Cube Handling

 With the Jacoby rule

 From: Gary Wong Address: gary@cs.auckland.ac.nz Date: 4 December 1997 Subject: Re: jacoby rule doubling Forum: rec.games.backgammon Google: ieyzpmhpxyq.fsf@cs20.cs.auckland.ac.nz

```MJR writes:
> In money play using the Jacoby rule, people will double earlier to
> activate their gammons.  I am wondering if this notion is correct
> according to doubling theory.  The way I see it, the Jacoby Rule doesn't
> affect take decisions, it just means you have to cash cube-centered
> games when you would otherwise play on for the gammon.  Given that the
> rule doesn't affect the take decision, wouldn't the doubling point be
> the same as it would be without it?  If there aren't enough market
> losing sequences w/o the Jacoby rule to justify doubling, then how can
> it be correct to double the same position with the Jacoby rule?

In my opinion you're right about the take decision being unaffected, but
there can be factors which justify doubling under the Jacoby rule which
wouldn't be normal doubles.  In particular, market losers in gammonish
games hurt you more with the Jacoby rule than without -- if you are in a
very volatile position where you are reluctant to double because your
overall chances are relatively weak, but you have outside shots at a
gammon, then losing your market under the Jacoby rule is a disaster (you
suddenly find yourself in a position that is too good to double, and you
have big gammon chances that are no use to you).  Without the Jacoby rule
-- well, at least you can keep playing for 2 points.

So in ungammonish games (races and high anchor holding games), I assert
that cube handling under the Jacoby rule is essentially the same as for
normal money play; for gammonish positions (prime-vs-prime, blitzes, back
games) you might be forced to double early under the Jacoby rule if the
position is volatile enough.

Time for an example, I think: here's a very volatile position where O's
chances aren't huge overall, but if he rolls well he could end up with big
gammon potential:

+13-14-15-16-17-18-------19-20-21-22-23-24-+
| O  X        X  X |   |  X  X           O |
| O  X           X | X |  X  X             |
|                  |   |  X                |
|                  |   |                   |
|                  |   |                   |
v|                  |BAR|                   | O on roll, 1 cube, money game,
|                  |   |                   | Jacoby rule in effect.
|                  |   |                   |
| X                |   |                   |
| X           O    |   |  O           O  O |
| X     O     O  O |   |  O  X  O  O  O  O |
+12-11-10--9--8--7--------6--5--4--3--2--1-+

Let's assume that over the next exchange, there are only two possibilities
(these numbers are contrived to give a result that demonstrates the effect
of the Jacoby rule, I don't give a damn if Jellyfish rollouts show I'm out
by 72% :-) --

a) O hits and covers; X fails to anchor or hit: 40%
b) X hits or anchors and ends the blitz: 60%

Under a), let's give O a 70% chance of pulling off the gammon, 20% single
wins, no gammon losses and 10% single losses.  For b), we'll say the
numbers are 10%, 20%, 20% and 50% respectively.  So, O's cubeless equity
is:

Gammons count     Gammons don't count
a)      1.5                  0.8
b)     -0.5                 -0.4

For overall cubeless equity of 0.3 (if gammons count) or 0.08 (if they
don't).

If O does not double, his equity is:

when the blitz continues (30%), cubeless equity is 0.8 and he's lost his
market; he can claim with the cube next turn for equity 1.0;

otherwise, his cubeless equity is -0.4, the cube is still centred and
I'll value the cube's worth at 0.2 points to him and 0.45 to X (see my
previous article) for equity -0.65;

0.4 x 1.0 + 0.6 x -0.65 = 0.010 cubeless equity at a 1 cube is 0.010
points.

If O does double, his equity becomes:

when the blitz continues (30%), cubeless equity is 1.5 and X owns the
cube which I'll value at 0.05 points worth of recube vig for 10% wins;
overall equity 1.45;

otherwise, his cubeless equity is -0.5 and X has enormous recube vig
(I'll say 0.45 points) for equity of -0.95.

0.4 x 1.45 + 0.6 x -0.95 = 0.010 cubeless equity at a 2 cube, for 0.020
points.

If the game was played without the Jacoby rule, and O did not double, his
equity would be:

1.5 cubeless equity when the blitz continues, the cube is centred and
almost dead but worth 0.1 points to him and 0.05 to X for equity of
1.55;

if X enters, -0.5 cubeless equity and the cube is again worth 0.2 to O
and 0.45 to X for equity -0.75.

0.4 x 1.55 + 0.6 x -0.75 = 0.170, and the cube is at 1 for 0.170 points.

So under the Jacoby rule, O should double (to win 0.02 points instead of
0.01); without the Jacoby rule, he should not (0.170 points against 0.02).
Note that X has a massive take in each case; it is very close to being a

Cheers,
Gary (GaryW on FIBS).
--
Gary Wong, Computer Science Department, University of Auckland, New
Zealand
gary@cs.auckland.ac.nz        http://www.cs.auckland.ac.nz/~gary/
```

### Cube Handling

Against a weaker opponent  (Kit Woolsey, July 1994)
Closed board cube decisions  (Dan Pelton+, Jan 2009)
Cube concepts  (Peter Bell, Aug 1995)
Early game blitzes  (kruidenbuiltje, Jan 2011)
Early-late ratio  (Tom Keith, Sept 2003)
Endgame close out: Michael's 432 rule  (Michael Bo Hansen+, Feb 1998)
Endgame close out: Spleischft formula  (Simon Larsen, Sept 1999)
Endgame closeout: win percentages  (David Rubin+, Oct 2010)
Evaluating the position  (Daniel Murphy, Feb 2001)
Evaluating the position  (Daniel Murphy, Mar 2000)
How does rake affect cube actions?  (Paul Epstein+, Sept 2005)
How to use the doubling cube  (Michael J. Zehr, Nov 1993)
Liveliness of the cube  (Kit Woolsey, Apr 1997)
PRAT--Position, Race, and Threats  (Alan Webb, Feb 2001)
Playing your opponent  (Morris Pearl+, Jan 2002)
References  (Chuck Bower, Nov 1997)
Robertie's rule  (Chuck Bower, Sept 2006)
Rough guidelines  (Michael J. Zehr, Dec 1993)
The take/pass decision  (Otis+, Aug 2007)
Too good to double  (Michael J. Zehr, May 1997)
Too good to double--Janowski's formula  (Chuck Bower, Jan 1997)
Value of an ace-point game  (Raccoon+, June 2006)
Value of an ace-point game  (Øystein Johansen, Aug 2000)
Volatility  (Chuck Bower, Oct 1998)
Volatility  (Kit Woolsey, Sept 1996)
When to accept a double  (Daniel Murphy+, Feb 2001)
When to beaver  (Walter Trice, Aug 1999)
When to double  (Kit Woolsey, Nov 1994)
With the Jacoby rule  (KL Gerber+, Nov 2002)
With the Jacoby rule  (Gary Wong, Dec 1997)
Woolsey's law  (PersianLord+, Mar 2008)
Woolsey's law  (Kit Woolsey, Sept 1996)
Words of wisdom  (Chris C., Dec 2003)