1 view

Skip to first unread message

Jun 20, 1999, 3:00:00 AM6/20/99

to

Hi

I rolled out the starting position 50.000 times using Jellyfish

Level 5 to produce the table below to show cubeful distribution.

I rolled out the starting position 50.000 times using Jellyfish

Level 5 to produce the table below to show cubeful distribution.

Cube Level 1 2 4 8 16 32 Total

Cashes 37.83 13.54 1.78 0.28 0.03 0.01 53.47

Single 26.63 5.03 0.59 0.06 32.31

Gammon 1.45 10.9 1.17 0.10 0.01 13.63

Backgammon 0.07 0.46 0.04 0.01 0.01 0.59

100.0

Just in case it's not clear. Cashes are games that end with a cube

turn.

Singles Gammons and Backgammons are games played to conclusion.

I'm not technically minded enough to make use of these numbers, but

would they maybe affect match equity tables etc or could they shed

any sort of light on recube vig?

Roland Sutter

Jun 20, 1999, 3:00:00 AM6/20/99

to

Hi. Thanks for the numbers.

Just a question: How can there be 27% single games with the cube at 1?

Shouldn't this only happen in some very rare games?

Stig Eide

Just a question: How can there be 27% single games with the cube at 1?

Shouldn't this only happen in some very rare games?

Stig Eide

In article <376c496f...@news.which.net>,

Sent via Deja.com http://www.deja.com/

Share what you know. Learn what you don't.

Jun 20, 1999, 3:00:00 AM6/20/99

to

On Sun, 20 Jun 1999 10:49:39 GMT, Stig Eide <stig...@yahoo.com>

wrote:

wrote:

>Hi. Thanks for the numbers.

>Just a question: How can there be 27% single games with the cube at 1?

>Shouldn't this only happen in some very rare games?

>Stig Eide

Oh Sh**

Sorry I aligned the table wrong here is the corrected version!

Cube Level 1 2 4 8 16 32 Total

Cashes 37.83 13.54 1.78 0.28 0.03 0.01 53.47

Single 0.00 26.63 5.03 0.59 0.06 32.31

Gammon 1.45 10.90 1.17 0.10 0.01 13.63

Backgammon 0.07 0.46 0.04 0.01 0.01 0.59

100.00

Roland Sutter

Jun 20, 1999, 3:00:00 AM6/20/99

to

(B...@ckgammon.com) writes:

> I rolled out the starting position 50.000 times using Jellyfish

> Level 5 to produce the table below to show cubeful distribution.

>

[table edited]> I rolled out the starting position 50.000 times using Jellyfish

> Level 5 to produce the table below to show cubeful distribution.

>

> Cube 1 2 4 8 16 32 Total

>

> Cashes 37.83 13.54 1.78 0.28 0.03 0.01 53.47

> Single 0.00 26.63 5.03 0.59 0.06 32.31

> Gammon 1.45 10.90 1.17 0.10 0.01 13.63

> Backgammon 0.07 0.46 0.04 0.01 0.01 0.59

> 39.35 51.53 8.02 0.98 0.11 0.01 100.00

Thanks very much for that data!

> I'm not technically minded enough to make use of these numbers, but

> would they maybe affect match equity tables etc or could they shed

> any sort of light on recube vig?

Unfortunately the results are probably inapplicable to match play (where

cube behaviour is likely to vary drastically from money play depending

on the score) but they ought to help us model certain features of money

games.

I have attempted to produce a simple Markov process which would produce

a distribution similar to that above. It is:

If the cube is centred:

- it is offered and dropped with probability 0.378 (terminal)

- it is offered and taken with probability 0.606 (go to the state below)

- a player wins a gammon with probability 0.015 (terminal)

- a player wins a backgammon with probability 0.07 (terminal)

If the cube is owned:

- it is offered and dropped with probability 0.220 (terminal)

- it is offered and taken with probability 0.152 (remain in this state)

- a player wins a single game with probability 0.455 (terminal)

(These wins can reasonably expected to belong to the player who last

turned the cube; we presume the cube holder can always reach a point

where she has a correct double before she wins a single game).

- a player wins a gammon with probability 0.172 (terminal)

- a player wins a backgammon with probability 0.001 (terminal)

(It's hard to determine who the gammon and backgammon wins belong to.

Certainly the vast majority will be the player who turned the cube, but

there will be occasions where the cube owner becomes too good to double

and goes on to win a gammon or backgammon without having had a correct

double.)

If two players happen to play with cube behaviour described by the above

model, then we can make the following observations about the results of

their games:

- Most (62%) initial doubles are takes. This value agrees reasonably

closely to an earlier result at:

http://x24.deja.com/=dnc/getdoc.xp?AN=376082872

- Most (59%) redoubles are drops.

- The final cube value follows the following (geometric-like) distribution:

p(X=1) = 0.394

p(X=2^n) = 0.514 x 0.152^{n-1} for n = 1, 2, 3...

- The cube is turned and accepted 0.71 times per game on average; the

average final value of the cube is 1.87.

- A single game is worth 2.2 points on average; the standard deviation is

3.0. I have previously assumed 2 and 3 respectively for these parameters

in my own games.

Those statistics do not change a significant amount if the Jacoby rule

is used in interpreting the score (naturally, the parameters of the model

might change depending on the use of the rule).

- Assuming all gammon and backgammon wins belong to the player who last

cubed, a double/take leaves the taker with an average normalised cubeful

equity of -0.446. (If all doubles were perfectly efficient, this figure

would be -0.5.)

With a few more assumptions it may be possible to come up with other

statistics on cube efficiencies, recube vig, etc. I don't have time

to think about it right now, though -- more another day perhaps.

Cheers,

Gary.

--

Gary Wong, Department of Computer Science, University of Arizona

ga...@cs.arizona.edu http://www.cs.arizona.edu/~gary/

Reply all

Reply to author

Forward

0 new messages

Search

Clear search

Close search

Google apps

Main menu