Two Plus Two Forums
Sports and Games
Chess and Other Board Games
Backgammon Forum hosted by Bill Robertie.
Do you have the same bug in gnu?
07-15-2015
, 10:13 AM
I get the following rollout:
18/14 8/5 Eq.: +0,517
0,617 0,002 0,000 - 0,383 0,012 0,000 CL +0,223 CF +0,517
18/15 8/4 Eq.: +0,354 ( -0,163)
0,588 0,001 0,000 - 0,412 0,016 0,000 CL +0,162 CF +0,354
I see the merits of the first move, but can't imagine that big a difference.
07-15-2015
, 01:05 PM
Say White rolls 6-1, played 8/1, after Black plays. Regardless of what Black did, the cube action is double/take. But if Black played 18/14 8/5, White will be much closer to a pass than if Black played 18/15 8/4.
The closeness of White to the take/pass line is called "cube efficiency". The more efficient the cube, the more Black gains by using it. Like this situation, Black has a cube, but it's not very efficient, as White is miles from a pass:
Black wouldn't be much worse off if he didn't use the cube at all. It costs him something like 0.05 to hold the cube. But this situation, the cube is very efficient, as White is right on the take/pass line:
It would cost Black ten times as much, 0.50, to hold the cube.
In some situations, it's worth making a play that's lower in cubeless equity if it means you will be maximizing cube efficiency for yourself or minimizing it for your opponent. I'll post a position like this later.
The closeness of White to the take/pass line is called "cube efficiency". The more efficient the cube, the more Black gains by using it. Like this situation, Black has a cube, but it's not very efficient, as White is miles from a pass:
Black wouldn't be much worse off if he didn't use the cube at all. It costs him something like 0.05 to hold the cube. But this situation, the cube is very efficient, as White is right on the take/pass line:
It would cost Black ten times as much, 0.50, to hold the cube.
In some situations, it's worth making a play that's lower in cubeless equity if it means you will be maximizing cube efficiency for yourself or minimizing it for your opponent. I'll post a position like this later.
07-15-2015
, 01:23 PM
This will make this the theme of my next problem.
But first I have to do penance. The position I showed you is a development of problem 42, but topsy turvy. That means that the white checkers are turned into black checkers and vice versa, and the positions of both colors are turned upside down. In this way I am able to do rollouts for white.
To my big shame I have to admit that it is since recently that I also have switched the cube from one side to the other. I hope it hasn't had big consequences.
Fortunately it is also since recently that I do those rollouts, and the cube is not always turned.
But first I have to do penance. The position I showed you is a development of problem 42, but topsy turvy. That means that the white checkers are turned into black checkers and vice versa, and the positions of both colors are turned upside down. In this way I am able to do rollouts for white.
To my big shame I have to admit that it is since recently that I also have switched the cube from one side to the other. I hope it hasn't had big consequences.
Fortunately it is also since recently that I do those rollouts, and the cube is not always turned.
07-15-2015
, 01:30 PM
Oh, wait, did you just want an explanation of why Black is a lot better off after playing 18/14 8/5 and getting missed? 
The one pip closer to home makes a big difference because it means you can get by White more often and get closer to White, minimizing shots, when you do have to leave a shot. Also, you save a 4 which is useful for staying out range of White when you roll 4-1 and 4-2. Kind of big deal when getting hit loses. But the cube arguments do sort of magnify everything, equity-wise.
The one pip closer to home makes a big difference because it means you can get by White more often and get closer to White, minimizing shots, when you do have to leave a shot. Also, you save a 4 which is useful for staying out range of White when you roll 4-1 and 4-2. Kind of big deal when getting hit loses. But the cube arguments do sort of magnify everything, equity-wise.
07-15-2015
, 02:04 PM
Here's another situation where the cube efficiency arguments matter a large amount. The best play to win, and the one with the highest cubeless equity involves leaving something slotted in the homeboard. Something like 8/3* 4/3. But it doesn't lead to efficient cubes -- White will have a huge pass when he dances. If instead, Black plays 8/3*/2 and White dances, Black gets an efficient cube in. (White has a take BTW)
Cubeless, 8/3*/2 is 0.1 worse than 8/3* 4/3, but cubeful it's better by 0.06. So were seeing a huge swing on just cube efficiency arguments.
Code:
1. Rollout 8/3*/2 Eq.: +0.729
0.691 0.015 0.000 - 0.309 0.012 0.000 CL +0.384 CF +0.729
[0.001 0.000 0.000 - 0.001 0.000 0.000 CL 0.001 CF 0.003]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 747064782 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]
2. Rollout 8/3* 4/3 Eq.: +0.669 ( -0.060)
0.762 0.021 0.000 - 0.238 0.058 0.000 CL +0.489 CF +0.669
[0.000 0.000 0.000 - 0.000 0.001 0.000 CL 0.001 CF 0.002]
Full cubeful rollout with var.redn.
1296 games, Mersenne Twister dice gen. with seed 747064782 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]
07-15-2015
, 08:15 PM
And here's the cube action after each play and then a 6-1 by White.
White - Pips 69
Black - Pips 43
Black on roll. Cube action?
Created with www.BGdiagram.com
White - Pips 69
Black - Pips 43
Black on roll. Cube action?
Created with www.BGdiagram.com
Black - Pips 43
Black on roll. Cube action?
Created with www.BGdiagram.com
Code:
Analyzed in XG Roller++
Player Winning Chances: 71.95% (G:0.01% B:0.00%)
Opponent Winning Chances: 28.05% (G:0.57% B:0.01%)
Cubeless Equities: No Double=+0.433, Double=+0.871
Cubeful Equities:
No redouble: +0.597 (-0.200)
Redouble/Take: +0.797
Redouble/Pass: +1.000 (+0.203)
Best Cube action: Redouble / Take
eXtreme Gammon Version: 2.10
White - Pips 69
Black - Pips 43
Black on roll. Cube action?
Created with www.BGdiagram.com
Code:
Analyzed in XG Roller++
Player Winning Chances: 65.59% (G:0.01% B:0.00%)
Opponent Winning Chances: 34.41% (G:1.08% B:0.03%)
Cubeless Equities: No Double=+0.301, Double=+0.612
Cubeful Equities:
No redouble: +0.438 (-0.074)
Redouble/Take: +0.512
Redouble/Pass: +1.000 (+0.488)
Best Cube action: Redouble / Take
eXtreme Gammon Version: 2.10
07-15-2015
, 09:24 PM
Quote:
Oh, wait, did you just want an explanation of why Black is a lot better off after playing 18/14 8/5 and getting missed?
The one pip closer to home makes a big difference because it means you can get by White more often and get closer to White, minimizing shots, when you do have to leave a shot. Also, you save a 4 which is useful for staying out range of White when you roll 4-1 and 4-2. Kind of big deal when getting hit loses. But the cube arguments do sort of magnify everything, equity-wise.
The one pip closer to home makes a big difference because it means you can get by White more often and get closer to White, minimizing shots, when you do have to leave a shot. Also, you save a 4 which is useful for staying out range of White when you roll 4-1 and 4-2. Kind of big deal when getting hit loses. But the cube arguments do sort of magnify everything, equity-wise.
Thanks for the thorough explanation!