jacoby rule doubling
MJR
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?
Gary Wong
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 beaver (the
Kauder Paradox).
Cheers,
Gary (GaryW on FIBS).
--
Gary Wong, Computer Science Department, University of Auckland, New Zealand
ga...@cs.auckland.ac.nz http://www.cs.auckland.ac.nz/~gary/
Chuck Messenger
MJR wrote:
>
> 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?
Could somebody explain what the Jacoby rule is?
- Chuck Messenger
Daniel Murphy
On Fri, 05 Dec 1997 09:29:12 -0500, Chuck Messenger <c...@servtech.com>
wrote:
>Could somebody explain what the Jacoby rule is?
The Jacoby rule, invented by Oswald Jacoby, says:
In money play, the game winner receives no extra credit for gammons or
backgammons unless the cube has been doubled at least once.
The Jacoby rule is standard for money play almost everywhere, although
it's still a good idea to establish that you're using the rule when
you start a money play session.
The sole purpose of the rule is to speed up the game -- add a little
more excitement -- finish this game and move on to the next. The
Jacoby rule is never used in match play. The rule avoids those long
games where, having missed the market by a mile, one might play on
with little chance for either a gammon or a loss, or where, in match
play with a centered cube, a position is too good to double.
The Jacoby rule has some influence on both checker play and cube
decisions, mostly on checker play.
It encourages more aggressive checker play to achieve a gammonish
doubling position. The idea (simply put) is that if the strategy
works, you double and win four points; if it fails, you pass and lose
one, since unless the cube is turned you can't lose a gammon.
The rule's affect on cube decisions is harder to pin down. It seems
sensible that there will be positions which are not good enough to
double in a match but may be money doubles, if much of the doubler's
equity comes from gammons won, even if the doubler's overall winning
chances aren't terrific. In actual money play the rule probably
encourages typical players to double -- not just earlier -- but too
early, for fear of missing out on four points by not "activating
gammons." But against opponents who are known to be afraid to take a
double in a gammonish position, or to redouble if the game turns
around, the "early" double can still be a money winner.
_______________________________________________
Daniel Murphy http://www.cityraccoon.com
backgammon on-line: http://www.fibs.com
in San Francisco: http://www.backgammon.org
in Denmark: http://www.cityraccoon.com/hbk.html
Bob2ndWave
The Jacoby Rule is generally used only in money games. In short, it is that
there will be no gammons allowed unless the cube has turned.