Blitz versus prime cube action

[Timothy Chow]

XGID=aBBCCC--------A-bbbddA----:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+
| X O O O | | O O X |
| O O O | | O O |
| | | O O |
| | | O O |
| | | |
| |BAR| |
| | O | |
| | | |
| | | X X X | +---+
| | | X X X X X | | 2 |
| | | X X X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 77 O: 117 X-O: 0-0
Cube: 2, X own cube
X on roll, cube action

---
Tim Chow

[Robert Zimmerman]

With the cube in the center this should be a double by O'Hagan's rule: 11/36 get X over the prime and in good shape. 11/36 then get O in and maybe 1/3 of the time after that X will wind up being hit and back behind the prime. So 11/36 (1-(11/36 * 1/3)) = 27% would be my crude guess for O's winning chances. What I don't know is how much cube ownership is worth in a situation like this that can remain volatile. I'm guessing that it's valuable enough to hang onto the cube and not redouble.

Bob

[peps...@gmail.com]

You have to consider the gammons, too.

D/T for me, with a fair amount of confidence but I can't be bothered to justify it.

Paul

[peps...@gmail.com]

On Sunday, March 5, 2023 at 6:37:06 PM UTC, Robert Zimmerman wrote:

I don't think estimating the winning chances is practical here.
It's clear to me that it's a huge double.
Having said that, plenty of things that are "clear to me" are in fact false --
I'm not saying "you're wrong", just explaining my thought processes.

One thing is that our sixes seem to win us quite a few gammons bearing in mind the
extra six crossovers in addition to the checker at the bar.
Superficially, it seems there's a kind of symmetry. Whoever gets the first six has a great
position. But our sixes are far stronger than the opponent's sixes. If our opponent enters first,
our straggler will be difficult to contain without us getting shots.


Paul

[Robert Zimmerman]

Yeah, I can see your point about trying to calculate winning chances, and gammons for that matter. Maybe approaching futility without a reference position?
O'Hagan's rule (would love to know how it was derived) says double from a centered cube when you have 9 out of 36 market losing sequences, provided you still have a good game going if you don't roll one of those market losers. It applies to situations that are a challenge to evaluate by position, race, threats. This is definitely a double from the center by those criteria. But any ideas on how to adjust for cube ownership? It seems intuitive to hold onto the cube when you think some volatility will persist for another sequence or two or three. Is that correct?
Thanks,
Bob

[Timothy Chow]

Bob mentioned O'Hagan's law, and I think this is a pretty good
example of it. (By the way, I don't think that O'Hagan "derived"
it; I believe it's just a rule of thumb that he came up with by
experimental observation.) Any 6 is a huge market loser, and even
if X doesn't roll an immediate 6, he's still doing okay. Even if
O enters and hits loose, X gets a return shot.

Analyzed in Rollout
No redouble
Player Winning Chances: 67.71% (G:11.93% B:0.03%)
Opponent Winning Chances: 32.29% (G:2.30% B:0.05%)
Redouble/Take
Player Winning Chances: 68.35% (G:12.31% B:0.03%)
Opponent Winning Chances: 31.65% (G:2.14% B:0.04%)

Cubeful Equities:
No redouble: +0.593 (-0.082)
Redouble/Take: +0.675
Redouble/Pass: +1.000 (+0.325)

Best Cube action: Redouble / Take

Rollout:
1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves: 3-ply, cube decisions: XG Roller
Confidence No Double: ± 0.010 (+0.583..+0.603)
Confidence Double: ± 0.012 (+0.663..+0.687)

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow

[peps...@gmail.com]

It's not an enormous double -- only 0.08 equity is lost by holding which isn't huge by normal non-expert
standards of cube play.

What mistakes may you have made by holding? Well, the fact that the opponent has those ugly 4 stacks on the 6 and 5,
compromising their ability to attack our blot is a highly significant and unusual feature of the position.
More usual positions would be easier to evaluate. So I would suggest mentally improving the opponent's position by
taking one each off the 6 and 5 and smoothing by putting them on the 7 and 8.
If your conclusion is that this new standardised position is "almost a double but not quite" then clearly the position in
the thread becomes a double because the position in the thread greatly improves on the standardised variant.

