RE: [Bug-gnubg] Proposal - Luck rating

[David Levy]

Hello,

I have a question or two about how luck is reported, followed by a comment
on Massimiliano's suggestion. 

Both players begin play at 50% to win a match. One of them wins, going to
100%, the other loses going to 0%. It seems to me that as a matter of
definition, the “net luck” plus the “net skill” (difference in MWC of the
two players’ errors) should be exactly 50%. Correct?

gnubg often reports results quite close to 50%. For example:

                                      opponent                  Me

Error total EMG (MWC)              -0.6945 (-12.422%)      -1.3522
(-14.624%)
Luck total EMG (MWC)               +1.0533 (+35.787%)      -1.1830 (
-8.598%)

Net luck was 44% against me and net errors were another 2%. Close to 50%,
but not exact. 

But sometimes the results are substantially different. Can anyone explain
this?

My thoughts:

(1) Perhaps gnubg uses 2-ply for checker play, but 0-ply for calculating
luck. 
(2) Perhaps gnubg uses the bearoff database for checker play, but some-ply
analysis for luck and the two won't be 100% consistent.
(3) When you rollout a position, errors are updated. Luck is not.
(4) Amusingly, when an opponent resigns in a position that is not a 100%
loss, that is an error not reflected in the error total!        
(5) Other ideas?

Bonus question. Can anyone come up with an EMG transformation that preserves
the idea that net luck and net skill expressed in EMG, exactly and
consistently replicate the match outcome (as it should, I contend, when
expressed in MWC)?

The suggestion for reporting "net luck" is interesting as an addition. But I
would not like to lose the reporting of raw luck in MWC. You can have a +20%
net luck, but it FEELS very different as a player when that is +80% for you
and +60% for the opponent versus -40% for you and -60% for the opponent!

Best,

David



From: address@hidden
[mailto:address@hidden On Behalf Of
Massimiliano Maini
Sent: Monday, July 06, 2009 2:38 AM
To: address@hidden
Subject: [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. 


MaX.