From: jrk2v@galen.med.Virginia.EDU (John Robert Klein)
Newsgroups: rec.games.backgammon
Subject: Re: O to play 4-2
Date: 10 Apr 92 13:48:27 GMT
Organization: University of Virginia

In article <MARTYS.92Apr9134145@escalus.juliet.ll.mit.edu> martys@juliet.ll.mit.edu ( Marty Storer ) writes:
>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.
>
Actually, I mistakenly didn't think about "X" getting  gammoned since it
didn't matter at the given match score - but of course it does matter for
money.  So "O"s wins, such as 60% with safe play, mean 60% wins or gammons.

>  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.
>
True.  X also gets gammoned a fair amount of the time with the risky play.

>  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.
>
>:
>:   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
>:
>:   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.
>
My numbers come out differently.
I get around 86.4 % with the safe play and 88% with the risky play

Using Woolsey's 66% and my 60-40, 80-20 and 40-40-20 I get --

safe play: O wins the match:

  a) safe play:  .6 (1) + .4 (.66) =  86.4%

  b) risky play: .7x.8 (1) + .7x.2 (.66)  (if missed)
                
               + .3x.4 (1) + .3x.4 (.66) + .3x.2 (.5) (if hit)

                =  88%

Of course its likely my numbers are off at least by a little which could
certainly change the results.  In any case it does look close to me.

jk
Newsgroups: rec.games.backgammon