5-away/4-away cube action

[Timothy Chow]

XGID=--aBB-BaB--BcCb--b-d-b--B-:0:0:1:00:2:3:0:7:10

Score is X:2 O:3 7 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O O X |
| X O O | | O O X |
| X | | O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| O | | |
| O X X | | X X X |
| O X X O | | X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 151 O: 150 X-O: 2-3/7
Cube: 1
X on roll, cube action

---
Tim Chow

[Timothy Chow]

In general, I'm still not quick enough to double at match scores like
this one, so in an effort at correcting that tendency, I pulled the
trigger here. Too soon, says XG. See also the rollout below at
5-away/3-away.

Analyzed in Rollout
No double
Player Winning Chances: 56.18% (G:24.73% B:1.13%)
Opponent Winning Chances: 43.82% (G:13.39% B:1.65%)
Double/Take
Player Winning Chances: 56.11% (G:25.64% B:1.15%)
Opponent Winning Chances: 43.89% (G:14.06% B:2.36%)

Cubeful Equities:
No double: +0.345
Double/Take: +0.233 (-0.112)
Double/Pass: +1.000 (+0.655)

Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 14.6%

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.018 (+0.327..+0.363)
Confidence Double: ± 0.025 (+0.208..+0.258)

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

----
5a3a
----

XGID=--aBB-BaB--BcCb--b-d-b--B-:0:0:1:00:2:4:0:7:10

Score is X:2 O:4 7 pt.(s) match.

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

Pip count X: 151 O: 150 X-O: 2-4/7

Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 56.16% (G:25.36% B:0.95%)
Opponent Winning Chances: 43.84% (G:13.65% B:1.92%)
Double/Take
Player Winning Chances: 56.43% (G:25.92% B:0.95%)
Opponent Winning Chances: 43.57% (G:13.57% B:3.03%)

Cubeful Equities:
No double: +0.494 (-0.024)
Double/Take: +0.518
Double/Pass: +1.000 (+0.482)

Best Cube action: Double / Take

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.015 (+0.479..+0.510)
Confidence Double: ± 0.018 (+0.500..+0.536)

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

---
Tim Chow

[Bradley K. Sherman]

Timothy Chow <tchow...@yahoo.com> wrote:
> ...

>Best Cube action: No double / Take
>Percentage of wrong pass needed to make the double decision right: 14.6%

> ...

What if it's me playing, say, Stick? Is the double still wrong?

--bks

[Timothy Chow]

I don't think that such questions have definitive answers. But the
justification for such a double wouldn't be that your opponent might
pass; it would rather be that your gammon value is higher relative
to that of your opponent, so that you lose your market more easily
in gammonish positions.

---
Tim Chow

[Bradley K. Sherman]

And that my winning chances are lower than 50% in unplayed games.

--bks

[peps...@gmail.com]

Don't be so modest. The probability of Stick beating you in a match to 11 is less than 53%, I think.
Absolutely no reason to deviate from your extraordinarily precise play when you meet him.
Great to see you back, by the way!

Paul

[Bradley K. Sherman]

peps...@gmail.com <peps...@gmail.com> wrote:
>On Wednesday, May 31, 2023 at 1:18:55 PM UTC+1, Bradley K. Sherman wrote:
>> Timothy Chow <tchow...@yahoo.com> wrote:
>> > ...
>> >Best Cube action: No double / Take
>> >Percentage of wrong pass needed to make the double decision right: 14.6%
>> > ...
>>
>> What if it's me playing, say, Stick? Is the double still wrong?
>

>Don't be so modest. The probability of Stick beating you in a match to
>11 is less than 53%, I think.

> ...

Thanks! But I think it's probably more like 60-70%.

--bks

[Stick Rice]

I definitely think questions like this can have definitive answers. I don't want to get into it fully because it takes a long time to include the whats and the whys, a good place to start is GNU where you can load a weighted match equity table. If we load the jac100 table which basically assumed a 100 ELO difference/3 PR difference, it already has it as a small/medium sized cube depending on your own definition of it. For simplification, let's assume I play a 3 PR, what do you play? No need to answer but if it's greater than 6 PR then you can extrapolate from the information you already have to how big of a cube it potentially is. In fact, if you're like an aggressive checker play 10 PR player I could even put forth the argument this is a pass.

Cube decisions at lopsided ELOs/PRs is tricky. Some big factors already mentioned are that in future games you aren't 50/50 to win (or whatever the bot assumes in bot v. bot play at that score). It also assumes that whatever the gammon value is reported by the bot is (quite) low as it's far more important for you to win a gammon than it is for me. So not only is your gammon value elevated, mine is also reduced. One other issue especially in potentially blitzy positions like this one is that often the worse the PR, the more one tends to (over) blitz in this type of position. While some plays may be dinged by the bots, it may actually be correct because of the skewed strength of you and your opponent to do so.

