From: martys@juliet.ll.mit.edu ( Marty Storer )
Subject: Re: Backgame problem
Organization: M.I.T. Lincoln Lab - Group 43
	<1992Apr6.161812.14674@murdoch.acc.Virginia.EDU>
Date: 8 Apr 92 20:07:29

In article <1992Apr6.161812.14674@murdoch.acc.Virginia.EDU> jrk2v@galen.med.Virginia.EDU (John Robert Klein) writes:

:   In article <1992Apr05.054542.171012@cs.cmu.edu> mnr+@cs.cmu.edu (Marc Ringuette) writes:
:   >>                                       X inner board
:   >>     + --  --  --  --  --  -- +++++ --  --  --  --  --  -- +
:   >>     |  X   X       X   X   X |   |  X   X   X   O   O     |
:   >>     |              X   X   X |   |  X   X   X   O   O     |
:   >>     |                        |   |              O         |
:   >>     |                        |   |                        |
:   >>     |                        |   |                        |  +---+
:   >>     |                        |   |                        |  | 1 |
:   >>     |                        |   |                        |  +---+
:   >>     |                  O   O |   |                        |
:   >>     |                  O   O |   |  O   O                 |
:   >>     |                  O   O |   |  O   O   X             |
:   >>     + --  --  --  --  --  -- +++++ --  --  --  --  --  -- +
:   >>                           O to play 43
:   >
:   >Best: 8-5,7-3 (move past)
:   >2nd:  8-4,7-4 (point on him)
:   >3rd:  7-4,7-3 (make blots)
:   >
:   >Our timing is bad, but blotting doesn't help it much since we quickly enter.
:   >Pointing on X gives us a small chance of keeping the last checker back, but
:   >otherwise slows him down and lets him off the hook on the 9 rolls where he
:   >dances, which otherwise would be bad for him.  So just move past and hope
:   >he rolls faster than you do.
:   >
:   >
:
:   I think  you're right Mark and I was wrong in my earlier reply to this
:   problem where I said to  leave lots of blts to preserve Xs timing.
:   O's timing isn't soooo bad so (s)he may be able to keep much of hir board
:   (i'm  trying "gender neutral" pronouns  :) until s/he can escape  the back
:   checkers.  O may even be able  to win the game this way and is likely to
:   at least  avoid the gammon.  So,  I agree 100% with your rankings.  Good
:   analysis.

  (My rankings would be the same as Marc's except with the second and third
  reversed.  See below...)


  This is another previously published problem:  #97 from Barclay Cooke's
  _Paradoxes_and_Probabilities_.

  It is a somewhat silly problem because the cube is in the middle.  It would
  be more interesting if O owned the cube.  Here, most of the time X ends up
  winning by doubling O out, as he can (but shouldn't) do right away.  

  Cooke sees two alternatives, making the 4 point, and leaving blots with
  7/3, 7/4* to try to adjust timing.  Nowhere does he mention the cube;
  it doesn't figure into his analysis.  He rejects making the 4 point in
  favor of trying to improve timing by being hit.

  Here's how I analyze this position:  O's timing is rotten, so X is playing
  for gammon.  How should O (1) play to avoid the gammon, (2) play to win
  the game?

  Playing to win is dangerous, because the best tries to win are those that
  get more men sent back.  X can double O out if things start to look
  dangerous, and even when X regains his market it's very seldom by much.
  Meanwhile, the more men sent back, the more likely X is to win a gammon.
  Do blotting plays make a gammon less likely for X because they force X
  to take more double-outs?  I don't think so, but as usual I haven't
  rolled this out.

  Playing to avoid the gammon *by refusing to leave more blots* is also
  dangerous, because O moves forward faster, thus decreasing winning
  chances and allowing X to play for gammon longer.

  I don't know the answer, but I'd play 8/5, 7/3.  This at least lets X
  play all of his big numbers and even gives him one number to break his
  prime (44).  I'm more afraid of the variations where X sends another
  man or two back and O cracks his board anyway, than I am of the variations
  where O cracks his board but remains with only five men back.

  How about if O owns the cube?

  Then I think I'd play 7/3, 7/4*.  O is in it to the end; I think leaving
  the blots increases her chances to win, and doesn't increase her chance of
  getting gammoned by twice as much as it increases her winning chances
  (assuming a money game).  Just instinct (in-stink?) talking.

  There's another blotting play that I think someone mentioned:  8/4*, 6/3,
  activating X's 66 and 65, which doesn't happen after 7/3, 7/4*.  I
  wouldn't make that play whether I owned the cube or not--it wrecks the
  board possibly beyond repair, and makes it more likely that X can send
  some men back and still leave O with a cheesy and hard-to-improve board
  or a busted one.

			Play well,

			Marty


  PS  Walter Trice claims to have the Master Error List for _P_and_P_.
      I'll ask what the line is on this one.
Newsgroups: rec.games.backgammon