Forum Archive : Puzzles

Not-so-greedy bearoff

From:   Kit Woolsey
Address:   kwoolsey@netcom.com
Date:   26 March 1997
Subject:   Re: when is greedy bearoff wrong?
Forum:   rec.games.backgammon
Google:   kwoolseyE7o3JC.MzJ@netcom.com

Don Woods wrote:
> I know that if there's still contact, I need to be careful about how
> I bear off to reduce the chance of leaving blots, etc.  But once
> contact is broken, is it ever wrong to bear off the most men possible
> on every roll?  E.g., are there cases where I could bear off 4 men on
> a doublet or 2 men on a non-doublet, but shouldn't?  Failing that, are
> there times when I do better to bear off fewer men than I could, e.g.
> bearing off 2 instead of 3 on a doublet or zero instead of 1, etc.?

Yes, there are rare situations where toggle greedy will not lead you to
the best play.  The best known one (from Magriel's book) is:
5 on ace, 1 on two, 5 on three, 2 on four -- 6-2 to play.  Here 4/2 4/off
is superior to 4/off, 2/off.  The reason is that if you roll a non-two
next turn and then roll a two the following two turns you will miss twice
if you had taken two men off, costing you a roll.

There are others.  The three point provides a similar sort of situation.
Consider:  3 on ace, 3 on two, 1 on three, 4 on four, 2 on six.  6-3 to
play.  6/3, 6/off is superior to 6/off, 3/off because of the danger of
rolling subsequent threes.

Even with a four there are possibilities.  For example, consider:
5 on ace, 4 on three, 1 on four, 2 on five, 1 on six.  6-4 to play.  6/2,
5/off is superior to 6/off, 4/off due the the great value of filling in
the gaps -- taking two men off leaves you missing on twos and fours for
quite a while.

I'm sure there are plenty of other examples.  Perhaps someone with a
bearoff database and the programming tools to get inside it could rattle
off a list of such positions if it isn't too large.

In practice, I always toggle greedy when there is no contact anyway.  The
chance of running across one of these positions combined with the cost of
making the wrong play is small indeed, so it is worth taking this
risk in order to save time.

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