XGID=---B-bD-CC--bC--acbcb-----:0:0:1:00:3:2:0:5:10

X:You O:O
Score is X:3 O:2 5 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O O | | O O |
| X O O | | O O |
| X O | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| X X | | X |
| O X X | | X O X |
| O X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 120 O: 141 X-O: 3-2/5
Cube: 1
X on roll, cube action

On 5/11/2021 1:30 PM, ah...Clem wrote:
> XGID=---B-bD-CC--bC--acbcb-----:0:0:1:00:3:2:0:5:10
>
> X:You O:O
> Score is X:3 O:2 5 pt.(s) match.
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X O O O | | O O |
> | X O O | | O O |
> | X O | | O |
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | X |
> | X X | | X |
> | O X X | | X O X |
> | O X X | | X O X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 120 O: 141 X-O: 3-2/5
> Cube: 1
> X on roll, cube action

This would be a standard D/T for money. ATS, O's take point
is 25%, so that might push it into pass territory, but I'm
guessing that the computer takes this.

---
Tim Chow

A blind spot that I have is reluctance to cube at 2a since my opponent
has an auto recube to play for the match. As Tim points out, O's
takepoint is about 25% so I should be more willing to cube AtS than for
money.

Applying the Rule of fours, with a lead of 21 pips X has more than the
~13 needed to cube for money, and since the takepoint is elevated here
it must be a cube here too. As for the take, for money O would be able
to take up to ~26 pips behind, but with the elevated takepoint XG says
it's a whopper with cheese to take here. Unfortunately, I don't have a
good formula for adjusting for match score.

And just eyeballing the rollout numbers says it's D/T for money.

XGID=---B-bD-CC--bC--acbcb-----:0:0:1:00:3:2:0:5:10

X:Player 1 O:Player 2
Score is X:3 O:2 5 pt.(s) match.
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O O | | O O |
| X O O | | O O |
| X O | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | X |
| X X | | X |
| O X X | | X O X |
| O X X | | X O X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 120 O: 141 X-O: 3-2/5
Cube: 1
X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 76.18% (G:2.07% B:0.03%)
Opponent Winning Chances: 23.82% (G:1.02% B:0.02%)
Double/Take
Player Winning Chances: 77.01% (G:3.46% B:0.05%)
Opponent Winning Chances: 22.99% (G:0.85% B:0.11%)

Cubeless Equities: No Double=+0.550, Double=+1.724

Cubeful Equities:
No double: +0.954 (-0.046)
Double/Take: +1.154 (+0.154)
Double/Pass: +1.000

Best Cube action: Double / Pass

Rollout:
1296 Games rolled with Variance Reduction.
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.005 (+0.949..+0.959)
Confidence Double: ± 0.012 (+1.142..+1.167)

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

Duration: 6 minutes 25 seconds

eXtreme Gammon Version: 2.10, MET: Kazaross XG2

On 5/14/2021 10:54 AM, ah...Clem wrote:
> A blind spot that I have is reluctance to cube at 2a since my opponent
> has an auto recube to play for the match. As Tim points out, O's
> takepoint is about 25% so I should be more willing to cube AtS than for
> money.

That's assuming you win negligible gammons, which is the case here, but
often is not.

> Applying the Rule of fours, with a lead of 21 pips X has more than the
> ~13 needed to cube for money, and since the takepoint is elevated here
> it must be a cube here too. As for the take, for money O would be able
> to take up to ~26 pips behind, but with the elevated takepoint XG says
> it's a whopper with cheese to take here. Unfortunately, I don't have a
> good formula for adjusting for match score.

I think it would require estimating actual winning chances. That's not
something I've taken the time to master for holding games. I'm a bit
surprised that the rollout says that O wins only about 23% from here.

---
Tim Chow

On 5/14/2021 6:44 PM, Timothy Chow wrote:
> On 5/14/2021 10:54 AM, ah...Clem wrote:
>> A blind spot that I have is reluctance to cube at 2a since my opponent
>> has an auto recube to play for the match.  As Tim points out, O's
>> takepoint is about 25% so I should be more willing to cube AtS than for
>> money.
>
> That's assuming you win negligible gammons, which is the case here, but
> often is not.

Agreed. But since this series is about applying the rule of fours it
should be a good assumption - high anchor holding games provide few
gammons.

>> Applying the Rule of fours, with a lead of 21 pips X has more than the
>> ~13 needed to cube for money, and since the takepoint is elevated here
>> it must be a cube here too. As for the take, for money O would be able
>> to take up to ~26 pips behind, but with the elevated takepoint XG says
>> it's a whopper with cheese to take here.  Unfortunately, I don't have a
>> good formula for adjusting for match score.
>
> I think it would require estimating actual winning chances.  That's not
> something I've taken the time to master for holding games.  I'm a bit
> surprised that the rollout says that O wins only about 23% from here.
>

A simple but crude way to adjust for match score would be to note that
the money-play doubling window is 8 percentage points wide (22 to 30)
and do a simple linear interpolation or extrapolation. Here, the (money)
doubling window opens at 131 and closes at 144. Or [13,26] as expressed
in terms of how far O is behind in the race. 13 behind should
correspond to 30% GWC, and 26 behind should correspond to 22% GWC. At
20 behind, assuming linear progression (a big "if") so that each pip is
worth 8/13ths of a percentage point we get 6 * 8 /13 == 3.7, giving an
estimate of 22 + 3.7 == 25.7 GWC.

This is the first attempt at a linear interpolation approach, and it
doesn't seem to have worked all that well. I'll have to try a few other
positions before binning the idea.