It gets tricky for the better player when facing some of these potentially gammonish AtS cubes. In a long match, I forget the exact length, I once faced a 4 cube from a player who was a solid 7 PR or more worse than myself. Mochy was watching at the time. It was a position that was very easy to play out for the other side, basically they either gammoned me or I won. I dropped without hesitation knowing the bot would say it's not even a double. After the match Mochy asked me if I passed because of who I was playing. Of course, and he knew on the spot.

I also agree with you I'm probably 65% +/- v. you in an 11pt match and you should, when applicable, adjust your play as best you can versus this type of player. Even when I play XG if I'm playing to see how often I can actually beat XG itself I will deviate from how I'd play a top tier player.

Stick

[Timothy Chow]

On 6/1/2023 7:14 AM, Stick Rice wrote:
> I also agree with you I'm probably 65% +/- v. you in an 11pt match

XG/GNU is less than 60% against him in an 11pt match. How are you
getting more of an advantage against him when you don't even know
his specific strengths and weaknesses?

---
Tim Chow

[Bradley K. Sherman]

Even I don't know what my record would be against the bots
in 11-pt matches, so let's not argue about that. The question
is whether cube decisions in match play should be affected by
relative strengths of the players.

I suppose a further question would be whether ChatGPT-GNUBG
should alter its play based on its (running) estimate of the
human player's strength.

--bks

[Stick Rice]

Where in the world did you pull XG/GNU is less than 60% against him in 11pt matches?

Stick

[peps...@gmail.com]

On Thursday, June 1, 2023 at 1:42:49 PM UTC+1, Bradley K. Sherman wrote:
> Timothy Chow <tchow...@yahoo.com> wrote:
> >On 6/1/2023 7:14 AM, Stick Rice wrote:
> >> I also agree with you I'm probably 65% +/- v. you in an 11pt match
> >
> >XG/GNU is less than 60% against him in an 11pt match. How are you
> >getting more of an advantage against him when you don't even know
> >his specific strengths and weaknesses?
> Even I don't know what my record would be against the bots

> in 11-pt matches, so let's not argue about that. ...

You opened up a can of worms by posing you vs Stick as an example, rather
than making the question of different strengths purely a theoretical one.

Paul

[Timothy Chow]

On 6/1/2023 8:42 AM, Bradley K. Sherman wrote:
> Even I don't know what my record would be against the bots
> in 11-pt matches, so let's not argue about that.

Yes, sorry, I got confused about the match length. What I
remembered was that you reported a 40% win rate against GNUBG,
but when I checked, I saw that you were talking about 5-point
matches, not 11-point matches.

https://groups.google.com/g/rec.games.backgammon/c/wrm1Ic3bEYw/m/-SEsPQ9AAUQJ

On the other hand, the current issue of the USBGF PrimeTime
magazine has an interesting article by Art Benjamin, Richard
Stubbe, and Susan Martonosi, who collected approximately
19,000 matches from Backgammon Studio Heroes, courtesy of Terje
Pedersen. They ran the stats and came to the unexpected
conclusion that while PR difference does a pretty good job of
predicting the win rate, the *match length doesn't matter*.
If D is the PR difference, then their predicted win percentage
for the stronger player (if D >= 1) is

50.32 + 2.23 D

and the match length doesn't enter the formula. (But note that
they only considered match lengths from 5 points to 17 points.)

They don't claim to have the "correct" explanation for their
results. One obvious possibility is that 19,000 matches is not
enough data, or at least not enough high-quality data. Another
thing that's odd, and that I plan to ask Art about, is that they
say that they used GNUBG to calculate PR. I didn't know that
GNUBG was able to calculate PR (of course, it computes Snowie ER
and its own home-grown error rate measure, but PR is defined in
a different way). So maybe they made a mistake calculating PR
(though even so, they probably did calculate something close to PR).

Among their proposed explanations, the one that sounds most plausible
to me (if we assume that match length really doesn't matter much,
at least in the range between 5-pointers and 17-pointers) is that
errors don't affect your match-winning chances much until near the
end of the match. That means that the stronger player is only a
very slight favorite to be ahead by the time the match score gets
down to 5-away/X-away.

In any case, if we are to believe that the data from the 19,000
matches is reliable, then it suggests that your PR is around 5
and that your chances against Stick---assuming Stick's PR is
around 2---would be about 43%, whether it's a 5-pointer or an
11-pointer.

---
Tim Chow

[Timothy Chow]

Sorry, I was relying on my memory of what Bradley said here on
r.g.b. about ten years ago, but when I checked, he was talking
about 5-pointers and not 11-pointers. See my other post in this
thread for more detail.

---
Tim Chow