From: martys@juliet.ll.mit.edu ( Marty Storer )
Newsgroups: rec.games.backgammon
Subject: Re: 42 problem
Date: 6 Apr 92 13:32:17 GMT
	<HUNTER.92Apr2185041@work.nlm.nih.gov>
	<MARTYS.92Apr3110510@escalus.juliet.ll.mit.edu>
	<HUNTER.92Apr3164137@work.nlm.nih.gov>
Organization: M.I.T. Lincoln Lab - Group 43

In article <HUNTER.92Apr3164137@work.nlm.nih.gov> hunter@work.nlm.nih.gov (Larry Hunter) writes:

	     24  23  22  21  20 19        18  17  16  15  14  13  
	   + --  --  --  --  --  -- +++++ --  --  --  --  --  -- +
	   |             O   X   O  |   |     O           O   X  |
	   |             O   X   O  |   |     O               X  |
	   |             O       O  |   |                     X  |
	   |                     O  |   |                        |
	   |                        |   |                        |
	   |                        |   |                        |  +---+
	   |                        |   |                        |  | $ |
	   |                        |   |                        |  +---+
	   |                        |   |                        |
	   |                     X  |   |     X                  |
	   |                     X  |   |     X               O  |
	   |             X   O   X  |   |     X               O  |
	   |             X   O   X  |   |     X               O  |
	   + --  --  --  --  --  -- +++++ --  --  --  --  --  -- +
	      1   2   3   4   5   6        7   8   9  10  11  12

				X to play 42

>   I say:
>
>	 20/14*?  Eight of O's rolls hit 12/14*, but then the positions
>	 are again even and there are eight rolls that rehit her. Double
>	 1s and double 3s are moderately bad news for X, but not
>	 catastrophic.  Better than 2 out of 3 to come out a full roll
>	 ahead in a game headed for a race.
>
>   Marty replies
>
>	X has to worry about being hit loose on the 20 point, too, and
>	getting in trouble subsequently because he abandoned his anchor.
>	So the game may not be headed for a race.
>
>   I thought about that.  There are 7 rolls that hit the 20 and leave a
>   blot, but does this really benefit O?  She has a 15/36 chance of
>   having that blot hit; 2 of the 7 shots at the 20 leave another blot on
>   the 17, leaving X some major good rolls to hope for.  I suppose in the
>   worst of all possible worlds, X fans and O covers the 20.  Even in
>   this case, X is only margninally behind in pips and O has only a 3
>   point prime with moderate-at-best building chances in the next couple
>   of rolls.  It wouldn't be pretty, but it's not gammon-city, either.
>
>   Shuman Lloyd Lee says:
>
>      ... running off the 20 and hitting is not what we want to do.
>      Tactically, one could go about computing return shots and what-not,
>      but that isn't the point.  Running off the 20 destroys your
>      game-plan.
>
>      13/11 and 8/4 (or another similar move) is played with the
>      objective of making an outside point or two, as well an another
>      inner board point or two.  Then X can go about deciding the right
>      time to break off the 20., depending on how O's position develops
>      as well.
>
>   Hmm.  I don't like that at all.  If I were determined to keep the
>   anchor, and didn't mind leaving a blot in my outfield, I would play
>   13/7.  13/11 has a 16/36 chance of getting hit, and no real
>   advantages.  At least with 13/7 X has five fewer ways of getting hit,
>   and a better than 38% chance of making his bar point on the next roll
>   (25/36*20/36).  In email, Marty argued that leaving an outfield blot
>   is not a good idea at all, but he can explain himself.


  This position is Position 5 from Magriel's "Golden Point" chapter.
  Magriel says

	In Position 5...you should not hit and relinquish the golden
	point since O's control of _your_ five point and your weak
	inner board pose no strong threat to him...

	Instead of hitting simply play 8/2.
	                                    (Magriel, _Backgammon_, p. 252)

  That's it for his analysis!

  But Larry has it right.  By hitting, X gains ground in the race and
  threatens to link his back men with a 6.  O hits back somewhere with
  half her rolls, but the danger posed by O's returns isn't so bad
  because X then has good chances to hit or relink on the 20.  The only
  thing X is really afraid of is the immediate 33 or 11, plus small
  parlays like hit-fan.

  The point is that X's lead in the race does pose a threat to O.  The
  game is nowhere near over even if O misses and X makes the 14, but then
  X has a clear edge.  In any case, the static advantage of a racing lead
  is worth something here, and since the risk of taking it isn't bad
  (X doesn't look worse than even on average in variations where O hits
  back), X should hit.  If X doesn't hit, the game is even or so close the
  difference can barely be noticed; if X hits, he has a slight but clear
  advantage.

  If you decide your game plan is to wait on the anchor and hope to run
  with doubles or out-time O, then that's that--you have to decide between
  8/2 and other plays that leave a blot in your outfield.  If you're really
  gung-ho on trying to restrain O's back men, and you think leaving the
  anchor to hit is clearly wrong, then you'll look at plays like 13/7,
  13/11, 8/4, and 13/9, 6/4.  Everyone who wanted to keep the anchor,
  including people who sent me email but didn't post, advocated one of
  these three plays.

  But if I weren't going to hit, I'd follow Magriel's advice.  Leaving
  an outfield blot is wrong because it risks a few good hitting numbers
  (doubles etc.) in return for a very small chance to improve the outfield
  position by making the bar point (leaving more blots by breaking the
  midpoint to make some other outfield point is worth next to nothing),
  the value of which is very small.  13/7 is the best of the three blot-
  leavers, because it gives the best chance to make the bar point without
  having to break the midpoint, leaves fewest shots, and leaves fewest
  numbers with which O should hit (no way to hit and cover the 11 point
  except with 22).

  Another bad aspect of leaving an outside blot is that X has to leave
  it a second time if O misses and X escapes with 66 or 55.


			Play well,

			Marty