[Bug-gnubg] Proposal - Luck rating

Hi all,

2 details about "luck rating"
computation (Go to bed, ..., Go to Vegas).

1. Luck is computed for each player
independently: this leads to situations where
players are both very lucky (or very
unlucky). Despite this being mathematically
understandable, the average user probabaly
expects a "differential rating":
when player A has been "very lucky",
he expects player B to be "very unlucky"
(zero sum).

Said otherwise, in matchplay, if player
A and Player B Total Luck (MWC) are
+10%/+10% or +20%/+20%, the luck rating
will be (let's say) "lucky/lucky" and
"very lucky/very lucky" respectively,
but the average user probably expects
"none/none".

2. Looking into the code it seems to
me that the luck rating for each player is
computed from the normalized luck rate.
This does not make much sense to me.

The reference value to look at in order
to understand who has been lucky is the diff
between the two players in Total Luck
(in MWC for match, in Points for money).

The normalized luck (and luck rate)
"factors out" the cube value/score (score
considerations are somehow factored
out by EMG).

In matchplay, imagine a situation where
a very long match goes up to DMP without
any particular luck for the two players.
Then , at DMP bearoff, one roll a super joker
and wins. In terms of Total Luck this
will appear clearly (like a +50% in MWC), but in 
normalized luck this will not. The same
situation in a much shorter match, despite
having the same total luck (+50%) could
have a "Go to Vegas" rating instead of
a "lucky" or a "none"
rating.

I would advise the following:

* For player A, take his total luck
(in MWC for match, in Points for money) and subtract
player B's total luck: let's call this
Net Luck. Of course NetLuck(A)+NetLuck(B)=0. 

* Compare the actual result with the
net luck and see which share of the actual result
is due to the net luck.

* For money, for player A:
        Actual
Res                Net
Luck                Ratio
               
       Rating
        +2
               
       +2        
               +100%
               -->
       Very Lucky
        +2
               
       +1        
               +50%
               -->
        Lucky
        +2
               
       +0        
               +0%
               -->
        None
        +2
               
       -1        
               -50%
               -->
       Unlucky        
        +2
               
       -2        
               -100%
               -->
       Very Unlucky

*For match, actual result is either
+100% or -100%, do the same computations and apply
the same table to convert from the ratio
to the rating.

I have no idea about how to convert
the ratios into meaningful ratings, figures above are
just to illustrate.


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