Réf. : Re: [Bug-gnubg] G/BG rates [minor ?]

[Massimiliano . Maini]

>On Mon, Sep 08, 2003 at 12:16:09PM +0200, address@hidden
wrote
>>
>>
>> Hi all,
>>
>> I do the following :
>>
>> - evaluate a position (anyone where market window make sense/is allowed)
>>
>> - write down the static, 1 ply and 2 ply [Win, W(g), W(bg)] percentages
>>
>> - open the "Market Window Analyzer" and try to see if the indicated gammon
>>   and backgammon rates matches the ones you can compute manually
>>
>> EXAMPLE :
>>
>> This is the output of the Evaluation :
>>
>>   Position ID: 4HPiQSDgc/ABMA
>>   Match ID:    cAngAAAAAAAA
>>
>>   Evaluator:   CONTACT
>>
>>   <SNIP ... SNIP>
>>
>>           Win     W(g)    W(bg)   L(g)    L(bg)   Equity    Cubeful
>>   static:  48,46%  13,86%   0,41%  13,49%   0,72%  -0,0304   -0,0458
>>    1 ply:  50,32%  14,01%   0,50%  12,90%   0,48%  +0,0186   +0,0232
>>    2 ply:  48,58%  13,59%   0,44%  13,58%   0,63%  -0,0305   -0,0436
>>
>> Now I was expecting :
>>
>> gammon rate (static) = 13.86/48.46 = 28.60%
>> gammon rate (1 ply)  = 14.01/50.32 = 27.84%
>> gammon rate (2 ply)  = 13.59/48.58 = 27.97%
>
>Note as well as Win includes W(g) and W(bg), W(g) includes W(bg), so I'd
>expect:
>
>gammon rate (static) = (13.86-0.41)/48.46 = 27.75%
>gammon rate (1-ply)  = (14.01-0.50)/50.32 = 26.85%
>gammon rate( 2-ply)  = (13.59-0.44)/48.58 = 27.07%
>
>I guess the small differences to the ones calculaetd by the market
>window is due to rounding errors.

You're right, but I find this a bit confusing.

In the beginning I was asking myself why in the hell the Win/Lose
percentages are defined like that (W includes W(g) and W(bg), W(g)
includes W(bg), same for L, L(g), L(bg)). Wouldn't be easyier to
have W(so), W(go), W(bo) (respectively single only, gammon only
and backgammon only) ?

Now that I've finally understood why (cause the average cubeless
value of a Win for money play will simply be [W + W(g) + W(bg)],
instead of [W(so) + 2*W(go) + 3*W(bo)], right ?) I was thinking
that :

(W + W(g) + W(bg)) == W * (1 + GR + BR)

where GR and BR are gammon and backgammon rates in my onw (wrong)
definition, i.e. :

GR =  W(g) / W
BR = W(bg) / W

I was supposing that the gammon rate includes the backgammon wins,
just like the W(g) includes W(bg). But it looks like that's not
the case ... too bad, just few extra terms into some of the
alredy-too-long equations of backgammon theory :))

Thx,

MaX.