when is greedy bearoff wrong?

[Don Woods]

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.?

-- Don.

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-- Don Woods (d...@clari.net) ClariNet provides on-line news.
-- http://www.clari.net/~don I provide personal opinions.
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[Stephen Turner]

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?

Yes, but they're rare and the difference in equity is typically small.
Occasionally it's slightly better to fill a hole than bear off. E.g. with
6 men on 1, 7 on 3, 1 on 2 and 1 on 4, roll 62, I suspect 4/2 3/off is better
than 4/off 2/off to prevent wastage on later 2s. I'm not entirely sure this
is a true example, but they're of this type. See Robertie's book Advanced
Backgammon for some genuine examples. In any case, there is only one such
position with fewer than 12 of your men left.

> 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.?
>

This is more common. Sometimes it's better not to bear off with a combination
roll, but smooth out your position instead. (E.g., if you've only got men on 5
and 6, not bear off a 5 with 23 but play something like 6/4 6/3).

--
Stephen Turner sr...@cam.ac.uk http://www.statslab.cam.ac.uk/~sret1/
Statistical Laboratory, 16 Mill Lane, Cambridge, CB2 1SB, England
"This store will remain open during modernisation. We apologise
for any inconvenience this may cause" Topshop, Cambridge

[John Greenwood]

d...@madrigal.clari.net (Don Woods) wrote:

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.?

One case on the last example is where you need to maximise your
chances of winning next roll because your oppo will win if you don't.
An example from Magriel's backgammon is a s follows.
You : Two men on 3 point, 0ne man on each of 4 and 5 points.
Oppo: Three men on 1 point.
Your roll of 2-1.

You must play 4/3, 5/3 (and not bearoff a man from the 3 point ) so
you can now also win with a 33 next roll.

[Kit Woolsey]

Don Woods (d...@madrigal.clari.net) 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.

Kit