🚀 go-pugleaf

In article <C0D3oC.KD4.1@cs.cmu.edu> Marc.Ringuette@GS80.SP.CS.CMU.EDU writes:
>24 23 22 21 20 19 | | 18 17 16 15 14 13
> O  O  O  O  O    | |
> O  O  O  O  O    | |
> O           O    | |
>             O    | |
>                  | |
>                  |X|
> X  X             | |
> X  X             | |
> X  X  X  X  X    | |                       +-+
> X  X  X  X  X    | |                       |2|
> 1  2  3  4  5  6 | |  7  8  9 10 11 12     +-+
>
>Money game:  O to play 1-1
>
>O (a good player) played 24/off 24/off 24/off 20/21, which I think
>is a horrible play.  He couldn't be right, could he?
>
>
>-- Marc Ringuette (mnr@cs.cmu.edu)


I think he's right.

What risk is he taking?  

  1: X dances or lands on the 1 point and stays there.

  2: O rolls 5-6 3-5 3-6 and blots, taking off 2.

  3: O gets nuked

  4: X wins, despite having no 6 or 5 point and an opponent with only 8
     checkers on the board.


or other smaller risks involving later hits.  So making this play costs perhaps
1/36 of a point from this parley and perhaps another 1/36 or 1/72 from getting
hit later when he has even more men off.


What does he get in return?  A mild increase in the gammon chances; he should
be off in 5 rolls [budgeting one double and two misses via aces] wheras he
would have needed 6 rolls playing safe.  If X dances once it's really close;
figure he increases his gammon chances by this table:

  1: X dances.  8/18.  Gammon chances improve perhaps 1/4 as compared with the
     safe play.  Loss chances are perhaps 1/6[blot]*1/3[hit]*1/8[lose] = 1/144

  2: X comes in and stays on the 1.  1-1 1-2 1-3 1-4.  4/18.  Gammon chances
     are a bit less than they would have been with the safe play [which would
     have made X dance] and loss chances are again 1/144.  This is the worst
     case 

  3: X passes by.  Gammon chances improve somewhat [it's a hard gammon even
     with the agressive play].  No risk.

I think O made a fine play.

-dk