"California" rule for chouette
Peter Anderson
know why it's called that)
Goes like this:
On the opening roll....the winner can either play the roll like
normal....Or...has the option of rerolling (with both dice) if the cube is
turned (and stays in the middle).
Local strategy in this loose game is as follows:
If you win the opener with a natural 3-1, 4-2, or 6-1....take the roll
otherwise.....turn the cube and re-roll.
Does anyone know if this is optimum?
Thanks.
Gary Wong
> On the opening roll....the winner can either play the roll like
> normal....Or...has the option of rerolling (with both dice) if the cube is
> turned (and stays in the middle).
>
> Local strategy in this loose game is as follows:
>
> If you win the opener with a natural 3-1, 4-2, or 6-1....take the roll
>
> otherwise.....turn the cube and re-roll.
>
> Does anyone know if this is optimum?
GNU Backgammon thinks so. Assuming you're not allowed doubles on the
reroll, its cubeless evaluation of the equity being on roll in the
starting position with a centred 2-cube is +0.069, whereas the equities
after each of the 15 legal opening rolls are:
31: 8/5 6/5 +0.108
61: 13/7 8/7 +0.078
42: 8/4 6/4 +0.077
65: 24/13 +0.065
53: 8/3 6/3 +0.037
54: 24/20 13/8 +0.031
62: 24/18 13/11 +0.024
63: 24/18 13/10 +0.023
64: 24/18 13/9 +0.021
32: 24/21 13/11 +0.017
43: 24/20 13/10 +0.016
52: 24/22 13/8 +0.013
51: 24/23 13/8 +0.008
21: 24/23 13/11 +0.002
41: 24/23 13/9 -0.001
So only 31, 61 and 42 are better than rerolling with a centred 2-cube.
(65 is very close.)
Cheers,
Gary.
--
Gary Wong g...@gnu.org http://www.cs.arizona.edu/~gary/
Peter Anderson
allowed doubles.....how does that change the strategy ????
"Gary Wong" <g...@gnu.org> wrote in message
news:dh6y9kr...@pc-gtw.research.att.com...
Gary Wong
> "Gary Wong" <g...@gnu.org> wrote in message
> news:dh6y9kr...@pc-gtw.research.att.com...
> > "Peter Anderson" <pand...@hotmail.com> writes:
> > > On the opening roll....the winner can either play the roll like
> > > normal....Or...has the option of rerolling (with both dice) if the cube
> > > is turned (and stays in the middle).
> >
> > rerolled]. Assuming you're not allowed doubles on the reroll [...]
>
> Thanks Gary...exactly what I was wondering.....however, the re-roll IS
> allowed doubles.....how does that change the strategy ????
If doubles are allowed, then gnubg thinks it is always better to
turn the cube and re-roll than to play the first roll you get. The
combination of the chance of the 6 possible doubles and the benefit
of increasing the stakes in a position where you have an advantage
without forsaking cube access is too valuable to keep even a initial
31.
(To be precise, its evaluation of the cubeless equity for being on
roll in the starting position when doubles are permitted is 0.061 on a
1-cube, and so 0.122 on a 2-cube. This is greater than the equity
following any of the non-double opening rolls on a 1-cube, including
31 which is worth 0.108.)
Paul Tanenbaum
> "Peter Anderson" <pand...@hotmail.com> writes:
> > "Gary Wong" wrote:
> > > > On the opening roll....the winner can either play the roll like
> > > > normal....Or...has the option of rerolling (with both dice) if
the cube
> > > > is turned (and stays in the middle).
> > >
> > > GNU Backgammon thinks [every roll except 31, 42 and 61 should be
> > > rerolled]. Assuming you're not allowed doubles on the reroll
[...]
> If doubles are allowed, then gnubg thinks it is always better to
> turn the cube and re-roll than to play the first roll you get. The
> combination of the chance of the 6 possible doubles and the benefit
> of increasing the stakes in a position where you have an advantage
> without forsaking cube access is too valuable to keep even a initial
> 31.
How does it play the opening rolls of 11, 22, 33, 44?
My plays:
11 6/5(2), 24/22
22 6/4(2), 24/22(2)
33 8/5(2), 24/21(2)
44 8/4(2), 24/20(2)
Equities?
---
Paul T.
Paul Hankin
"Paul Tanenbaum" <ptane...@consultant.com> wrote in message
news:9u4sh8$60mg1$1...@ID-82218.news.dfncis.de...
I would guess none of these are the correct plays.
I'd move:
11: 6/5(2) 8/7(2)
22: 6/4(2) 13/11(2)
33: 8/5(2) 6/3(2)
44: 24/20(2) 13/9(2)
--
Paul Hankin
Peter Anderson
or 13/10 (2)... along with the 8/5(2)