I've rolled at the opening position again, at money play. 27000 trials at 0-ply and 1-ply. 135000 trials at 2-ply. There's almost no difference in value between the rollout that took 8 minutes and the one that tool 23 hours, which speaks to the strength of the initial evaluation.
The rollout suggests that the value of cube ownership in the initial position is worth about 0.36 points. One thing to notice is that the rollout has the on-roll player winning about 1% less than the evaluations posted by MK. I think this is due to the evaluation assuming that initial doubles may be played, whereas I set the rollout to play as the initial position. Ply Cube Pwin Pwin2 Pwin3 Plose Plose2 Plose3 Ecl End Edt Action 0 1Cen 0.5135 0.1425 0.0065 0.4865 0.1310 0.0055 +0.0395 +0.0599 8 m 2Opp 0.5141 0.1428 0.0064 0.4859 0.1317 0.0056 +0.0804 -0.2941 NB (27.4%) 1 1Cen 0.5136 0.1472 0.0071 0.4864 0.1352 0.0059 +0.0405 +0.0594 38 m 2Opp 0.5136 0.1495 0.0074 0.4864 0.1350 0.0060 +0.0867 -0.2977 NB (27.5%) 2 1Cen 0.5130 0.1461 0.0069 0.4870 0.1336 0.0058 +0.0395 +0.0580 23 h 2Opp 0.5147 0.1468 0.0068 0.4853 0.1332 0.0059 +0.0881 -0.3002 NB (27.6%) I haven't found a way toa ask gnubg for an evaluation for the initial roll. Is there one? You could get a 1-ply evaluation by combining all 15 0-ply evaluations of the first roll, and so forth. Cheers, Ian From: bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org <bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org> On Behalf Of Ian Shaw via Bug reports for and general discussion about GNU Backgammon. Sent: Thursday, February 8, 2024 11:39 AM To: playbg-...@yahoo.com; bug-gnubg@gnu.org Cc: Philippe Michel <philippe.mich...@free.fr> Subject: RE: Interesting question/experiment about value of cube ownership It just so happens that I rolled out the opening position a few days ago for another reason. This was at 7-away 7-away rather than $ play, because I was interested in match play. I doubt that makes a huge difference. This was using gnubg-1_08_dev-20240103-setup.exe not the newest gnubg-1_08_001-20240204-setup.exe that Philippe released recently. Philippe, am I correct in thinking that the cube handling on these two versions is the same? Your announcement emails both include the same comment. "Improvement to cube decisions at 0- and 1-ply and weaker levels. Cube error rates are approximately halved and the repartition of errors (premature doubles vs. missed doubles vs. take or pass errors) is now similar to higher plies instead of being mostly premature doubles." The rollout results indicate about 1% fewer wins for the roller than the evaluations. 4HPwATDgc/ABMA:cAngAAAAAAAE Cube analysis Rollout cubeless equity +0.0408 (Money: +0.0396) Cubeful equities: 1. No double +0.0655 2. Double, pass +1.0000 (+0.9345) 3. Double, take -0.2999 (-0.3654) Proper cube action: No double, take (28.1%) Rollout details: Centered 1-cube: 0.5129 0.1480 0.0083 - 0.4871 0.1351 0.0073 CL +0.0408 CF +0.0655 [0.0001 0.0002 0.0001 - 0.0001 0.0001 0.0001 CL 0.0003 CF 0.0008] gnubg owns 2-cube: 0.5156 0.1522 0.0091 - 0.4844 0.1375 0.0150 CL +0.1216 CF -0.2999 [0.0001 0.0002 0.0001 - 0.0001 0.0002 0.0002 CL 0.0007 CF 0.0012] Full cubeful rollout with variance reduction 186624 games, rollout as initial position, Mersenne Twister dice generator with seed 823069761 Play: world class 2-ply cubeful prune [world class] keep the first 0 0-ply moves and up to 8 more moves within equity 0.16 Skip pruning for 1-ply moves. Cube: 2-ply cubeful prune [world class] Cheers, Ian -----Original Message----- From: bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org<mailto:bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org> <bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org<mailto:bug-gnubg-bounces+ian.shaw=riverauto.co...@gnu.org>> On Behalf Of MK Sent: Thursday, February 8, 2024 2:23 AM To: bug-gnubg@gnu.org<mailto:bug-gnubg@gnu.org> Subject: Interesting question/experiment about value of cube ownership I'm chugging along with my mutant cube skill experiments as I can spare time, saving all games, which I will share on my web site, when I'm done, along with my scripts. While doing the double at > 50% experiment, I remembered an old question I had asked in RGB about a year ago: What if the winner of the opening roll is allowed pre-double? See thread: https://groups.google.com/g/rec.games.backgammon/c/BVEnaqGM6dg/m/2c685q4DAAAJ When you evaluate the opening position in GnuBG, this is what you get: ========================================================= Position ID: 4HPwATDgc/ABMA Match ID: cAkAAAAAAAAA Evaluator: Contact Win W(g) W(bg) L(g) L(bg) Equity Cubeful static: 52.1 15.4 0.8 13.0 0.8 +0.067 +0.084 1 ply: 52.7 14.8 0.9 12.9 0.5 +0.076 +0.098 2 ply: 52.5 14.9 0.7 12.5 0.5 +0.076 +0.099 Cube analysis 2-ply cubeless equity +0.076 52.5 14.9 0.7 - 47.5 12.5 0.5 Cubeful equities: 1. No double +0.099 2. Double, pass +1.000 (+0.901) 3. Double, take -0.171 (-0.270) Proper cube action: No double, take (23.0%) ========================================================= I have created a Python script to intervene if the human player wins the opening roll, to set the cube at 2 owned by the bot, and then to execute "end game" command, for the bot to play for both sides at the same checker and cube skill settings. So, you know the equity gained by winning the opening roll and the equity lost by making the cube error at the same time, before the first move. Can anyone tell me what I will be expecting to see after, let's say, 10,000 games, in terms of which side will win/lose by what percentage? BTW: I already know. ;) I'm asking to see how confident are you in GnuBG's equity and/or error calculations and how competent are you to make mathematical predictions? MK
