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OLM 20141102A The Prime Factors
Posted By: kruidenbuiltje In Response To: OLM 20141102A The Prime Factors (Jason Lee)
Date: Monday, 3 November 2014, at 8:42 a.m.
Let's categorize the white moves and estimate our wins from there:
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Group 1: The hits
{53,43,54,D4,D5} = 8/36
In half the cases blue gets some returns like {16,52,21,D2} a total of 7/36.
Blue will get 1 (out of 36) win out of this, and maybe half a win out of late hits.
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Group 2: The 'normal' holding
Of course white will also get later attack possibillities against the 3-blot.
But we will round the result of this group down for this later.
Let's first presume it's a normal 5-pt holding.
Even after initial doubles (except D2) blue will have to clear the mid- and the 11-point.
How often will the midpoint and 11-point leave a shot.
+++++++++++++++++++++
Clearing the midpoint:
The stripped midpoint with landing points at 2,5 and 6 distance has 5/36 (doubles) + 6/36 (singles) = 11/36 chance of safe clearance.
After the first stripping move blue will have somewhere between 16 and 22 pips to perform this task.
That's somewhere between 3 and 4 moves, say 3,5 moves.
The chance of leaving a shot is (25/36) ^ 3,5 = 28%.
The 1 + 8-shot has a hit-chance of 14/36, that makes 11% hits.
++++++++++++++++++++++
Clearing the 11-point:
The stripped 11-point has 5 doubles and 3 landing points, so also 11/36 safe clearances.
It's hard to say how many free pips white has after clearing his midpoint.
But to make a guess, let's take half of the old free pips (9,5 pips)
and add something between 6 and 16 for the pips coming from the midpoint.
That makes on average about 20 pips, that's 2,5 moves + off course the clearing move makes 3,5 moves again for clearing.
Again 28% shots, and this time the hitchance is also 14/36, again 11% hits.
++++++++++++++++++++++++++++++++++++++++++++++
Now some fine-tuning for this holding group:
- When clearing the midpoint results in a hit, we shouldn't count the clearing of the 11-point,
so I discount 1% of the 11-point group, making 10% hits there.
- The total of 11% + 10% = 21% has to be corrected for later hits on the 3-point, I guess that leaves us somewhere around 18% for this group.
- A hit is not a win, but it will be close, about 90% I guess, so this group will score 16% wins.
16% of 28/36 makes about 4,5 wins for this group.
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The total of both groups adds up to about 6 wins. That's almost 17%.
We might add to this a few percent race-chances, and a few percent later hits.
And I think the gammons are on our side, since after an early hit, white doesn't have an anchor and a lot of extra crossovers.
I estimate our total wins somewhere between 20 and 24%, and I think we get a few percent gammons to take us over the taking edge.
Answer: Take
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