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Opening 54 at 4 away 4 away - a variance trip

Posted By: Stick
Date: Wednesday, 26 January 2011, at 12:49 a.m.

I hadn't planned on extending this rollout as ridiculously long as I did but once I started I couldn't stop. The final rollout is posted below. What happened was after the first 5184 trials bringing two down from the midpoint, 13/9 13/8, nactated as D, was ahead by .022 over the splitting play, 24/20 13/18, or S.

This is when I decided to record the results every 5k. In my mind there was no way this was going to be close to the absolute equities or the difference in plays if I extended the rollout enough to clear out most of the variance. I have listed the nacbrac'ed results below after every 5k trials including the amount of variance the bot reported at the time and the confidence it reported.

  • [D S22] 5k (+/- 15/16) [98%]
  • [D S17] 10k (+/- 11) [99]
  • [D S9] 15k (+/- 9) [91%]
  • [D S12] 20k (+/- 8) [98.5%]
  • [D S8] 25k (+/- 7) [95%]
  • [D S9] 31k (+/- 6) [98%]
  • [D S7] 36k (+/- 6) [95%]
  • [D S6] 41k (+/- 5) [94%]
  • [D S5] 46k (+/- 5) [94%]
  • [D S6] 51k (+/- 5) [95.5%]
  • [D S5] 57k (+/- 5) [95%]
  • [D S6] 62k (+/- 4) [95.5%]
  • [D S5] 67k (+/- 4) [95%]
  • [D S5] 72k (+/- 4) [96%]
  • [D S6] 78k (+/- 4) [96%]
  • [D S5] 83k (+/- 4) [98%]
  • [D S6] 88k (+/- 4) [98%]
  • [D S6] 93k (+/- 4) [98%]

As you can see there are some big swings early on. I don't mean this to imply anything reported by XG was outside the acceptable realm of variance. I'm presenting it so people get a better understanding for what the numbers mean, how they can change, and how few 5k trials sometimes is. It is common even here at BGO to post rollout results with lots of variance left in them and draw far reaching conclusions.

The first 5k was [D S22] and the third 5k block would have had to have been [S D12]. If we would have accepted either 5k block as 'enough' we'd have quite a different picture of the position. This is also a good example to show just how hard it is to grind out all the variance in a position.

is Player 2

score: 1
pip: 167
5 point match
pip: 167
score: 1

is Player 1
XGID=-b----E-C---eE---c-e----B-:0:0:1:54:1:1:0:5:10
to play 54

1.Rollout113/9 13/8eq: +0.025
Player:
Opponent:		 50.27% (G:15.26% B:1.90%)
49.73% (G:13.92% B:1.53%)		Conf: ± 0.004 (+0.021...+0.029)
Duration: 21 hours 30 minutes
2.Rollout124/20 13/8eq: +0.019 (-0.006)
Player:
Opponent:		 50.69% (G:13.99% B:1.72%)
49.31% (G:13.56% B:1.32%)		Conf: ± 0.004 (+0.015...+0.023)
Duration: 22 hours 49 minutes
1 93312 Games rolled with Variance Reduction.
Dice Seed: 21140344
Moves and cube decisions: 3 ply

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