Tried to follow O'Hagan's law
But the play just came out wrong
So I'll have to refer to O'Hagan
In a song.

XGID=---BCCB-BAb-aB-----bbcbba-:0:0:1:00:4:3:3:0:X:Daniel O:eXtremeGammon
10

Score is X:4 O:3. Unlimited Game, Jacoby Beaver
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X | | O O O O O O |
| X | | O O O O O |
| | | O |
| | | |
| | | |
| |BAR| |
| | | |
| | | |
| | | X X |
| O X | | X X X X |
| O O X X | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 96 O: 88 X-O: 4-3
Cube: 1
X on roll, cube action

In the above position, the 11 hits are very strong and missing leads to
approximate equality. My instinct was that it looks like a hold, but this
seemed counter to O'Hagan's principle. I don't have the patience
for a rollout but my cube does seem like a major blunder.
I'm really not sure that O'Hagan's law is all that helpful.
It seems like more of a tool for justifying a cube after the fact, than
reaching a good decision OTB.

Paul

Analyzed in XG Roller+
Player Winning Chances: 57.41% (G:4.00% B:0.08%)
Opponent Winning Chances: 42.59% (G:1.26% B:0.03%)

Cubeless Equities: No Double=+0.176, Double=+0.339

Cubeful Equities:
No double: +0.220
Double/Take: +0.065 (-0.155)
Double/Pass: +1.000 (+0.780)

Best Cube action: No double / Take
Percentage of wrong pass needed to make the double decision right: 14.2%

eXtreme Gammon Version: 2.10

On 2/5/2022 5:38 AM, peps...@gmail.com wrote:
> In the above position, the 11 hits are very strong and missing leads to
> approximate equality.

I can't say for sure what the intent of O'Hagan's law is,
but I think that after you're mediocre rolls you're supposed
to have a slight but definite advantage, as opposed to being
equal or slightly worse. Certainly in this sort of position,
where you're close to disengaging but have a powerful direct
shot, I tend to use the positions in Trice's chapter on
"End-contact positions" as a guide. If the race is even and
hitting totally locks up the game, and there's minimal contact
otherwise, then the double is clear. Here there are caveats
on all three points---you're behind in the race, hitting does
not necessarily lock up the game because you have only a
four-point board, and there's a bit of contact even if you
miss. Of these I think being behind in the race is the most
significant. If it turns into a race, your opponent will be
delighted that you gave up cube access.

---
Tim Chow

On Saturday, February 5, 2022 at 5:38:19 AM UTC-5, peps...@gmail.com wrote:
> Tried to follow O'Hagan's law
> But the play just came out wrong
> So I'll have to refer to O'Hagan
> In a song.
>
> XGID=---BCCB-BAb-aB-----bbcbba-:0:0:1:00:4:3:3:0:X:Daniel O:eXtremeGammon
> 10
>
> Score is X:4 O:3. Unlimited Game, Jacoby Beaver
> +13-14-15-16-17-18------19-20-21-22-23-24-+
> | X | | O O O O O O |
> | X | | O O O O O |
> | | | O |
> | | | |
> | | | |
> | |BAR| |
> | | | |
> | | | |
> | | | X X |
> | O X | | X X X X |
> | O O X X | | X X X X |
> +12-11-10--9--8--7-------6--5--4--3--2--1-+
> Pip count X: 96 O: 88 X-O: 4-3
> Cube: 1
> X on roll, cube action
>
> In the above position, the 11 hits are very strong and missing leads to
> approximate equality. My instinct was that it looks like a hold, but this
> seemed counter to O'Hagan's principle. I don't have the patience
> for a rollout but my cube does seem like a major blunder.
> I'm really not sure that O'Hagan's law is all that helpful.
> It seems like more of a tool for justifying a cube after the fact, than
> reaching a good decision OTB.
>
> Paul
>
>
> Analyzed in XG Roller+
> Player Winning Chances: 57.41% (G:4.00% B:0.08%)
> Opponent Winning Chances: 42.59% (G:1.26% B:0.03%)
>
> Cubeless Equities: No Double=+0.176, Double=+0.339
>
> Cubeful Equities:
> No double: +0.220
> Double/Take: +0.065 (-0.155)
> Double/Pass: +1.000 (+0.780)
>
> Best Cube action: No double / Take
> Percentage of wrong pass needed to make the double decision right: 14.2%
>
> eXtreme Gammon Version: 2.10

It is definitely useful for reaching the correct decision OtB. Like most bg maxims, the end user needs to be familiar with the exact rule and application to successfully use it OtB. For eg in your eg you said that the 11 hits are pretty strong but what does that mean in relation to trying to apply the rule? Do you lose your market every time you hit? If not, how often? You also said missing would lead to 'approximate equality'. O'Hagan's Law states loosely that you're 'doing ok' on the rest of the rolls. While this is a bit waffly, it definitely does not mean we're negative equity in general on a bunch of rolls. (as we are here)

Stick