0 views

Skip to first unread message

Sep 8, 1999, 3:00:00 AM9/8/99

to

What is this article about?

How to calculate you opponents chances of winning the game in situations

like this:

You are about to bear off, and you opponent has ONE checker on the bar and

maybe he has borne some of his checkers off too.

How to calculate you opponents chances of winning the game in situations

like this:

You are about to bear off, and you opponent has ONE checker on the bar and

maybe he has borne some of his checkers off too.

The End-game-spleischft formula:

conditions:

1) Your opponent is on the bar (only one checker)

2) You have a closed inner table with spare checkers on 4,5 and 6.

3) your opponents innertable-checkers are smoothly distributed.

4) Its your turn.

5) Claus Thomsen is a killer on FIBS.

If your opponent has borne x checkers off, his chance of winning the game

is:

************************************************

if x is between 0 and 7:

opponent wins 2*x*(x+1)/3+5 out of 100 games.

if x is between 8 and 14:

opponent wins 6*(x+1) out of 100 games.

************************************************

examples:

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+

| O O O O | | |

| O O O O | | |

| O O | | |

| | | |

| | | |

| | | |

| | | |

| | O | |

| X X X | | |

| X X X X X X | | |

| X X X X X X | | |

+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

the conditions is ok so: how many checkers has white borne off? -> 4

4*5=20 20*2=40 40/3=13 13+5=18

opponent wins 18% of all games

Example 2

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+

| O O | | |

| O O | | |

| O O | | |

| O | | |

| O | | |

| | | |

| | | |

| | O | |

| X X X | | |

| X X X X X X | | |

| X X X X X X | | |

+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

White has borne 6 pieces off.

6*7=42 42*2=84 84/3=28 28+5=33

BUT whites checkers is not smoothly distributed! the two checkers on 24

should have been on 22 - but since white dont need any extra rolls because

of this we will not give him extra %'s.

opponent wins: 33%

The hard one :-)

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+

| O O O | | |

| O O O | | |

| O | | |

| | | |

| | | |

| | | |

| | | |

| | O | |

| X X X | | |

| X X X X X X | | |

| X X X X X X | | |

+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

white has borne 7 checkers off but white doesn't have a smooth distribution

of checkers :-(((

- We will have to create a equivalent-diagram. How? Lets say O would need

one or two more rolls now than if his checkers was smoothly distributed. So

I will add two checkers to his innertable and distribute his checkers.

new equivalent diagram

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+

| O O O | | |

| O O O | | |

| O O O | | |

| | | |

| | | |

| | | |

| | | |

| | O | |

| X X X | | |

| X X X X X X | | |

| X X X X X X | | |

+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

now: white has 5 checkers borne off.

5*6=30 30*2=60 60/3=20 20+5=25

but the players checkers is placed worse than in the standard condition

(spare checkers on 4-5-6) so we will give white 9%

opponent wins: 25% + 9% = 34%

In the last diagram I gave white 9% and here is why:

this *NEW* table tells us the how many %'s we should give the opponent if

our spare checkers is on 1-2-3 instead of 4-5-6:

opponent has again borne (X) checkers off

the BLUWDUCH table:

(X), (5's to add)

--------------------------

1, 1%

2, 2%

3, 3%

4, 5%

.

9, 9% (here is x=9 and we see that we need to add 9% :-D)

.

14,5%

interpolate between 4 and 9. ANd interpolate between 9 and 14

Final example to show the use of the formula for x between 9 and 14:

+24-23-22-21-20-19-+---+18-17-16-15-14-13-+

| O O | | |

| O O | | |

| | | |

| | | |

| | | |

| | | |

| | | |

| | O | |

| X X X | | |

| X X X X X X | | |

| X X X X X X | | |

+-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+

white has borne 10 checkers off. x is now greater than 7, so we will use the

other formula

6*(10+1)=6*11=66 (6*(X+1))

opponent wins: 66%

What do you think?

__ : this thing sucks.

__ : power to the spleischft and bluwduch formula.

Reply all

Reply to author

Forward

0 new messages

Search

Clear search

Close search

Google apps

Main menu