The position below seems highly OHaganistic.
We have a number of devastating hits.
On the other hand, our misses give a more-or-less even position.
How many hits do we have -- 15 -- fours + 31 + 22 + 66
O Hagan would say that we only need 9 for a double and we have 15.
But our double is ultra-thin, very borderline.
So I think we needed all 15 of our shots to justify the double.
A variantization of this position to give only 9 shots would have to be
a hold. This position seems to OHaganize really badly.

Paul

XGID=-B--BBBBBa--cA---cbd-B-b--:0:0:1:00:3:7:3:0:10
X:Daniel O:eXtremeGammon

Score is X:3 O:7. Unlimited Game, Jacoby Beaver
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O X O |
| O O | | O X O |
| O | | O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| O | | |
| O X 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: 117 O: 121 X-O: 3-7
Cube: 1
X on roll, cube action

Analyzed in 4-ply
Player Winning Chances: 59.61% (G:17.86% B:0.13%)
Opponent Winning Chances: 40.39% (G:3.55% B:0.08%)

Cubeless Equities: No Double=+0.336, Double=+0.669

Cubeful Equities:
No double: +0.368 (-0.015)
Double/Take: +0.382
Double/Pass: +1.000 (+0.618)

Best Cube action: Double / Take

eXtreme Gammon Version: 2.10

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On Tuesday, November 16, 2021 at 6:09:26 PM UTC-5, peps...@gmail.com wrote:

The position below seems highly OHaganistic.
We have a number of devastating hits.
On the other hand, our misses give a more-or-less even position.
How many hits do we have -- 15 -- fours + 31 + 22 + 66
O Hagan would say that we only need 9 for a double and we have 15.
But our double is ultra-thin, very borderline.
So I think we needed all 15 of our shots to justify the double.
A variantization of this position to give only 9 shots would have to be
a hold. This position seems to OHaganize really badly.

Paul

XGID=-B--BBBBBa--cA---cbd-B-b--:0:0:1:00:3:7:3:0:10
X:Daniel O:eXtremeGammon

Score is X:3 O:7. Unlimited Game, Jacoby Beaver +13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O | | O X O |
| O O | | O X O |
| O | | O |
| | | O |
| | | |
| |BAR| |
| | | |
| | | |
| O | | |
| O X 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: 117 O: 121 X-O: 3-7
Cube: 1
X on roll, cube action

Analyzed in 4-ply
Player Winning Chances: 59.61% (G:17.86% B:0.13%)
Opponent Winning Chances: 40.39% (G:3.55% B:0.08%)

Cubeless Equities: No Double=+0.336, Double=+0.669

Cubeful Equities:
No double: +0.368 (-0.015)
Double/Take: +0.382
Double/Pass: +1.000 (+0.618)

Best Cube action: Double / Take

eXtreme Gammon Version: 2.10

That's because you don't always lose the market when you hit and sometimes you will lose you market when you hit by only a tiny amount. O'Hagan's Law works fine, again, like most bg axioms, it just needs to be understood in its entirety.

Stick

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On 11/17/2021 1:59 PM, J R wrote:

On Tuesday, November 16, 2021 at 6:09:26 PM UTC-5, peps...@gmail.com wrote:

The position below seems highly OHaganistic.
We have a number of devastating hits.
On the other hand, our misses give a more-or-less even position.

eXtreme Gammon Version: 2.10

That's because you don't always lose the market when you hit and sometimes you will lose you market when you hit by only a tiny amount. O'Hagan's Law works fine, again, like most bg axioms, it just needs to be understood in its entirety.

That, and O'Hagan's law says nine market losers AND nothing really bad.
Here, a miss followed by big doubles makes for a bad game for X.

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On Wednesday, November 17, 2021 at 11:08:12 PM UTC, ah...Clem wrote:

On 11/17/2021 1:59 PM, J R wrote:

On Tuesday, November 16, 2021 at 6:09:26 PM UTC-5, peps...@gmail.com wrote:

The position below seems highly OHaganistic.
We have a number of devastating hits.
On the other hand, our misses give a more-or-less even position.
eXtreme Gammon Version: 2.10

That's because you don't always lose the market when you hit and sometimes you will lose you market when you hit by only a tiny amount. O'Hagan's Law works fine, again, like most bg axioms, it just needs to be understood in its entirety.

That, and O'Hagan's law says nine market losers AND nothing really bad.
Here, a miss followed by big doubles makes for a bad game for X.

Assume "big doubles" means "bigger than average doubles".
The probability of a miss combined with big doubles for the opponent is then (1 - 15/36) * 1/6 * 1/2 which is less than 5%.

If you make the conditions for O'Hagan stringent enough, then you will probably find that you never meet an O'Hagan position ever in your entire bg experience.
For example, these could be the conditions:
1) Probability of a market-losing sequence >= 25%.
2) None of the non-market-losing sequences lead to an equity of -0.5 or lower. 3) The average equity of the non-market-losing sequences for the on-roll player is > - 0.1 (Basically we're okay even if we don't lose our market).

Is this what the O'Hagan supporters mean??
My guess is that, in positions which are considered good O'Hagan examples, it is almost always the case that one of these rules is broken.

Paul

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