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A Fifth Play is Possibly Best at Another Score

Posted By: Nack Ballard
Date: Saturday, 16 June 2012, at 5:00 p.m.

In Response To: A Fifth Play is Possibly Best at Another Score (Paul Weaver)

I certainly admit that this is only of theoretical and not practical interest. How could White own a 4-cube so early in the game? Very unlikely, but I suppose Nack could find a sequence of rolls and plays that would lead to this position with White owning a 4-cube...

For money, it is possible to repeat the opening position in just 5 rolls allowing bad play (minimum total checker errors of .170, plus cube-turning blunders to get the cube on 4). I'll assume that you require perfect play on both sides, in which case a reopening position with cube on 4 can be achieved in as few as 21 rolls. Reaching your diagrammed (near-starting) position should require approximately the same number of rolls (perhaps a couple fewer); however, there are two issues to address:

The first issue is that it is no longer a second roll position -- it can't be called 63S-32. I believe we will eventually find many positions, possibly as early as the third roll, or possibly even 63S-32 itself at a yet undiscovered score, that classify as T4+1 (i.e., a different best play at each of the four main scores plus a different best play at some fifth score and/or cube position). Finding the first T4+1 would admittedly be an accomplishment (and I don't want to discourage someone from rolling out your position 4-ply), but it would be more of an accomplishment to discover a T4+1 that can be reached in fewer rolls and/or with the fifth score being less of an outlier.

The second issue is that for the 𣈂 leader to properly offer an initial double I imagine the position must be considerably developed and it may not be possible to subsequently "unwind" (break/unmake all the points) within the constraints of perfect play. (It's even harder than it sounds.) One probably either needs a less unusual score and/or cube position, or be willing to lower the standard and accept that the position was merely reached legally rather than by good or perfect play.

Nack

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