Chances: 33.92% (G:5.64% B:0.27%)

Cubeful Equities:
No double: +0.921 (-0.079)
Double/Take: +1.148 (+0.148)
Double/Pass: +1.000

Best Cube action: Double / Pass

eXtreme Gammon Version: 2.19.211.pre-release, MET: Kazaross XG2

---
Tim Chow

On Saturday, February 10, 2024 at 6:08:17 AM UTC, Timothy Chow wrote:
> On 2/9/2024 9:31 AM, Bradley K. Sherman wrote:
> > Timothy Chow <tchow...@yahoo.com> wrote:
> >> ...
> >> Technically, the two scores aren't exactly the same, because at
> >> 3-away post-Crawford, you can try "the trick."
> >>
> >> https://www.bkgm.com/rgb/rgb.cgi?view+437
> >
> > But what if you get a lucky roll and the position turns *very*
> > gammonish? Then the waiting to double trick backfires.
> Yes. Here's an example from Gus Hansen versus Bob Koca.
>
> https://vimeo.com/10287279#t=2471
>
> The commentators (one of whom I think was Sander Lyllof) thought
> that Bob Koca's pass was a blunder, but XG says the pass was correct.
>
> XGID=aaBBc-B-C---aD--AAcdb-----:0:0:1:00:10:12:0:13:10
>
> Score is X:10 O:12 13 pt.(s) match.
> +24-23-22-21-20-19------18-17-16-15-14-13-+
> | O O | | O X X X |
> | O O | | O X |
> | O | | O X |
> | O | | X |
> | | | |
> | |BAR| |
> | | O | |
> | | | |
> | O | | X |
> | X X O X | | X |
> | O X X O X | | X O |
> +-1--2--3--4--5--6-------7--8--9-10-11-12-+
> Pip count X: 131 O: 180 X-O: 10-12/13
> Cube: 1
> X on roll, cube action
>
> Analyzed in XG Roller++
> Player Winning Chances: 66.08% (G:36.87% B:2.18%)
> Opponent Winning Chances: 33.92% (G:5.64% B:0.27%)
>
> Cubeful Equities:
> No double: +0.921 (-0.079)
> Double/Take: +1.148 (+0.148)
> Double/Pass: +1.000
>
> Best Cube action: Double / Pass

Thanks for the clip.
A number of comments follow.
I thought the commentating was naive. Bob Koca is an extraordinarily
accomplished mathematician (by normal standards -- not saying he's Terry Tao)
just like you are.
Bob Koca seems to have anticipated the "free take, must take" response and therefore
did a great pantomime act of using exaggerated hand gestures and head movements
to loudly broadcast to the audience: "Hey guys! I'm a mathematician here, just
figuring out all the details mathematically. I know that the slogan says it's a take but
I'm working out the details. Ok?"
Bizarrely, the commentators seem to have ignored the very obvious point that Bob
gave the matter intense (although quick) thought and assumed he was just blundering carelessly.
However, it's refreshing that we get a real human response rather than just copying XG.
Maybe the whole "trick" concept can be revisited thanks to the feedback of the dynamic trio
of Tim, Bob and Bradley. If Bradley doesn't mind shortening his name to "Brad", we definitely
can launch a pilot for a new backgammon series -- "Tim, Bob and Brad".
Of course, the trick can be well-executed if we can be sure of no market losers but that
leaves 441 sequences to check.
I remember you correcting my spelling of someone's name. (Can't remember if that was this
forum or another context -- perhaps private email).
So you might like to note that there are two f's in the backgammon Lylloff.

Thank You.

Paul

On Saturday, February 10, 2024 at 6:08:17 AM UTC, Timothy Chow wrote:
> On 2/9/2024 9:31 AM, Bradley K. Sherman wrote:
> > Timothy Chow <tchow...@yahoo.com> wrote:
> >> ...
> >> Technically, the two scores aren't exactly the same, because at
> >> 3-away post-Crawford, you can try "the trick."
> >>
> >> https://www.bkgm.com/rgb/rgb.cgi?view+437
> >
> > But what if you get a lucky roll and the position turns *very*
> > gammonish? Then the waiting to double trick backfires.
> Yes. Here's an example from Gus Hansen versus Bob Koca.
>
> https://vimeo.com/10287279#t=2471
>
> The commentators (one of whom I think was Sander Lyllof) thought
> that Bob Koca's pass was a blunder, but XG says the pass was correct.
>
> XGID=aaBBc-B-C---aD--AAcdb-----:0:0:1:00:10:12:0:13:10
>
> Score is X:10 O:12 13 pt.(s) match.
> +24-23-22-21-20-19------18-17-16-15-14-13-+
> | O O | | O X X X |
> | O O | | O X |
> | O | | O X |
> | O | | X |
> | | | |
> | |BAR| |
> | | O | |
> | | | |
> | O | | X |
> | X X O X | | X |
> | O X X O X | | X O |
> +-1--2--3--4--5--6-------7--8--9-10-11-12-+
> Pip count X: 131 O: 180 X-O: 10-12/13
> Cube: 1
> X on roll, cube action
>
> Analyzed in XG Roller++
> Player Winning Chances: 66.08% (G:36.87% B:2.18%)
> Opponent Winning Chances: 33.92% (G:5.64% B:0.27%)
>
> Cubeful Equities:
> No double: +0.921 (-0.079)
> Double/Take: +1.148 (+0.148)
> Double/Pass: +1.000
>
> Best Cube action: Double / Pass

