Forum Archive :
Cube Handling
Endgame close out: Michael's 432 rule

Michael's 432Rule
I have analysed some positions when bearing off.
The positions were about being hit while you are bearing off,
and your opponent has a closed board. An example is shown below.
O is bearing off, and sometime in the bearoff, he was hit.
After that X managed to closed his board with O on the bar.
This sequence is quite common in BG today.
++
   O 
   O 
   O 
   O 
   O 
  O  
   
   X X X 
   X X X X X X 
   X X X X X X 
++ X on roll
12 11 10 9 8 7 6 5 4 3 2 1
The question is now:
What is the probability of X winning the game?
I have found out a simple rule that can give you the necessary information,
and I've named the rule "Michael's 432 rule"
The rule is as follows: When O have 4 men left on his ace point, the
probability of X winning is between 30 and 20% (4,3,2), dependent of where
his extra builders are placed (cube less). For an optimum distribution of
spares on the 6,5 and 4 point (see figure) will give X 30% of winning
chances, while having all the spares on the acepoint, which is the worst
condition, will give X 20% probability of winning the game. You just have
to remember the 4,3,2 sequence: When the opponent has N builders left ,
your chances of winning are between 10*(N1)% and 10*(N2)%. The formula
can be extended up to O having 9 men on the acepoint. Then X's probability
of winning is between 80% and 70% (9,8,7). The formula is accurate within
23%, which is accurate enough for human players. When O has below 4 men
and beyond 9 men, the formula isn't accurate enough. The formula also work
"in reverse". This means, that if you are hit while bearing off, you have a
take (in MG) when you have a maximum number of 7 men on the ace point. Then
the opponent's winning chances are between 60 and 70%. The 7 men is also
what Bill Robertie consider to be the turning point. I've used this formula
a lot, and I found it quiet easy to use. I hope it can help other players
around the world.
Hi from
Michael Bo (snog at FIBS)


Michael Bo Hansen writes:
It seems that my 432rule has been greatly commentated here in the r.g.b.,
even though there is a small error in the last part of the text. When YOU
have 7 men on the ace point, the OPPONENT has between 50% and 60% of
winning, meaning YOU have between 40% and 50%. If using the formula YOU
have a take (in moneygame) having upto 8 men on your own acepoint, and one
on the bar.
Michael Bo




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)
 Earlylate 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)
 PRATPosition, 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 doubleJanowski's formula (Chuck Bower, Jan 1997)
 Value of an acepoint game (Raccoon+, June 2006)
 Value of an acepoint 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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