Forum Archive :
Cube Handling
Endgame close out: Spleischft formula
|
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.
|
|
|
|
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)
From GammOnLine
Long message
Recommended reading
Recent addition
|
| |
|