With there being no recubing possibilities, it's a straightforward
matter to determine that take/pass decision from XG's statistical
estimates.
A pass leads to 1A 2A post Crawford -- which gives the leader
51.2% [I learned something -- I thought this was much more, would
have guessed something like 54%].
A take leads to two distinct winning parlays -- he can win the
game immediately with probability 33.92%. Alternatively, he
can lose a single game and win from there.
The probability of winning after losing a single game is 50%.
The probability of losing a single game is 66.08% - 36.87% - 2.18% = 27.03%.
[Here I'm assuming that "G" in XG-speak means "gammon" rather than "at least
a gammon". Would be great if someone could confirm?]
So combined winning probability after the take is 27.03% * 50% + 33.92%
which is approximately 47.44%. However, this is hugely less than the 51.2% from
dropping and would indicate that the take error is greater than 0.15.
So I think that "G" in XG-speak means "at least a gammon".
Therefore the (revised) combined winning probability after the take is:
(66.08% - 36.87%) * 50% + 33.92% = 48.53% which is a bit less than 51.2%.

Paul

On 2/10/2024 5:26 AM, peps...@gmail.com wrote:

> So I think that "G" in XG-speak means "at least a gammon".

Yes, that's right. You can confirm this by setting up a position
with a lot of backgammons.

Thanks for the spelling correction of Lylloff's name. I also agree
with your other assessment that the take point (if there are no
gammons) is slightly over 2%, and not 1%.

---
Tim Chow

On Saturday, February 10, 2024 at 10:16:01 PM UTC, Timothy Chow wrote:
> On 2/10/2024 5:26 AM, peps...@gmail.com wrote:
>
> > So I think that "G" in XG-speak means "at least a gammon".
> Yes, that's right. You can confirm this by setting up a position
> with a lot of backgammons.
>
> Thanks for the spelling correction of Lylloff's name. I also agree
> with your other assessment that the take point (if there are no
> gammons) is slightly over 2%, and not 1%.

It's 2.4% if we assume the Rockwell-Kazaross MET.
It's an interesting (to me) English usage point as to whether 2.4% is
"slightly" over 2% or "well" over 2%.
"Slightly" from an additive standpoint because 0.4% is generally
a small number in this contest but more than slightly from a multiplicative
standpoint because 2.4% is 20% greater than 2%.

Paul

On Saturday, February 10, 2024 at 10:16:01 PM UTC, Timothy Chow wrote:
> On 2/10/2024 5:26 AM, peps...@gmail.com wrote:
>
> > So I think that "G" in XG-speak means "at least a gammon".
> Yes, that's right. You can confirm this by setting up a position
> with a lot of backgammons.
>
> Thanks for the spelling correction of Lylloff's name. I also agree
> with your other assessment that the take point (if there are no
> gammons) is slightly over 2%, and not 1%.

In practical terms, if you're on roll in a bearoff and you have 2 checkers:
1 on your 3 point and one on your acepoint, and I also have 2 checkers:
one on my 6 point and 1 on my acepoint.
Then I should take your double at this score -> 1/18 * 5/12 = 5/216 > 2.4%.

Paul

On Sunday, February 11, 2024 at 12:04:45 AM UTC, peps...@gmail.com wrote:
> On Saturday, February 10, 2024 at 10:16:01 PM UTC, Timothy Chow wrote:
> > On 2/10/2024 5:26 AM, peps...@gmail.com wrote:
> >
> > > So I think that "G" in XG-speak means "at least a gammon".
> > Yes, that's right. You can confirm this by setting up a position
> > with a lot of backgammons.
> >
> > Thanks for the spelling correction of Lylloff's name. I also agree
> > with your other assessment that the take point (if there are no
> > gammons) is slightly over 2%, and not 1%.
> In practical terms, if you're on roll in a bearoff and you have 2 checkers:
> 1 on your 3 point and one on your acepoint, and I also have 2 checkers:
> one on my 6 point and 1 on my acepoint.
> Then I should take your double at this score -> 1/18 * 5/12 = 5/216 > 2..4%.
>
> Paul
Errr...no. 5/216 < 2.4%.

Paul