RE: [Bug-gnubg] New formula for estimating bearoff GWC

[Ian Shaw]

> -----Original Message-----
> From: Joachim Matussek [mailto:address@hidden
> Sent: Wednesday, June 16, 2004 10:55 PM
> i want to introduce a new formula for calculating game winning chances
> for bearoff positions with up to 8 checkers. It gives an accurate
> estimate of the effective pipcount (EPC) and uses these results to
> calculate the GWC. Accuracy is +- 2 % GWC.
> 
Hi Joachim,

I'm finding your article very stimulating. Thanks for putting in the hard work. 
I'm still thinking about it, but there are a few things I'd like to discuss 
already.

1 EPC Count

1.1 Why does the formula stop at 8 chequers? Is it because that's how far 
you've tested, or does it break down later?

1.2 Your wastage per pip is linear. Douglas Zare uses a non-linear adjustment 
for chequers on the ace-point 0, 1, 2, 2, 2 ..., and something similar for the 
2 point. Have you tried any such method?

1.3 You make no allowances for gaps. This seems a likely source of inaccuracy. 
Perhaps Chuck Bower's of a "useless gap" might be useful.

1.4 You penalise stacks equally, irrespective of their position. This seems 
unnatural. With only 8 chequers and a stack, you are likely to have gaps 
elsewhere, so perhaps this ties in with the previous point.

1.5 Have you any idea which type of positions give the largest error? . Do they 
err in a particular direction? Nearly 10% are off by a pip or more, and I worry 
that they may be the less trivial positions.

2 EPC to GWC

2.1 Is this part of your article only concerned with 8 chequer positions? I'm 
assuming not.

2.2 Your table of %/pip is a great idea. I was planning on constructing such a 
table myself (I don't have the tools to extract from the database so I was 
planning on just using some hand-selected examples).

2.3 How many samples were taken for each epc?

2.4 As I understand it, you have taken examples with a 1 epc difference between 
the players. I believe that the %/pip is not linear as the pip difference 
changes. I believe the %/pip differs between an even race and a close 
take/pass. (I don't know the direction; this is something I'm planning to look 
at.) I also believe the %/pip tails off as you move further into pass territory.

I would be extremely interested in a table with samples at a 4 pip deficit 
(i.e. even race), even pips (some advantage to roller), borderline take/pass, 
and larger pass (say 5 pips).

2.5 The 0.5% and 1% adjustments for pip-roll and roll-roll positions are very 
exciting because they are so simple to remember and use. How confident are you 
with these.

Regards
Ian Shaw