GNU Backgammon

 Luck rate

 From: Kees van den Doel Address: kvandoel@xs4all.nl Date: 20 May 2002 Subject: gnubg "luck rate" Forum: rec.games.backgammon Google: 3ce87d1f\$0\$3876\$e4fe514c@dreader4.news.xs4all.nl

```What's the definition of the gnubg "luck rate"?

Whatever it is, it does not seem to reflect the intuitive notion of "the
part of the matchscore due to luck".

The winner of the match is always the "luckiest". I tested it by playing
some  matches against gnubg 0  ply  noise level  1.0. Of  course I win a
gammon every  game (it still knows to  avoid bg's at  this level) but in
the analysis my "luck" is always bigger than gnu's.

A   better definition  of   "luck" would show that   in  such matches as
described above the  "luck" evens out  (the result being almost entirely
due to "skill").

Anyways,  if someone  would be  kind enough  to  define  "luck" in gnubg
analysis, one can try to improve on this definition. Something that
captures the intuitive notion of "skill" versus "luck".

Kees
```

 Adam Stocks  writes: ```The calculation of the luck rate is similar in principle to the calculation of the error rate - that is, it is the difference in equity between two 'moves'. The error rate is the average amount of equity loss between the 'best move' and the actual move played. To calculate the luck rate, the bot looks at the position before the dice are rolled, and works out the average equity of the various positions resulting from each of the possible dice rolls. Then after the roll, the equity of the 'best move' will be either above or below that average. Doug Zare explains this in more detail in his article 'A Measure of Luck' : http://www.bkgm.com/articles/Zare/AMeasureOfLuck.html where he defines the luck rate: 'The mathematical measure of luck gained on a roll of the dice is your equity after the roll minus your equity before the roll, i.e., luck is the equity you gain through the roll of the dice. It is the equity of your best possible play minus your equity before the roll, or your equity after your opponent's best play minus your equity before the roll.' Snowie for instance tells you (on it's default settings) that you rolled a 'joker' when this equity difference is greater than 0.5 (i.e. you effectively won half a game on one roll - you had a luck rate of +0.5 for that roll. Of course, your opponent would have lost 0.5 equity, so your good luck is, de facto, the same as your opponent's bad luck, and vice versa. > Whatever it is, it does not seem to reflect the intuitive notion of "the > part of the matchscore due to luck". > > The winner of the match is always the "luckiest". I tested it by playing > some matches against gnubg 0 ply noise level 1.0. Of course I win a > gammon every game (it still knows to avoid bg's at this level) but in > the analysis my "luck" is always bigger than gnu's. For players of equal skill, the winner of each game needs a total luck of +0.5 (EMG equity), because they both started off with an equal chance of 50% (0.00 EMG equity), but the winner ends up with 100% (+1.00 EMG equity). In a match of more than 1 point, the luck rates (and error rates) is usually measured in Normalised EMG (Equivalent to Money Game) units, so the actual figures you see will usually be much greater than +0.5 for each player. However, it is not necessarily true that the winner of a game or match is always the 'luckiest'. That is normally true when the players are faily close in ability, but if the world class gnu (2(3)-ply, no noise) plays a novice, the novice will still be the underdog even if he is significantly luckier than gnu during the game/match. > A better definition of "luck" would show that in such matches as > described above the "luck" evens out (the result being almost entirely > due to "skill"). You would need to play a large sample of matches to be statistically sure that you weren't simply experiencing a run of good luck over a short series of matches. Adam ```

### GNU Backgammon

Analyzing GamesGrid matches  (Roy Passfield, Dec 2001)
Batch analysis tool  (Øystein Johansen, June 2004)
Cache size  (Ned Cross+, Mar 2004)
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)
Error rates: Gnu vs. Snowie  (Raccoon, Mar 2006)
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)
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)
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)
JSD's and confidence intervals  (Daniel Murphy+, Jan 2005)
Logging rollouts  (Øystein Johansen, Oct 2004)
Luck rate  (Kees van den Doel+, May 2002)
MWC versus Equity (EMG)  (Ken+, Apr 2005)
Manually entering first roll  (Andreas Graf+, Apr 2005)
Match equity tables  (Raccoon, July 2005)
Personal reflections  (Louis Nardy Pillards, Sept 2002)
Playing two computers against each other  (Stanley E. Richards+, Mar 2008)
Python scripting  (Øystein Johansen+, Nov 2004)
Quasi-random dice in rollouts  (Ian Shaw, Mar 2004)
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)
Restarting a rollout with different settings  (Robert-Jan Veldhuizen, Apr 2004)
Rollout settings  (geoff arnold+, Apr 2007)
Rollout settings  (Stick+, Nov 2005)
Rollout settings  (Robert-Jan Veldhuizen, Mar 2004)
Rollout settings  (Ian Dunstan, Aug 2003)
Rollout settings for the impatient  (Robert-Jan Veldhuizen, June 2004)
Running rollouts in background  (Bruce+, Apr 2004)
Saving rollout results from command-line interface  (Jeremy Bagai+, Apr 2006)
Saving rollouts  (Mislav Radica+, May 2006)
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)
What's GNU?  (Gary Wong, Oct 2001)
Which player is player 0?  (Neil Kazaross+, Oct 2004)