"Michael's 432 rule" by Michael Bo Hansen
Mary Warnk
OK - I'll bite, what is it and where can it be found?
If it is brief enough to explain here, please do.
If not, please guide me to a source that explains it.
Thank you,
Richard E. Warnk
Chuck Bower
In article <357E8093...@home.com>,
Mary Warnk <divd...@home.com> wrote:
>OK - I'll bite, what is it and where can it be found?
>
>If it is brief enough to explain here, please do.
>If not, please guide me to a source that explains it.
Here is the original message from February, downloaded for
DejaNews:
Subject: Michael's 432 rule
From: micha...@yahoo.com
Date: 1998/02/27
Message-ID: <6d71vu$o$1...@nnrp1.dejanews.com>
Newsgroups: rec.games.backgammon
Michael's 432-Rule
I have analyzed some positions when bearing off.
The positions were about beeing 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 bear-off, 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 probality of X winning the game?
I have found out a simple rule that can give you the neccesarry information,
and I've named the rule "Michael4s 432 rule"
The rule is as follows: When O have 4 men left on his ace point, the
probality of X winnning is between 30 and 20% (4,3,2), dependent of where his
extra builders are placed (cubeless). 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 ace-point, which is the worst condition,
will give X 20% probality of winnning 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*(N-1)% and 10*(N-2)%. The formular can be extended up
to O having 9 men on the ace-point. Then X's probality of winning is between
80% and 70% (9,8,7). The formular is accurate within 2-3%, which is accurate
enough for human players. When O has below 4 men and beyond 9 men, the
formular isn't accurrate enough. The formular 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
winnning chances are between 60 and 70%. The 7 men is also what Bill Robertie
consider to be the turning point. I've used this formular 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)
Richard E. Warnk
Thank you Chuck - Food for thought.
Is there a standing reaction to this
concept. Valid, usable, impractical,
will save your butt or kick it?????
Thanks again,
Richard
micha...@yahoo.com
In article <357EED7F...@home.com>,
It seems that my 432-rule 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 OPPONENThas 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 ace-point, and one on the bar.
Michael Bo
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