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42P-43: more data

Posted By: Nack Ballard
Date: Monday, 15 February 2010, at 11:51 p.m.

In Response To: 42P-43: more data (Chuck Bower)

Would you please elaborate, preferably with an example? I don't understand what "create significantly larger discrepancies between margins" means.

Sure. What I mean is this: Forget about cubeless for now. We (Stick, Paul and I) have a large number of rollouts, and for simplicity let's say that the rollouts in our "alpha" set use no live cube (the actual case with most of our less-than-recent Snowie rollouts) and the rollouts in the "beta" set use only live cube (the actual case with Gnu rollouts, which AFAIK don't have cube-adjusted equities as well, though we can also group what Snowie live cube results we do have in the beta set).

Sometimes two rollouts (in either the alpha or beta set) are of the identical position. This can happen by accident, or if we don't get an assignment back and so reassign but then both people end up completing the assignment, or someone else is interested in the same position and we find out later we rolled out the same position independently -- this happens a lot with early game positions.

In comparing rollouts of identical positions, alpha to alpha (no live cube is used), the margin of two plays will often be different, purely by the effects of variance. That is, play A might beat play B by .007 in one rollout but by .016 in the other rollout. The difference/discrepancy between the margins in this example is .009. Having observed (though admittedly not logged) a large number of these instances, we have a feel for the average size and distribution of these differences.

In similarly comparing rollouts of identical positions, beta to beta (where a live cube is used), we have a feel for the average size and distribution of those differences/discrepancies as well. I'd say that you'll see a .014 discrepancy in a beta comparison about as often as you'll see a .009 discrepancy in an alpha comparison.

The pair of rollout results that I posted earlier in this thread are alpha (no live cube). There happened to be a live cube used in one of the rollouts but the resulting equity was not addressed (because there was no live cube equity in the other rollout to which to compare it). The plays in one rollout have 5184 and 5184 and in the other have 10727 and 10368 trials.

The margin in one rollout is .021 and in the other it is -.003. The difference/discrepancy in margins for this 5k/5k 10k/10k rollout pair is .024.

From my observations, I would guess that a .024 alpha discrepancy (though very unlikely) occurs about as often as .037 beta discrepancy. Or, at least the 1.5+ multiple I'm representing is about right at more commonly arising levels.

My main point (earlier post) was that it is improper to use beta (live cube) confidence intervals to assess the likelihood/unlikelihood of alpha discrepancies. By contrast, Daniel's analysis of the cubeless confidence intervals appears to be correct, and you can see that it suggests the higher degree of unlikelihood I would project onto this pair of alpha results (I say "project" because Snowie doesn't actually report cube-adjusted confidence intervals.)

Below is a pair of beta (live cube) results, one with 5k 5k trials and the other with 10k 10k, that has a .038 discrepancy. Please ignore the 24/23 8/7(2) 6/5 play (ranked second in one rollout and third in the other) and compare only the relevant two plays of each rollout. Have fun, and I encourage you or Daniel to do the math on it if you like. :)

Nack

161


2O ' ' '1X4X '4X ' ' '4O

2X ' ' '1O4O '3O ' '1O4X

user164

Position ID: 0PPgATDQc+QBMA Match ID: cIkEAAAAAAAA

# Ply Move Equity
1 R 11/10 8/7(2) 6/5 +0.3524
58.02 18.47 1.13- 41.98 12.58 0.63 +0.2243 +0.3524
0.11 0.12 0.08- 0.11 0.08 0.02 0.0031 0.0103
Full cubeful rollout with var.redn.
5184 games, Mersenne Twister dice gen. with seed 835201847 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 12 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
• 2 R 24/23 8/7(2) 6/5 +0.3266 ( -0.0258)
57.61 17.74 1.18- 42.39 12.89 0.59 +0.2066 +0.3266
0.10 0.12 0.08- 0.10 0.08 0.02 0.0033 0.0080
Full cubeful rollout with var.redn.
5184 games, Mersenne Twister dice gen. with seed 835201847 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 12 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
3 R 8/7(2) 6/5(2) +0.2846 ( -0.0678)
57.14 17.31 1.02- 42.86 12.78 0.65 +0.1916 +0.2846
0.09 0.10 0.04- 0.09 0.08 0.03 0.0025 0.0067
Full cubeful rollout with var.redn.
5184 games, Mersenne Twister dice gen. with seed 835201847 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 12 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

gnubg161


2O ' ' '1X4X '4X ' ' '4O

2X ' ' '1O4O '3O ' '1O4X

user164

Position ID: 0PPgATDQc+QBMA Match ID: cIkEAAAAAAAA

# Ply Move Equity
• 1 R 11/10 8/7(2) 6/5 +0.3351
57.83 18.41 1.11- 42.17 12.44 0.67 +0.2206 +0.3351
0.07 0.08 0.04- 0.07 0.06 0.02 0.0019 0.0052
Full cubeful rollout with var.redn.
10368 games, Mersenne Twister dice gen. with seed 809895948 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 12 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
2 R 8/7(2) 6/5(2) +0.3054 ( -0.0298)
57.30 17.75 1.08- 42.70 12.71 0.69 +0.2003 +0.3054
0.07 0.08 0.04- 0.07 0.06 0.02 0.0019 0.0050
Full cubeful rollout with var.redn.
10368 games, Mersenne Twister dice gen. with seed 809895948 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 12 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]
3 R 24/23 8/7(2) 6/5 +0.2990 ( -0.0361)
57.27 17.71 1.02- 42.73 12.89 0.63 +0.1974 +0.2990
0.10 0.11 0.05- 0.10 0.08 0.02 0.0028 0.0072
Full cubeful rollout with var.redn.
5184 games, Mersenne Twister dice gen. with seed 809895948 and quasi-random dice
Play: 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 12 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

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