I am trying to understand the maths behind various GNU analysis parameters.
Got stuck on this.
Anyone knows how GNU calculates the Luck adjusted result?
I attach relevant image file
The luck adjusted result is calculated as the actual result plus the total unnormalised luck rate. This is also called variance reduction of skill as described in Douglas Zare's excellent article Hedging Toward Skill. This should give an unbiased measure of the strengths of the players. Whether it does or not is of course another matter!
http://www.bkgm.com/articles/Zare/HedgingTowardSkill.html (http://www.bkgm.com/articles/Zare/HedgingTowardSkill.html)
from http://www.gnubg.org/documentation/doku.php?id=working_with_matches&s=luck (http://www.gnubg.org/documentation/doku.php?id=working_with_matches&s=luck)
You can also adjust the classes for what GNU Backgammon considers lucky and unlucky rolls. The luck of a roll is defined as the differnce of equity after the best move after rolled dice and the equity after best move avergaged over all possible rolls.
Sorry guys but you are just repeating what GNU documentation says.
The data is all there and well understood the question is how did it compute the +2.84%??
True I did not read the question well and realized that after hittinbb the enter button. Bet when you are able to read C code you can find the answer in the code of gnubg which public.
As far as I know the exact number of +2.84% is not a simple arithmetic operation of some statistics 'that are already there', although it theoretically should. My guess this is due to (1) imperfectness of the neural nets and (2) due to differences in plies used for luck calculations (set to 0 by default to save time) and for equity loss calculations.
I would recommend re-analysing the match on 4 plies (via Settings | Analysis) and 2 plies (or even 4) for luck calculation. Discrepancies will probably be smaller, but prolly never be gone totally. Analysis times will explode, though.
There is no menu item to set plies for luck analysis, so you'll need to enter that in the command window.
See also http://www.fibsboard.com/fibsboard-forum-matches/how-do-%27luck%27-calculations-work/msg23294/#msg23294 (http://www.fibsboard.com/fibsboard-forum-matches/how-do-%27luck%27-calculations-work/msg23294/#msg23294)
Quote from: Phaedrus on December 29, 2014, 02:53:33 PM
True I did not read the question well and realized that after hittinbb the enter button. Bet when you are able to read C code you can find the answer in the code of gnubg which public.
Clever point! That's what I did actually.
I don't particularly understand C code but i was expecting to reach a point where formulae were used
I downloaded the source code, it calls functions upon functions there is no end to it.
And I detected no formulae anywhere :blink:
Perhaps the luck adjusted result is one of the Gnu features that hasn't been thought through properly and wouldn't mean anything useful even if it had.
Dr Tim Chow gave me the answer and I thought of copying it here. Thanks for your replies anyway.
http://www-math.mit.edu/~tchow/ (http://www-math.mit.edu/~tchow/)
Actual result for Player A = 50.00%
Luck of Player A = 9.164%
Luck of Player B = -37.992%
50.00 - 9.164 + (-37.992) = 2.844
NB. It seems statements made in older discussions suggesting that GNU does not take into account both players luck were not right .
When you have analysed a match it might happen that looking for each game of the match f.e. player X luck (just in words) was "none" and player O luck was "Go to bed". To me the bad luck is the luck of the other
Quote from: Phaedrus on January 04, 2015, 02:40:07 PM
When you have analysed a match it might happen that looking for each game of the match f.e. player X luck (just in words) was "none" and player O luck was "Go to bed". To me the bad luck is the luck of the other
That's partly correct. If you notice GNU sums up both Players luck. It depends how much + or - each one of the Players end up.
There are some problems regarding the thresholds that GNU "signals" outputs to the user as for example whether a roll is lucky/unlucky/very lucky etc. Same with the Humorous description "go to bed" ,"Go to Las vegas" etc
Notice however that those are just "signals" to the user, they have absolutely no effect in calculating total luck.
GNUBg does an amazing job of precision, evaluating each and every roll separately and then summing it up and presenting it in the statistics -overall tab. Even at luck ="none" the numbers are still there and should be allowed to talk for themselves.