Dear gnubg users,
tl;dr: running Luck analysis at 2-ply reduces the discrepancy between
Luck and Implied Luck, but not by that much.
Summary of my previous messages [1]
-----------------------------------
I asked why the difference between Error total% and Luck total% sometimes
did not follow this formula:
Result = ΔLck% + ΔErr%
Example game:
PlayerA PlayerB
-------- --------
Err% −39.614% −64.202%
Lck% +37.250% −2.534%
AR 50% −50%
Robert-Jan Veldhuizen noticed that Luck analysis is done by default at
0-ply. Moreover he explained that gnubg is not a perfect engine, so there
will always be discrepancies between the two calculations.
Luck analysis at 2-ply
----------------------
Robert-Jan Veldhuizen and Philippe Michel showed to me how to rerun
luck analysis at a higher number of plies. Very appreciated, thanks
to both of you!
I decided to batch-analyse on all of my games (≃450) with
set analysis luckanalysis plies 2
set analysis luckanalysis prune on
and calculate the difference between L “luck” `ΔLck%` and IL “implied
luck” `Result − ΔErr%`.
Squaring the difference `(L−IL)²` over each of those games,
averaging it and calculating the square root of the average `σ` leads
to the money shot.
games ply σ
----- --- -------
471 0 8.4
471 2 7.3
The average length of game is 5.3.
So running Luck analysis at 2-ply reduces the discrepancy between
Luck and Implied Luck, but not by that much.
More strats
-----------
Using 2-ply analysis, I checked whether σ is different for won or lost
games:
status games avg(pt) σ
--------- ----- --------- -------
running 5 5.0 31.3
lost 245 5.3 5.7
won 221 5.3 7.4
I did not calculate confidence intervals, it seems in my case the
discrepancy increases on won games.
There is no difference on “Better PR than opponent?” though.
Additionally, a similar analysis on match length:
points games σ
-------- -------- -------
7 108 8.3
5 332 6.9
3 24 6.5
1 7 8.1
Again no CI, but it seems discrepancy increases on longer matches.
[1] https://lists.gnu.org/archive/html/bug-gnubg/2025-09/msg00007.html
