Effective pip count

- Useful in endgame races 

- to use the cube efficiently

- there are some basics rules :

RULES

1. N roll position : 7n+1, each roll that not save a roll cost 0.2 effective pip, adjustement may be necessary
2. "nice"position waste 7 pips, 6,5 pips if half of the checkers are out and 6 pips when there's just 5 or 6 checkers left
3. "flat"position waste 10 pips
4. Know the stack and stragglers formula : 3.5n+p
5. Know the multiple stack and stragglers formula 3.5n+p1+P2...-4

N roll position have an EPC of 7n+1

Blue needs 5 rolls to bear off : 7x5+1 = 36

White needs 4 rolls to bear off : 7x4+1= 29

This is not a N roll position but it's close: we adjust by calculating the number of pips per checker:

- for blue pip count at 20 and 10 checkers: mean 2

- for white pip count at 20 and 10 checkers: mean 2

then we adjust with that table :

       even number of checker  odd number of checker

1              2                                 2,6

2              2,3                              2,9

3              2,6                              3,2

4              2,8                              3,4

5              3                                 3,6

here add 1 epc to the count of the 2 players because mean at 2 and number of checkers even, so 5 roll position : 7x5+1=36 plus adjustment +1 = 37

each roll that doesn't save a roll cost 0,2 effective pip. here white and blue miss on 11 so their effecive pip count is:

2 roll position

7x2+1+0,2=15,2

Nice position

waste 7 pips :

- blue: pip count à 75 + 7 = 82 EPC

- white: pip count à 77 + 7 = 84 EPC

With half of the checkers off and still a nice position,      add 6,5

With only 5 ou 6 checkers and still a nice position, add 6

FLAT position

waste 10 pips:

- blue pip count 42 = EPC of 52

- white as a usefull reference position to know : this one waste exactly ten pips. move one of the spare higher and it's between a nice and a flat position, move lower and the wastage is higher 

Stack and straggler formula

Blue count is:

3,5xn+p

n is the number of checkers on the board

p is the pip of the straggler

here 3,5x12+16=58

White as a nice position with adjustment odd number of checkers, mean at 26/13 = 2 adjustment less than 1.

7 roll position so 7x7+1 = 50 and just a little more with the adjustment.

Multiple stack and straggler formula

The same except that you add each pip of straggler and you add minus 4 at the end :

3,5x9+20+17-4=64,5

Application

how to use the cube with EPC ?

To use the cube :

- divide the epc of the doubler by 7 (round down)

- that number-3

- add the result to the EPC of the doubler: you have the point of last take

- if your opponent is within 2 points of the last take, you have a double

- if your opponent is within 1 point of the last take, you should redouble

- if your opponent is over the point of last take, he should drop

- beware of the number of roll, if there is few rolls left, there's no recube vig and everyone knows that a pure 3 roll position is a drop