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## [Bug-gnubg] Variance reduction efficiency

**From**: |
Philippe Michel |

**Subject**: |
[Bug-gnubg] Variance reduction efficiency |

**Date**: |
Thu, 24 Aug 2017 22:28:54 +0200 (CEST) |

**User-agent**: |
Alpine 2.21 (BSF 202 2017-01-01) |

On Thu, 24 Aug 2017, tchow wrote:

`O.K., so let me rephrase my suggestion: What happens if we use n-ply variance
``reduction for an n-ply rollout, at least for the first or second steps of a
``rollout trial?
`

`I don't have an answer to this specific question, but some (not
``statistically significant) data may give an idea.
`

`Rolling out some middle-game position at various plies gave (VR vs.
``no-VR) :
`
At 0-ply (VR at 0-ply) :
duration : x 21.3, SD : / 6.6, equivalent number of trials : x 44
At 1-ply (VR at 0-ply) :
duration : +45%, SD : / 6.4, equivalent number of trials : x 41
At 2-ply (VR at 1-ply) :
duration : +4.5%, SD : / 13.2, equivalent number of trials : x 174
At 3-ply (VR at 2-ply) :
duration : +3.7%, SD : / 17.4, equivalent number of trials : x 301

`So, a higher ply for variance reduction helps (although the returns are
``diminishing with higher plies). On the other hand, using the same ply as
``the rollout itself, while better than no VR, is extremely expensive.
`

`With your proposal used for the usual 2-ply rollouts the first few steps
``would be 20 times slower, the following ones unchanged. The total number
``of steps would depend of the position but the final cost may be in the
``x 1.5 to x 2 range, similar to the gain in accuracy when *all* steps use
``2-ply variance reduction.
`

**[Bug-gnubg] Variance reduction efficiency**,
*Philippe Michel* **<=**