From: martys@juliet.ll.mit.edu ( Marty Storer )
Subject: Re: O to play 4-2
Organization: M.I.T. Lincoln Lab - Group 43
	<MARTYS.92Apr7205225@cordelia.juliet.ll.mit.edu>
	<1992Apr9.143600.10515@murdoch.acc.Virginia.EDU>
Date: 9 Apr 92 13:41:45

In article <1992Apr9.143600.10515@murdoch.acc.Virginia.EDU> jrk2v@galen.med.Virginia.EDU (John Robert Klein) writes:


:   >>   13 14 15 16 17 18 | | 19 20 21 22 23 24
:   >>		         X | |  X  X        X  O
:   >>		         X | |  X  X        X
:   >>		         X | |  X  X
:   >>		           |X|  X
:   >>		           | |  X
:   >>		           |X|
:   >>		           | |                 O
:   >>		           | |        O  O     O
:   >>  		   | |     O  O  O  O  O  +-+
:   >>		           | |     O  O  O  O  O  |2|
:   >>   12 11 10  9  8  7 | |  6  5  4  3  2  1  +-+
:   >>
:   >>   7 point match
:   >>   Score O:5 X:1
:   >>   O to play 4-2  (John... notice... there are *two* on the bar.  :-)
:   >
:   This is a tough one.  I don't have much of an intuitive feel for it,
:   one way or the other so I'm going to try plugging in some numbers but
:   my estimates may be way off.
:
:   for a money game.
:
:   safe play:  X wins: 60%,  loses 40%
:   risky play:
:     a) miss (70%):  X wins 80%, loses 20%
:     b) hit (30%):   X wins 40%, loses 40%, gets gammoned 20%
:
:   If these numbers are right (am I close?) then
:
:   safe play: X wins .2 (times the cube)
:   risky play: X wins .3 (times  the cube)

  You're saying "X" when you mean "O".

  I think O wins more often than 60% after the safe play and probably does
  a little worse than you say after being hit.  (I take it that your
  win/loss numbers that don't include gammons factor gammons in, to get
  an equivalent winning probability.)  I'm not sure about the risky-&-miss
  variation, but it looks like your numbers there are in the ballpark.

  After the safe play, O gets gammoned about 0% since she'll hardly ever do
  any more cracking (3's and 2's advance) unless he's primed, while X gets
  gammoned a fair amount of the time.

  I'd play safe for money, but it looks to me like it's even more clearly
  right to play safe in the match situation.

:
:   so from these numbers the risky play is right for money.
:   but if these numbers are even a little off (say, X wins 65% after safe play)
:   then the results could change.
:
:   In the match you don't care so much about winning points as about winning the
:   match:
:
:   at 7-1 you're 100%
:   at 5-3 you're ~70%
:   at 5-5 you're 50%

  At 5-3 you're more like 66 or 67%.  66% according to latest work by Woolsey
  (I guess he's no longer around DC, so you can't dragoon him at bridge
  tournaments for opinions so easily...)--see latest issue of _Inside_B.G._.

  (I can't WAIT to see the response to Woolsey's article by Roy Friedman,
  whose numbers W. was rebutting with extreme prejudice...)

  (For those who don't know, the backgammon part of Kit Woolsey's brain
  operates like that of a super-advanced backgammon mutant.  He's awfully
  good at bridge, too, and other games:  probably poker and blackjack among
  others.)

:
:   These have to be factored into the above calculations too.
:   But it probably won't change the results.

  Using your numbers and Woolsey's, playing safe wins the match for O about
  87% of the time, and making the risky play wins the match only about 77%
  of the time.  So if your numbers are right, the risky play at the given
  match situation is a big blunder.  Even if you change your 20% gammon-loss
  figure to 0%, and make the gammon losses into simple wins for X, O wins
  the match only about 80% of the time.

  If my feelings about your numbers are right, the difference is even more
  pronounced in favor of the safe play.


			Play well,

			Marty