Cube Handling

 Endgame close out: Spleischft formula

 From: Simon Larsen Address: larsen@ostenfeld.dk Date: 8 September 1999 Subject: endgame Forum: rec.games.backgammon Google: 37d55210.0@news.k-net.dk

```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.

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.
```

 Did you find the information in this article useful?           Do you have any comments you'd like to add?

### Cube Handling

Against a weaker opponent  (Kit Woolsey, July 1994)
Closed board cube decisions  (Dan Pelton+, Jan 2009)
Cube concepts  (Peter Bell, Aug 1995)
Early game blitzes  (kruidenbuiltje, Jan 2011)
Early-late ratio  (Tom Keith, Sept 2003)
Endgame close out: Michael's 432 rule  (Michael Bo Hansen+, Feb 1998)
Endgame close out: Spleischft formula  (Simon Larsen, Sept 1999)
Endgame closeout: win percentages  (David Rubin+, Oct 2010)
Evaluating the position  (Daniel Murphy, Feb 2001)
Evaluating the position  (Daniel Murphy, Mar 2000)
How does rake affect cube actions?  (Paul Epstein+, Sept 2005)
How to use the doubling cube  (Michael J. Zehr, Nov 1993)
Liveliness of the cube  (Kit Woolsey, Apr 1997)
PRAT--Position, Race, and Threats  (Alan Webb, Feb 2001)
Playing your opponent  (Morris Pearl+, Jan 2002)
References  (Chuck Bower, Nov 1997)
Robertie's rule  (Chuck Bower, Sept 2006)
Rough guidelines  (Michael J. Zehr, Dec 1993)
Tells  (Tad Bright+, Nov 2003)
The take/pass decision  (Otis+, Aug 2007)
Too good to double  (Michael J. Zehr, May 1997)
Too good to double--Janowski's formula  (Chuck Bower, Jan 1997)
Value of an ace-point game  (Raccoon+, June 2006)
Value of an ace-point game  (Øystein Johansen, Aug 2000)
Volatility  (Chuck Bower, Oct 1998)
Volatility  (Kit Woolsey, Sept 1996)
When to accept a double  (Daniel Murphy+, Feb 2001)
When to beaver  (Walter Trice, Aug 1999)
When to double  (Kit Woolsey, Nov 1994)
With the Jacoby rule  (KL Gerber+, Nov 2002)
With the Jacoby rule  (Gary Wong, Dec 1997)
Woolsey's law  (PersianLord+, Mar 2008)
Woolsey's law  (Kit Woolsey, Sept 1996)
Words of wisdom  (Chris C., Dec 2003)

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