First, my understanding of how XG does things. Please
feel free to correct/clarify if/as needed.

1) According to XG's Dice Distribution, average equity for
opening rolls, (excuding doubles), is 1642 / 30 = +0.0547

2) XG keeps "luck rate" as a +/- zero-sum number for both
players.

3) XG keeps track of equities as gained/lost compared to
the best move (even if the best move also loses equity).

4) My comments follow ## signs.

With that said, let's start by looking at the 5-move game at:

https://www.bkgm.com/rgb/rgb.cgi?view+68

======================================
Player1
Dice-D for 31: +0.237 - +0.109 = +0.128

Luck after roll: +0.234(0) -0.234(0)

## XG doesn't subract the average eqity from the opening roll
## Luck should be +0.237 - +0.0547 = +0.182

Hint:
1. Book 8/5 6/5 Eq.: +0.234
5. Book 13/9 Eq.: -0.031 (-0.265)

Equity after play: -0.265 +0.000

======================================
Player2
Dice-D for 44 : +0.446 - +0.026 = +0.420

Luck after roll: -0.181(0) +0.181(1)

## It seems it added +0.415 not +0.420
## Luck should be -0.234 + +0.420 = +0.186
## This will ripple through all subsequent calculations

Hint:
1. 1-ply 24/16* 13/9(2) Eq.: +0.441
12. 1-ply 24/16* 13/5 Eq.: +0.150 (-0.282)

Equity after play: -0.265 -0.282

======================================
Player1
Dice-D for 32: -0.049 - -0.165 = +0.116

Luck after roll: -0.067(0) +0.067(1)

## It seems it added +0.114 not +0.116
## Luck should be -0.181 + +0.116 = -0.065
## Luck should be -0.186 + +0.116 = -0.070 per prior correction

Hint:
1. 1-ply bar/20* Eq.: -0.046

Equity after play: -0.265 -0.282

======================================
Player2
Dice-D for 31: +0.018 - +0.041 = -0.023

Luck after roll: -0.080(0) +0.080(1)

## It seems it added -0.013 to Player1 for some reason??
## Luck should be +0.067 + -0.023 = -0.044
## Luck should be +0.065 + -0.023 = +0.042 per prior correction
## Luck should be +0.070 + -0.023 = +0.047 per prior correction

Hint:
1. 1-ply bar/22 6/5* Eq.: +0.059
4. 1-ply bar/24 16/13 Eq.: -0.076 (-0.135)

Equity after play: -0.265 -0.416

## Should be -282 + -0.135 = -0.417 a minor inaccuracy

======================================
Player1
Dice-D for 43: +0.140 - +0.075 = +0.065

Luck after roll: -0.005(0) +0.005(1)

## Luck should be -0.080 + +0.065 = -0.015
## Luck should be -0.047 + +0.065 = +0.018 per last correction above

## If we tally luck figures manually after 5 rolls, we have:
## +0.234 +0.420
## +0.116 -0.023
## +0.065
## -------- --------
## +0.415 - +0.397 = +0.018 like magic, we end up with the same
## number above, after all my suggested corrections in between

Hint:
1. 1-ply 24/20 13/10 Eq.: +0.151
8. 1-ply 20/13 Eq.: -0.107 (-0.258)

Equity after play: -0.523 -0.416

======================================
At this point, we have recycled back to opening position
Now let's look at Nasti's opening 53 again

Dice-D for 53: +0.085 - +0.109 = -0.024

Luck after roll: +0.019(0) -0.019(1)

## This time XG subracts average eqity from "/opening roll/"
## But luck should be +0.018 + -0.024 = -0.006
## Instead it's calculated as +0.005 + -0.024 = -0.019
## and thus the error carries on...

Hint:
1. Cubeful 0-ply 8/3 6/3 Eq.: +0.083

Equity after play: -0.523 -0.416

======================================
And what about not-so-humorous luck ratings after each
play in Nasti's example of 4 rolls? Here:

After Nasti's 53
Average Luck It's in the wrist (+0.0829)
Average Luck Not your day (-0.0829)
Total luck +0.83 points

After Gnubg's 42
Average Luck Quite lucky (+0.0147)
Average Luck Quite unlucky (-0.0147)
Total luck +0.29 points

After Nasti's 66
Average Luck It's in the wrist (+0.2132)
Average Luck Not your day (-0.2132)
Total luck +0.64 points

After Gnubg's 62
Average Luck It's in the wrist (+0.1726)
Average Luck Not your day (-0.1726)
Total luck +0.69 points

======================================

I tried to be as sparing with words as I could.
If anything isn't obvious to you, please feel free
to ask and I will try to explain.

Happy XG-mas...! ;)

MK

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On December 26, 2022 at 3:52:41 AM UTC-7, MK wrote:

.....
At this point, we have recycled back to opening position
Now let's look at Nasti's opening 53 again
Dice-D for 53: +0.085 - +0.109 = -0.024
Luck after roll: +0.019(0) -0.019(1)
## This time XG subracts average eqity from "opening roll"
.....

