Difference and value of "cubeless" vs. "centered" roll outs

[Dean Gay]

The following is taken from from one of the annotated matches
graciously presented on the "Backgammon by the Bay" home page
(http://www.backgammon.org/bgbb/).

=============================================================

Game #5
Open Division Final
San Mateo, California
January 19, 1997
11 Point Match

David Simpson (Black) vs. Kevin Mansfield (White)
Score: 4 - 6

Analysis by Kit Woolsey

Play 5b
+-------------+---+-------------+
| O X X O X | | X O |
| O X X X | | O |
| X | | O |
| | | | 137 11 point match
| | | |
| | | | +---+ X: 4
| 1 2 3 4 5 6 |BAR| 7 8 9 0 1 2 | | | O: 6
| | | X | +---+
| | | X |
| | | X | 157
| O | | X |
| O O O | | O X |
| X O O O | | O X |
+-------------+---+-------------+

O to play. Double or roll?

Equity (centered)
O 76.0% G 2.8% BG 0.1%
X 24.0% G 1.1% BG 0.1%
Equity (O): +0.538

Equity (cubeless)
O 61.3% G 24.4% BG 0.9%
X 38.7% G 10.5% BG 0.7%
Equity (O): +0.367
=============================================================

My questions concern the terms "centered" and "cubeless" in the equity
evaluations.

1. Am I correct in assuming that "cubeless" means that the game is
played to completion with no doubling by either side?

2. Am I correct in assuming that "centered" means that the cube is
available for either side during the roll out?

3. Why are both "cubeless" and "centered" roll outs valuable in
determining whether to double? Is a different type of information
gleaned from each of them?

Chase

[Ron Karr]

Dean Gay wrote:
>
> My questions concern the terms "centered" and "cubeless" in the equity
> evaluations.
>
> 1. Am I correct in assuming that "cubeless" means that the game is
> played to completion with no doubling by either side?

Yes

>
> 2. Am I correct in assuming that "centered" means that the cube is
> available for either side during the roll out?

Yes

>
> 3. Why are both "cubeless" and "centered" roll outs valuable in
> determining whether to double? Is a different type of information
> gleaned from each of them?
>

Yes, you get different information. Cubeless tells you the results when
the game is played to the end. "Centered cube" means that both players
have access to the cube; when either player's equity gets to a point
greater than the "settlement limit" (usually set at .55), that player is
counted as winning a single game.

To determine whether to double (according to the level 5 rollouts), you
also need to look at the figures for "player not on roll owns cube".
You multiply that figure times 2 (because the guy being doubled owns a
2-cube), and if it's greater (for the doubler) than the center cube
equity, then doubling is correct. (And it's a pass if the "player not
on roll owns cube" equity is worse than -.5).

(If you're looking at redoubles, then you use "player on roll owns cube"
instead of "centered cube")

Ron

[Bill Taylor]

Ron Karr <ka...@best.com> writes:

|> ... both players

|> have access to the cube; when either player's equity gets to a point
|> greater than the "settlement limit" (usually set at .55), that player is
|> counted as winning a single game.

Sorry, I don't follow any of this.

Could you elaborate somewhat, please?

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Bill Taylor W.Ta...@math.canterbury.ac.nz
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Mother Nature:- Not so much a grand architect, as an inveterate tinkerer.
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