Forum Archive : GNU Backgammon

Even-ply/odd-ply effect From:   Tom Keith Address:   tom@bkgm.com Date:   17 October 2003 Subject:   GnuBG: Fractional-ply evaluators Forum:   rec.games.backgammon Google:   b650e130.0310171628.2bc5fafe@posting.google.com Let me describe an experiment I did comparing zero-ply and one-ply evaluations in GnuBG. When GnuBG evaluates a position, you can tell it how far ahead you want it to look. A zero-ply evaluation does no lookahead -- you just get the output of the program's neural net. A one-ply evaluation looks ahead one roll: it looks at all 21 possible rolls, makes what it believes the best play for each, and takes a weighted average of the resulting positions. Each additional ply of lookahead takes about 21 times as long as the previous level. When you do rollouts in GnuBG, one of the parameters you can set is what level of evaluation to use for checker plays. Presumably one-ply evaluation plays better than zero-ply, and two-ply plays better than one-ply, etc. However, there has been some discussion over the years about whether odd-ply evaluations are as reliable as even-ply. (See http://www.bkgm.com/rgb/rgb.cgi?view+1061). I thought I'd try an experiment comparing zero-ply and one-ply evaluations. Here's what I did: 1. I collected a large number backgammon games between good players, some human-vs-human, some human-vs-computer. From these I took a representative sample of positions. (However duplicate positions were deleted so early game positions are under-represented.) 2. I rolled out each position to the end of the game thirty-six times using cubelss zero-ply evaluation. Variance reduction was applied. 3. I took the root-mean-square average of the differences between GnuBG's zero-ply evaluation and the rollout results, and between GnuBG's one-play evaluation and the rollout results. I looked only at game-winning chances; I didn't look at gammons or backgammons. These are the results: Zero-ply evaluation: Average error = 0.0300 One-ply evaluation: Average error = 0.0284 So one-ply evaluation does do better on average. This is to be expected; being able to look ahead one ply should be a help, especially in volatile positions. In certain games GnuBG's evaluation seems to oscillate back and forth according to which side's turn it is to play. When this happens, a one-ply evaluation (which essentially looks at the game from the other player's side) can give quite different numbers than a zero-ply evaluation. You might expect when zero-ply and one-ply evaluations differ by a lot that the true value of the position is probably somewhere in between. I thought it would be interesting to see what would happen if you had an evaluator that used the average of zero-ply and one-ply. I called this a "0.5-ply evaluation." 0.5-ply evaluation: Average error = 0.0245 So 0.5-ply does do better! In fact, it does enough better to make you wonder if it does even better than two-ply. (I didn't look into this.) Can we do even better? Something I noticed is that you can often predict whether zero-ply or one-ply is better for a particular position by looking at the relative pipcount. (The relative pipcount is your own pipcount minus your opponent's pipcount.) When the relative pipcount is between -160 and -40, one-ply usually does better; when the relative pipcount is between 40 and 150, zero-ply usually does better. Let's call an evaluator based on this idea a "hybrid evaluator." How well does the hybrid evaluator perform? Hybrid evaluator: Average error = 0.0225 It should be noted that these tests show how well GnuBG performs at computing the ABSOLUTE equity of a position. They may or may not indicate an improvement in GnuBG's ability to *play* a position, since playing depends on having accurate RELATIVE equities. Nevertheless, I'm guessing that the 0.5-ply and hybrid evaluators play better than the integer-ply evaluators too. Tom Tom Keith  writes: To follow up on my own post ... It has been pointed out by some (most notably Robert-Jan Veldhuizen), that GnuBG seems to handle cube decisions better at zero-ply than at one-ply. To test this, I selected positions from actual games in which the player-on-roll's game-winning chances + gammons/2 was between 70% and 80%. In other words, I was trying to select positions in which a player might be thinking about doubling, or his opponent might have to think about whether to take or drop. Comparing 0-ply evaluations with untruncated rollouts gave a standard error of 0.0235. Comparing 1-ply evaluations with untruncated rollouts gave a standard error of 0.0288. So 0-ply does do significantly better in cube-likely positions. This despite the fact that 1-ply does better at estimating absolute equity in general. Comparing the hybrid evaluator described in my previous post with the untruncated rollouts gave a standard error of 0.0207. So the hybrid evaluator still does better than zero-ply, even on positions that zero-ply seems to be particularly good at. Tom Keith Backgammon Galore! http://www.bkgm.com   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) 

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) 

From GammOnLine         Long message         Recommended reading         Recent addition

 

Book Suggestions Books Cheating Chouettes Computer Dice Cube Handling Cube Handling in Races Equipment Etiquette Extreme Gammon Fun and frustration GNU Backgammon History Jellyfish Learning Luck versus Skill Magazines & E-zines Match Archives Match Equities Match Play Match Play at 2-away/2-away Miscellaneous Opening Rolls Pip Counting Play Sites Probability and Statistics Programming Propositions Puzzles Ratings Rollouts Rules Rulings Snowie Software Source Code Strategy--Backgames Strategy--Bearing Off Strategy--Checker play Terminology Theory Tournaments Uncategorized Variations