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BGonline.org Forums
Opening position with player on roll owning cube
Posted By: Nack Ballard In Response To: Opening position with player on roll owning cube (Bob Koca)
Date: Thursday, 21 October 2010, at 1:11 a.m.
From Tim's link you gave:
I would go so far as to conjecture that for the vast, vast majority of positions that can be legally reached, there is a sequence of rolls that reaches it with optimal play.
If true, that would greatly surprise me. The positions we are used to seeing comprise a very small percentage of legally reachable positions, most of which are riddled with blots and highly disorganized.
I would modify the statement to read: "For the set of positions from games that are played by backgammon players who are trying to win, even accounting for the many blunders that are inevitably committed, the vast majority of the time (if not all the time) it is possible to create a well-played if not perfectly-played sequence to reach the given position."
...once you can retract a single move then it's typically possible to continue retracting back to a "normal-looking" position without too much difficulty.
In my experience it is often easy to retract (back up the sequence) one or more moves when a player is on the bar. Inevitably, though, you have to retract to where neither player is on the bar and there may be too many blots to retro-engineer a play that is best; or you might find the first mutual-no-bar play but not the second. If we're limiting ourselves to non-blotty positions, then I agree that entire sequences from the opening position should be constructable.
Nack
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