GNU Backgammon

Forum Archive : GNU Backgammon

How luck factor is calculated

From:   Gregg Cattanach
Date:   13 August 2002
Subject:   Re: Calculating luck factor...
Google:   zYc69.1318$

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.

Did you find the information in this article useful?          

Do you have any comments you'd like to add?     


GNU Backgammon

Analyzing GamesGrid matches  (Roy Passfield, Dec 2001) 
Batch analysis tool  (Øystein Johansen, June 2004)  [GammOnLine forum]
Cache size  (Ned Cross+, Mar 2004)  [GammOnLine forum]
Compiling for Windows  (Øystein Johansen, Jan 2002) 
Edit mode removing checker from bar  (Scott Steiner+, May 2003) 
Entering an annotated match  (Albert Silver, Dec 2003)  [GammOnLine forum]
Error rates: Gnu vs. Snowie  (Raccoon, Mar 2006)  [GammOnLine forum]
Even-ply/odd-ply effect  (Raccoon, Nov 2004) 
Even-ply/odd-ply effect  (Tom Keith+, Oct 2003) 
Even-ply/odd-ply effect  (Scott Steiner+, Dec 2002) 
Filter settings  (Robert-Jan Veldhuizen, Nov 2004)  [GammOnLine forum]
Gnu 0.13 versus Jellyfish and Snowie  (Torsten Schoop, Aug 2003) 
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)  [GammOnLine forum]
Importing .gam files  (PAR+, Mar 2005) 
Importing PartyGammon matches  (rew+, July 2006) 
Improving your game using GnuBG  (D.U.G.+, Nov 2002) 
Installing on Windows  (maareyes, Oct 2001) 
Interpreting JSD's  (Adrian Wright+, Feb 2005)  [GammOnLine forum]
JSD's and confidence intervals  (Daniel Murphy+, Jan 2005) 
Logging rollouts  (Øystein Johansen, Oct 2004)  [GammOnLine forum]
Luck rate  (Kees van den Doel+, May 2002) 
MWC versus Equity (EMG)  (Ken+, Apr 2005)  [GammOnLine forum]
Manually entering first roll  (Andreas Graf+, Apr 2005) 
Match equity tables  (Raccoon, July 2005)  [GammOnLine forum]
Personal reflections  (Louis Nardy Pillards, Sept 2002) 
Playing two computers against each other  (Stanley E. Richards+, Mar 2008)  [GammOnLine forum]
Python scripting  (Øystein Johansen+, Nov 2004) 
Quasi-random dice in rollouts  (Ian Shaw, Mar 2004)  [GammOnLine forum]
Question marks in game list  (Jim Segrave, July 2005) 
Questions and answers  (Jim Segrave+, Jan 2003) 
Questions and answers  (Jørn Thyssen, Aug 2002) 
Restarting a rollout with different settings  (Jim Segrave, Apr 2005)  [GammOnLine forum]
Restarting a rollout with different settings  (Robert-Jan Veldhuizen, Apr 2004)  [GammOnLine forum]
Rollout settings  (geoff arnold+, Apr 2007) 
Rollout settings  (Stick+, Nov 2005)  [GammOnLine forum]
Rollout settings  (Robert-Jan Veldhuizen, Mar 2004)  [GammOnLine forum]
Rollout settings  (Ian Dunstan, Aug 2003)  [GammOnLine forum]
Rollout settings for the impatient  (Robert-Jan Veldhuizen, June 2004)  [GammOnLine forum]
Running rollouts in background  (Bruce+, Apr 2004)  [GammOnLine forum]
Saving rollout results from command-line interface  (Jeremy Bagai+, Apr 2006)  [GammOnLine forum]
Saving rollouts  (Mislav Radica+, May 2006)  [GammOnLine forum]
Setting GnuBG's playing strength  (JP White, Sept 2001) 
Setting skill level  (Jim Segrave, Apr 2004) 
Setting up and saving a rollout  (Albert Silver, Dec 2003)  [GammOnLine forum]
What's GNU?  (Gary Wong, Oct 2001) 
Which player is player 0?  (Neil Kazaross+, Oct 2004)  [GammOnLine forum]

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