GNU Backgammon

 How luck factor is calculated

 From: Gregg Cattanach Address: gcattanach@prodigy.net Date: 13 August 2002 Subject: Re: Calculating luck factor... Forum: rec.games.backgammon Google: zYc69.1318\$g_.16469204@newssvr15.news.prodigy.com

```Here is how Snowie calculates the luck factor, (and I'm pretty sure GnuBG
does it the same way):

It takes the equity of the 36 positions reached from the current position,
(based on moving each of the 36 rolls "correctly"), and averages those 36
numbers.  It then takes the equity reached from the roll actually rolled,
and the amount this is above or below the average is how lucky or unlucky
that roll was.  It does this for every roll of the game for both players
(all of this is done at 1-ply).  Also, it doesn't matter how the player
actually moved the checkers, this calculation is done based on its estimate
of what the best play is for all 36 rolls and the one actually rolled.

Snowie adds up all the pluses and minuses for both players and then has a
total luck factor for each game and the entire match.  GnuBG goes a little
bit further and keeps it separated with all of the luck factors for my
rolls being added up and a second number for all of the opponent's rolls.

The predictive value of this number in a match is pretty interesting, as
the correlation of who had the positive luck factor and who won the match
is dramatically better than the correlation of who had less errors vs. who
won. This isn't a defect in the error calculation, more it just
demonstrates that it is far better to be lucky than good.  Also, when two
players are very evenly matched their respective error rates may only
differ by 1.0 to 2.0 mppm (millipoints per move),  But luck factors are
routinely in the range of 5.0 to 10.0 or more mppm in many matches.  So
luck swamps skill a good deal of the time.

Also, the luck factor may not predict the result of the match as it isn't
taking the cube level into play, but looking at each game as equivalent to
a money game.  So being lucky in one game with the cube on 8, but your
opponent being lucky in 4 other games that ended in a double/pass, you may
show a negative total luck factor but won the match with the 8 cube.

Gregg
```

### GNU Backgammon

Analyzing GamesGrid matches  (Roy Passfield, Dec 2001)
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Gnu 0.13 vs. Snowie 4  (Albert Silver, June 2003)
Gnu 0.14 vs. Jellyfish  (Michael Howard+, July 2003)
Gnu versus Snowie and Jellyfish  (Michael Depreli, Oct 2005)
How luck factor is calculated  (Gregg Cattanach, Aug 2002)
How rollouts work  (Gary Wong, July 1999)
How to enter an illegal move  (Øystein Johansen, Aug 2003)
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