Hi Francesco, Your formulas are correct.
But luck evaluations/analysis uses a fundamentally different approach than error evaluations/analysis, regardless of any ply-depth. Only when the backgammon engine would produce perfect numbers for all positions, would the two different methods always lead to the same conclusions about the % skill and % luck. An important distinction between error analysis and luck analysis, is that the latter is unbiased. Which means that in the long run, the luck analysis numbers will approach the real values (inaccuracies of the bot will cancel out).This is not the case for error analysis, where inaccuracies of the bot may not cancel out and sometimes even pile up. With GnuBG, I believe the default luck analysis is unfortunately (still) set to 0-ply and not changeable from the GUI. 0-ply luck analysis is quite inaccurate. With a command "set analysis luckanalysis plies 2" (or even higher, although that might be slow) you can improve the quality of the luck analysis significantly. You'll probably find that doing luck analysis at higher settings reduces (but does not remove) the discrepancies between error analysis and luck analysis. Kind regards, Robert-Jan Veldhuizen On Tue, Sep 23, 2025 at 1:04 PM Francesco Ariis <[email protected]> wrote: > Hello gnubg users, > > I have a question about the relationship between “Error total (MWC)” > (Err%) and “Luck total (MWC)” (Lck%). > > Before I continue, some definitions to make sure I got this correctly: > - Err%(A) is the equity (in Match Winning Changes) that player A dropped > in the match, both chequer play and cube actions. This is expressed in > Match Winning Chances (MWC) and has always a negative sign. > - Lck%(A) is the equity player A gained/lost each time he rolled the dice. > This too is expressed in MWC, can have positive or negative sign. > - AR is the actual result in MWC, 50% if I win, -50% if I lose. > - Each of those variables above are non normalised. > > Example from a recent match I have played: > > PlayerA PlayerB > -------- -------- > Err% −39.614% −64.202% > Lck% +37.250% −2.534% > AR 50% −50% > > > > Now, the question. > I would think AR to be: > > R = Lck%(A) − Lck%(B) + Err%(A) − Err%(B) > > or in longhand, I expect “Result − Luck” to be equal to “Skill”; and vice > versa “Result − Skill” to be equal to “Luck”. > > But this seems not to be case: > > # From the perspective of PlayerA > Result = 50% > Luck = 37.250% + 2.534% = 39.784% > Skill = −39.614% + 64.202% = 24.588% > > Implied skill (Result − Luck) = 50% − 39.784% = 10.216% > # ↑ This is “Luck adjusted result” − 50%. > Implied luck (Result − Skill) = 50% − 20.588% = 29.412% > > I expected some minor discrepancies between the two numbers, because (if > I understood the calculation correctly), luck evaluations would have to be > done 1-ply deeper than error evaluations to perfectly match. > > But there has to be something else that eludes me, right? What other > factors > make one method of estimating skill so different from the other? > > Thanks in advance, happy rolls > —F > > <#m_-5805420678066633234_DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
