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Daily Quiz, race/bear-off positions

Posted By: kruidenbuiltje
Date: Tuesday, 3 January 2012, at 10:38 a.m.

In Response To: Daily Quiz, race/bear-off positions (rambiz)

Hi rambiz,

I will tell you how far I came until now.

I will give a few examples, at first the position DQ(daily quiz) 1/4/2011 nr. 3

The first rule = 7xN +1 for a N-roll no miss position.

So white's EPC is clearly 15

black's is a bit higher, but how much?

For this I use a table that Mr Majestyk once put on the forum, about the wastage of single checkers:

For the 6 pt. to the 1 pt. its respectively:

4.2 / 4.3 / 4.6 / 5.2 / 6.2 / 7.2

In black's position we will have to shift the checker on the 4-point to the 2-point to get a no-miss position.

4 pt. = 4.6 ; 2 pt. = 6.2

the difference is 1.6 so blacks EPC = 15 + 1.6 = 16.6.

I get 15.2-16.8 for the position

GNU gives 15.0-16.6, pretty close.

Next example: 5/4/2011 nr. 3

Black is easy: 22

Now white: if the checkers of 5 and 4 would be on the 3-point this would be a near 3-roll position

The shift costs 0.9 + 0.6 = 1.5

So white has an EPC = 23.5

GNU gives 22-23.4, pretty close again.

Example 3: 7/4/2011 nr. 5

This position is no way close to a no-miss, so we need another reference.

Rule: a balanced position (2 checkers on each point) has a waste of 10 pips.

The white position is pretty balanced, we only need to shift a few checkers.

Shift the 1 to the 6 and shift the 2 to the 3 and the position is completely balanced:

cost: 3+1 = 4 + the standard 10 = 14.

The blot on the midpoint will not unbalance the situation much when coming in.

So the EPC for white is 56 + 14 = 70.

Now blue, lets shift 4 from the checkers on the 2-point to the 4-point.

Cost = 4 x 1.6 = 6.4.

The blue EPC = 10 + 6.4 + the original pipcount 44 = 60,4

GNU gives 60.3 - 69.8.

The next thing is: how do i calculate the last takepoint.

This is quite simple.

Example 1: 15.0 - 16.6

Number of rolls for the doubler (black)= 2,2 (EPC 15 = 2 rolls, every 0,7 extra EPC = 0,1 roll)

The point of last take = Number of rolls - 3 = 2.2 - 3 = -0.8.

So the point of last take = 16.6 - 0.8 = 15.8

White has an EPC of 15, so he is on the safe side (15.9 would have meant a pass)

Example 2: 22-23.4

Number of rolls for the doubler = 3

Point of last take = 22 - 0 (3-3) = 22.

23.4 is too high , so pass

Example 3: 60.3 - 69.8

Since we now don't have a reference to a no-miss-position there is a change.

What is the number of rolls here?

Based on a no-miss-position it woulds be between 8 (EPC 57) and 9 (EPC 64), say 8.5

But based on the average pips per roll (=8.17) it would be a 7.5 roll position.

I don't know exactly here what to do.

The point of last take = 60.3 + 5.5 (or 4.5) = 68.8 (or 67.8)

In both cases a pass.

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