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## Re: [Bug-gnubg] Two-Sided Bearoff DB and Cube Analysis

 From: Neil Robins Subject: Re: [Bug-gnubg] Two-Sided Bearoff DB and Cube Analysis Date: Sat, 12 Dec 2009 17:55:23 -0000

Yes, but I'm only seeking to apply cubeless winning chance to the pure cubeless position that arises following D/T, when the winner of the game wins the match.
```
```
----- Original Message ----- From: "Christian Anthon" <address@hidden>
```To: "Neil Robins" <address@hidden>
Sent: Saturday, December 12, 2009 1:30 PM
Subject: Re: [Bug-gnubg] Two-Sided Bearoff DB and Cube Analysis

```
```The art of using cubeless winning chances in cubeful games is a gray
one at the best of times. The reason is that a) the plays may well
depend on the cube position and b) cubeactions leads to premature
ending of the games and c) the plied evaluation of the cube may
contain suboptimal plays because of the way that cubes and moves are
handled by the gnubg engine. So what seems simple is in fact not
because of the internals of the gnubg engine, which works fine in
general, but is quite puzzling to the human mind in positions we feel
we understand well.

Christian.

```
On Fri, Dec 11, 2009 at 7:14 AM, Neil Robins <address@hidden> wrote:
In the position below I received a cube which, if taken, is for the match. I
```have on disk the Two-Sided Bearoff DB for up to 11 chequers on 6 points,
which gives:

Player Opponent
Position 4049 6690

Cubeless equity : +0.5006
Owned cube : +0.7930
Centered cube : +0.7679
Opponent owns cube : +0.4452

```
It seems to me it is trivially easy to obtain from the Cubeless equity that,
```if the game is played out for the match, my opponent will win the match
75.03% of the time and my MWC is 24.97%. The rollout indeed concurs with
these figures and, for once, 0-ply agrees as well.
```
As you increase the number of plys from 1-ply through to 7-ply, not only are all the figures wrong, but, there is a straightforward relatiosnhip of every
```ply higher being just as bad or worse than a ply lower. Analysis at 7-ply
produces the worst result. Surely this is not what should be expected,
and shouldn't all plys be bringing the correct figure here?

GNU Backgammon Position ID: tW0AAKjNAQAAAA
Match ID : AQFgAAAAAAAA
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ O: gnubg (Cube: 2)
OO | O O O O O | | | 0 points
O | O O O | | | On roll
O | O | | |
O | | | |
O | | | |
| |BAR| |^ 3 point match
X | | | |
X | | | |
X | | | |
X | X X X X | | |
X | X X X X X X | | | 0 points
+24-23-22-21-20-19------18-17-16-15-14-13-+ X: Neil

Rollout details:
Player gnubg owns 2-cube:
0.744 0.000 0.000 - 0.256 0.000 0.000 CL 62.26% CF 70.82%
[0.000 0.000 0.000 - 0.000 0.000 0.000 CL 0.00% CF 0.00%]
Player Neil owns 4-cube:
0.750 0.000 0.000 - 0.250 0.000 0.000 CL 75.03% CF 75.03%
[0.000 0.000 0.000 - 0.000 0.000 0.000 CL 0.00% CF 0.00%]
Full cubeful rollout with var.redn.
```
25920 games, Mersenne Twister dice gen. with seed 839486310 and quasi-random
```dice
Play: world class 2-ply cubeful prune [world class]
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Skip pruning for 1-ply moves.
Cube: 2-ply cubeful prune [world class]

Cube analysis
0-ply cubeless MWC 62.55% (Money: +0.501)
0.750 0.000 0.000 - 0.250 0.000 0.000
Cubeful equities:
1. Double, take 75.03%
2. Double, pass 75.08% ( 0.05%)
3. No double 72.29% ( -2.74%)
Proper cube action: Redouble, take

Cube analysis
1-ply cubeless MWC 62.28% (Money: +0.490)
0.745 0.000 0.000 - 0.255 0.000 0.000
Cubeful equities:
1. Double, take 74.48%
2. Double, pass 75.08% ( 0.60%)
3. No double 71.73% ( -2.75%)
Proper cube action: Redouble, take

Cube analysis
2-ply cubeless MWC 62.28% (Money: +0.490)
0.745 0.000 0.000 - 0.255 0.000 0.000
Cubeful equities:
1. Double, take 74.48%
2. Double, pass 75.08% ( 0.59%)
3. No double 70.73% ( -3.76%)
Proper cube action: Redouble, take

Cube analysis
3-ply cubeless MWC 62.28% (Money: +0.490)
0.745 0.000 0.000 - 0.255 0.000 0.000
Cubeful equities:
1. Double, take 74.48%
2. Double, pass 75.08% ( 0.59%)
3. No double 70.64% ( -3.85%)
Proper cube action: Redouble, take

Cube analysis
4-ply cubeless MWC 61.99% (Money: +0.478)
0.739 0.000 0.000 - 0.261 0.000 0.000
Cubeful equities:
1. Double, take 73.92%
2. Double, pass 75.08% ( 1.16%)
3. No double 70.60% ( -3.31%)
Proper cube action: Redouble, take

Cube analysis
5-ply cubeless MWC 61.79% (Money: +0.470)
0.735 0.000 0.000 - 0.265 0.000 0.000
Cubeful equities:
1. Double, take 73.51%
2. Double, pass 75.08% ( 1.57%)
3. No double 70.48% ( -3.03%)
Proper cube action: Redouble, take

Cube analysis
6-ply cubeless MWC 61.77% (Money: +0.469)
0.735 0.000 0.000 - 0.265 0.000 0.000
Cubeful equities:
1. Double, take 73.46%
2. Double, pass 75.08% ( 1.61%)
3. No double 70.44% ( -3.02%)
Proper cube action: Redouble, take
Cube analysis
7-ply cubeless MWC 61.67% (Money: +0.465)
0.733 0.000 0.000 - 0.267 0.000 0.000
Cubeful equities:
1. Double, take 73.27%
2. Double, pass 75.08% ( 1.80%)
3. No double 70.34% ( -2.94%)
Proper cube action: Redouble, take
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