Small Cube Error Reported by XGR++. Why?
Posted By: Matt Cohn-Geier In Response To: Small Cube Error Reported by XGR++. Why? (Neil Robins)
Date: Wednesday, 12 February 2014, at 7:08 p.m.
In Response To: Small Cube Error Reported by XGR++. Why? (Neil Robins)
There are some things you can do to "artificially" lower your PR, like not doubling at odd-away post-Crawford. This is one sense in which PR doesn't accurately reflect skill. In fact, sometimes the methods to artificially lower your PR will involve not making the best plays and sacrificing some MWC%. Something about that feels pretty wrong.
However, there are problems with Snowie-style ER too. Suppose you make only one move and blunder and then get closed out and never move again. Your ER will be very low, despite making a blunder on your only decision. On XG-style PR it will be very high. There are both advantages and disadvantages to that.
Notably in the Saba-Petko match, the PR was very close (within 0.07). Had Saba or Petko rolled different numbers in the bearoff in the last game, it could easily have been a different outcome. This kind of 50-50 match where it all comes down to dice at the end is something the Dual-Duel PR bracket is probably attempting to avoid. Although Petko could also have won by making fewer errors earlier in the match.
Ultimately there will be problems with any method you use to tell you who played better in any given match. PR isn't very good at determining who played better in one match. It is pretty good as a long-run average across many matches, but with a sample size of 1 it has a lot of problems.
One idea is to have something like duplicate backgammon where each player has to make his or her play in a given position. Magriel does something similar where each player gives his or her play for the first 20 rolls of a game (10 for each side) and then the total equity loss is compared. This makes it similar to a quiz but without the additional quiz factor.
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