I am following up to my own article, in order to
make it clearer and conclusive. It's a little long
but easy to read and you will be well rewarded
at the end. :)

Initially I assumed that XG was calculating the
luck rate per the common, (including Gnubg's),
definition, i.e. adjusting actual equities of rolls
by average equities of positions because it did
so at the recycled starting position.

Discussing this in the Gnubg thread, I thought I
should verify it and also try to find out why my
manual tallying never matched XG's figures for
each individual roll.

Sure enough, XG's definition in the glossary of
its manual is different:

"Luck: Luck is determined as the equity after
"the roll (assuming the best move is played)
" - equity before the roll.

I also decided to recycle to the opening position
twice to check if luck equity and skill equity will
will zero out as they should.

So, here are the same sequence of 5 rolls twice,
omitting skill equity figures since those are okay.

Please feel free to duplicate this for yourself on
you own XG if that will convince you better.

======================================
Player1
Dice-D equity for 31: +0.237 (Dice-D = Dice Dictribution)

Luck after roll: +0.234(0) -0.234(0)
======================================
Player2
Dice-D equity for 44 : +0.442

Luck after roll: -0.187(0) +0.187(1)

## It added +0.421 not +0.442 (off by +0.021) ======================================
Player1
Dice-D equity for 32: -0.041

Luck after roll: -0.071(0) +0.071(1)

## It added +0.116 not -0.041 (off by +0.157) ======================================
Player2
Dice-D equity for 31: +0.030

Luck after roll: -0.051(0) +0.051(1)

## It added -0.020 not +0.030 (off by +0.050) ======================================
Player1
Dice-D equity for 43: +0.151

Luck after roll: +0.014(0) -0.014(1)

## It added +0.065 not +0.151 (off by +0.086)

## At this point, we recycled back to opening position

## If we tally luck manually after 5 rolls, we have:
## Player1 +0.237 +0.000 = +0.234
## Player2 -0.237 +0.442 = +0.205
## Player1 -0.205 -0.041 = -0.246
## Player2 +0.246 +0.030 = +0.276
## Player1 -0.276 +0.151 = -0.125 (XG is off by +0.139) ======================================
Now let's continue to reroll the same 5 rolls again,
with Player2 on roll at the current position.

Player2
Dice-D equity for 31: +0.234

Luck after roll: -0.108(0) +0.108(1)

## It added +0.122 not +0.234 (off by +0.112)

## Lo and behold! +0.122 is XG's average equity
## for the opening position and this time it did
## subract it from the equity of the 32 rolled. ======================================
Player1
Dice-D equity for 44 : +0.442

Luck after roll: +0.313(1) -0.313(1)

## It added +0.421 again not +0.442 (off by +0.021) ======================================
Player2
Dice-D equity for 32: -0.041

Luck after roll: +0.197(1) -0.197(1)

## It added again +0.116 not -0.041 (off by -0.157) ======================================
Player1
Dice-D equity for 31: +0.030

Luck after roll: +0.177(1) -0.177(1)

## It added again -0.020 not +0.030 (off by +0.050) ======================================
Player2
Dice-D equity for 43: +0.151

Luck after roll: +0.112(1) -0.112(1)

## It added again +0.065 not +0.151 (off by -0.086)

## Here, we recycled to opening position a second time.

## If we tally luck manually after 5 rolls, we have:
## Player2 +0.125 +0.237 = +0.362
## Player1 -0.362 +0.442 = +0.080
## Player2 -0.080 -0.041 = -0.121
## Player1 +0.121 +0.030 = +0.151
## Player2 -0.151 +0.151 = +0.000 Ta da!

## But XG is off by -0.112 which is the average that
## was subtracted from the 2nd opening roll above. ======================================
If we continue to reroll the same 5 rolls once more,
with now Player1 on roll, will it subtract again? Yup!

Player1
Dice-D equity for 31: +0.234

Luck after roll: +0.234(1) -0.234(1)

## It added again +0.122 not +0.234 (off by +0.112) ======================================

There you have it folks! Conclusive demonstration of
your worshipped XG being a "garbage generator"... :(

XG doesn't adjust equity of rolls by the average equity
of positions, including the rolls for the initial opening
positions, but some mysterious reason it does adjust
them for the subsequent "recycled" opening positions.

I could speculate on the reason for this one but I'll let
you guys take a first shot at it... ;)

Oh, also, XG doesn't just add the equity of the roll from
the Dice Distribution table at the same ply either but it
seems to be using some secret formula...(??)

MK

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On December 31, 2022 at 2:49:25 AM UTC-7, MK wrote:

XG doesn't adjust equity of rolls by the average equity
of positions, including the rolls for the initial opening
positions, but some mysterious reason it does adjust
them for the subsequent "recycled" opening positions.

I could speculate on the reason for this one but I'll let
you guys take a first shot at it... ;)

Come on, bozos..! Has someone duct taped
your mouths..? If it is what I think it is, a bug
like this could be the suspense in a film noir.
Why are you foregoing the fun of solving it? ;)

MK

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