Strategy--Checker play

 Saving gammon

 From: Ron Karr Address: karr@best.com Date: 13 December 1997 Subject: Re: match winning chances & saving gammons Forum: rec.games.backgammon Google: 3492D812.FA3@best.com

```Morten Wang wrote:
> O vs X, score is 2-2 in a 5-point match.
> O owns 2 cube.
>   +24-23-22-21-20-19-+---+18-17-16-15-14-13-+
>  8| O  O  X  O       |   |                  |
>  O|    O     O       |   |                  |
>  O|    O     O       |   |                  |
>  O|                  |   |                  |
>  O|                  |   |                  |
>  O|                  |   |                  |
>   |                  |   |                  |
>   |                  |   |                  |
>   |                X |   |                  |
>   |    X        X  X |   |                  |
>   |    X  X  X  X  X |   |                  |
>   |    X  X  X  X  X |   |                  |
>   +-1--2--3--4--5--6-+---+-7--8--9-10-11-12-+
> X rolls 5-1.
>
>
> Runs (22-16):
>     Wins G/BG  BG
> O: 100.0 10.1 0.0
> X:  0.0   0.0 0.0
> Equity O: 1.101
> Sd: 0.002
> Eq to: 22699
>
> Stays and makes 1:
>    Wins G/BG  BG
> O: 96.2 25.4 0.2
> X:  3.8  0.0 0.0
> Equity O: 1.180
> Sd: 0.003
> Eq to: 32000
>
>
> looking at a single game it's clear one has to run.  this was in a
> match so I tried to calculate the match winning chances for both moves
> from the result of the rollouts.
>
> O loses, score 3-away, 1-away, 25% wins.
> O wins single game, score 1-away, 3-away, 75% wins.
> O wins gammon, wins game, 100% wins.
>
> (lengthy calculation deleted)

There are three parts to solving this problem (if you're a human being
and not Jellyfish):

1. What are your winning chances if you stay back?
2. What is the gammon price?
3. By how much do you reduce your gammon chances if you run?

None of these require Jellyfish to answer, although #3 isn't obvious
without some research, so it's useful to look at JF's results.

1.  It's easy to figure out winning chances, since this is pretty much a
one-roll situation. ( If O fails to clear but doesn't leave a shot, X is
definitely running next time). So: O leaves a shot 1/3 of the time (I
find the easiest way to see this is that O plays SAFELY with all 1s and
2s (20 #s) + 4 doubles. = 24 numbers)

X hits with any 1 (30%).  So 1/3 x 30% = 10%.  How often does X then
win?  Clearly he's an underdog since O has 9 or 10 off.  I'd have
estimated slightly lower than JF's 3.8%, but somewhere around there.

2.  The gammon price measures the relative value of a gammon vs. a
win-loss swing.  It's useful in play decisions like this one; it's also
useful in cube decisions for determining how much gammons affect the
take point.

If you lose a gammon, you blow 2 points, while if you win the game, you
gain 4 points (compared with losing the game).  Therefore the gammon
price for money is always 2/4 = 50%.

At different match scores, the gammon price can vary.  At 3-away/3-away,
you gain 50% by winning the game and lose 25% by getting gammoned, so
again the gammon price is exactly 50%!.  So there's really no difference
between this score and money as far as gammons are concerned.

The way to use this figure:  in order for it to be correct to stay back,
my wins need to be at least 50% of my extra gammon losses.  So if I'm
winning, say 4%, by staying back, am I losing an additional 8% gammons?
This requires some information.

3.  If a gammon is very close, a single roll makes a huge difference..
around 30% gammon chances, I think.  The number drops as the gammon gets
more likely or more unlikely.  In this position, X is a favorite to get
off the gammon regardless (plus the roll is only 6 pips, slightly less
than average), so the extra gammon loss is only 15%, according to JF,
which makes sense.  But this is still way more than twice as great as
the winning chances, so running is clearly right.

Ron
```

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