Strategy--Bearing Off

Forum Archive : Strategy--Bearing Off

 
Playing for gammon

From:   Max Levenstein
Address:   medl@umich.edu
Date:   13 August 2011
Subject:   Bearoff checker play
Forum:   BGonline.org Forums

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

     X rolls 3-1

I have little understanding of this position, and therefore blundered very
nicely.

My gammon value is huge here and I want to increase my chance of gammons.
I have an even amount of checkers left, so taking one off would not
decrease the amount of rolls I need to get off that much.  I would like to
bear off without leaving a shot, although I may still be a favorite to win
a game (not a gammon) if I get hit and come around.  Therefore, I played
4/1, 4/3.  This helps clear the last point on the next roll.

Stick asks:
> Do you have any realistic fear of losing this game?

No, but I fear not having a good chance of gammons if hit.

Casper van der Tak  writes:

You are not in danger of losing, because you are very far ahead in the race
and have access to the cube.  You would like to win a gammon.  If you count
crossovers for both sides, or crossovers and pips in the gammon race, you
will see that you are an underdog to win the gammon.  So you look for plays
that increase your chances of winning a gammon.

4/3, 4/1 is a slow play, you will need 4-5 rolls to bear off. Your opponent
is on roll and likely needs 3.  Among the safe plays, 4/off looks better,
because you'd need 4 rolls only after that (you can afford a miss).  White
is not going to hang around waiting for a shot.

You should also look at the unsafe plays.  Two of them:

  a. 3/off, 1/off creates a 3 roll position with lots of misses (likely 4
     roll).
  b. 3/off, 3/2* creates a 4 roll position (you can afford a miss), and
     slows your opponent down, adding a crossover and 2 pips to the gammon-
     save finish line.

Both the risky plays risk getting hit and have a reduction in gammon
chances, but that should not worry you much as you are somewhat unlikely to
win a gammon to start with.

I think with this analysis you'd need to be able to see that one of the
risky plays is best, followed by 4/off. Among the 2 best plays, probably
you want to hit, because hit and dance is big.

Neil Kazaross  writes:

> "I have an even amount of checkers left, so taking one of would not
> decrease the amount of rolls I need to get off that much."

This is one of the causes for your blunder and a rather common
missconception. The even/odd thing applies when you have something very
close to a pure roll oriented speed board bearoff. After playing 4/3, 4/1
you have 8 checkers left and a persistant gap on the 2 pt. You're quite
likely to waste a turn by rolling a missing 2.

Compare with playing the clearly speedier 4/off. Now you still have that 2
gap, but you have 7 checkers left and can afford to miss once with a 2,
which currently fills the gap from the 4 pt and likely prevents further
misses.  4/off is probably close to half a roll quicker than 4/3, 4/1. So
if we ignore shot potential we see that 4/off is much better than 4/3, 4/1.

> "I would like to bear off without leaving a shot, although I may still be
> a favorite to win a game (not a gammon) if I get hit and come around."

Leaving a shot here is nowhere near as bad as it usually is when bearing
off since your opp has only a 2 pt board and other blots and you have many
checkers off. If you get hit, you probably still can play for a gammon for
a turn or two.  Safety in this position is only a minor consideration.
Speed of bearoff is most important.

> "Therefore, I played 4/1, 4/3. This helps clear the last point on the
> next roll."

Clearing the point doesn't matter here, speed to bearoff does!  4/off is
clearly better, and 3/off, 1/off and 3/off, 3/2* are probably still better.
Taking two checkers off is fastest.  Hitting is somewhat slower than even
4/off but sets the opponent back two pips and one crossover.  Hitting gains
huge if he dances with 4-4 which otherwise usually saves gammon, and gains
big on any of the other three dances.  I think it is slightly correct to
hit.

OK, here's a spoiler rollout for money play and with our opponent owning
the cube, and we see what we expect to see and that is that we can only
very rarely lose this game no matter what we play.  For money I'd probably
have played 4/off, to be honest, and in practical play may gain on some
opponent mistakes in whether to stay or go with his next roll.

Rollout:                Win               Lose
                  ----------------   ----------------
   Play            S     G     BG     S     G     BG    Equity
   ------------   ----  ----  ----   ----  ----  ----   -------
1. 3/off, 3/2*   .9895 .2273 .0030  .0105 .0000 .0000   +1.2064
2. 4/off         .9988 .2011 .0010  .0012 .0000 .0000   +1.1994 (-0.0071)
3. 3/off, 1/off  .9888 .2118 .0017  .0112 .0000 .0000   +1.1887 (-0.0178)
4. 4/3, 4/1      .9986 .1524 .0004  .0014 .0000 .0000   +1.1498 (-0.0566)
 
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Strategy--Bearing Off

Greedy bearoff exception  (Stick+, Jan 2011) 
Playing for gammon  (Max Levenstein+, Aug 2011) 
Rules of thumb  (Rich Munitz+, Oct 2009) 
Wastage  (David Montgomery, Apr 1996) 
Wastage--Positions that minimize  (Stig Eide, Apr 1996)  [Recommended reading]
Which gaps to fill  (Kit Woolsey, Mar 1996) 
Winning the bearoff race  (Dave Flaks+, Jan 2001) 

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