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VR is not perfect on a single game

Posted By: eXtreme Gammon
Date: Monday, 19 July 2010, at 1:11 p.m.

In Response To: Monte Carlo Last 8 (Bob Koca)

Variance reduction works on multiple game because the sum of the luck is 0 over the 36 possible dice.

Applying to a single game can (and will) biais the result.

for instance imagine a position where one roll lead to a equity (according to the bot ply level used for VR) of 0.035, while all other roll lead to an equity of -0.001. However RO show that the 0.035 is actualy 0.215! So the initial equity is not 0.000 but 0.005.

When used in RO the error will cancel itself after 36 games as you get luck added for +0.035 if you roll the one double and -0.001 for all the others (rather than +0.210 and -0.006 if the luck eval was using RO). Note that more accurate luck calculation make the RO converge faster.

In a single game it will introduce a biais of -0.005 most of the time or +0.175 if you happen to roll that one double.

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