I would guess that your mistake is not to pay enough attention to the ugly non-smooth nature of the opponent's prime.
And variantization with more standard positions is a great technique. Tim is a world-class master at constructing
variantizations and I'm sure it serves his backgammon well.

Paul

[Robert Zimmerman]

Thanks, Paul. I think my error was not to recognize that even if X fails to jump the prime this roll and O then comes in with a 6, the strength of the position often does not warrant a redouble from O on her next roll. So cube ownership for X is not so valuable we should hold onto the cube.

Bob

[Timothy Chow]

On 3/6/2023 8:09 AM, Robert Zimmerman wrote:
> Thanks, Paul. I think my error was not to recognize that even if X fails to jump the prime this roll and O then comes in with a 6, the strength of the position often does not warrant a redouble from O on her next roll. So cube ownership for X is not so valuable we should hold onto the cube.

Other than in pure races, I have found relatively few situations
in which the computer says to double but not redouble (for money,
of course---matches are an entirely different matter), and by and
large, such situations are so subtle that I don't think it's worth
trying to master them.

Sending the cube in a priming battle can be scary because there
can be sudden huge swings, but even in priming battles, I think
you have to work pretty hard to find positions where the computer
thinks it's a double but not a redouble.

---
Tim Chow

[peps...@gmail.com]

My laptop with XG doesn't work so I can't try this myself.
But how about this one from the opening?
I run with an opening 64. You roll 55 and I dance.
If you already had the cube, shouldn't you hold?

Paul

[Stick Rice]

There is no shortage of positions of all types where it's an initial cube but not a recube for unlimited play. Fairly common.

Stick

[Robert Zimmerman]

Why is the original position not one of those?
Bob

Lohengrin: Prelude to Act I, Claudio Abbado, Chor der Winer Staatsoper & Vienna Philharmonic

[peps...@gmail.com]

I don't understand why you're asking this question. A huge number of justifications have
already been given on this thread for doubling.
Your reasoning should lead you to conclude that holding initially is a greater mistake
than holding when you own the cube, but your reasoning does nothing to indicate
that holding when you own the cube is correct.

Paul

[peps...@gmail.com]

That's what I thought, too.

Paul

[Timothy Chow]

I don't disagree. This doesn't contradict what I said.

---
Tim Chow

[Robert Zimmerman]

Here's your answer.

XGID=aB-B--C-A--aeE---c-e----B-:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+

| X O | | O X |
| X O | | O X |
| X O | | O |
| X | | O |
| X | | O |
| |BAR| |
| O | O | |
| O | | |
| O | | X | +---+
| O | | X X X | | 2 |
| O O X | | X X X | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 147 O: 158 X-O: 0-0

Cube: 2, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble

Player Winning Chances: 63.76% (G:33.75% B:0.46%)
Opponent Winning Chances: 36.24% (G:7.47% B:0.44%)
Redouble/Take
Player Winning Chances: 63.91% (G:34.35% B:0.44%)
Opponent Winning Chances: 36.09% (G:7.49% B:0.38%)

Cubeless Equities: No Double=+0.538, Double=+1.095

Cubeful Equities:
No redouble: +0.763 (-0.041)
Redouble/Take: +0.804
Redouble/Pass: +1.000 (+0.196)

Best Cube action: Redouble / Take

Rollout:

822 Games rolled with Variance Reduction.

Moves: 3-ply, cube decisions: XG Roller

Confidence No Double: ± 0.014 (+0.749..+0.778)
Confidence Double: ± 0.025 (+0.780..+0.829)

Double Decision confidence: 99.7%
Take Decision confidence: 100.0%

Duration: 7 minutes 23 seconds

eXtreme Gammon Version: 2.10

[Robert Zimmerman]

I was looking for input from a local expert. The deluge of answers to my question weren't sufficient to wash it away. It just kept floating to the top. But I can let it go. *But First!*: Here's an example I've concocted for those who have the appetite.
I think this one has sufficient enduring volatility that it warrants holding the cube. Well, that's my explanation.
Bob

X owns Cube
------------------------------------------
XGID=a--bBCCBAB------bbabbcA-A-:1:1:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+

| O O O | | O O O X X |

| O O | | O O O |
| | | O |
| | | |
| | | |

| |BAR| |
| | O | |
| | | |
| | | X X | +---+
| X X | | X X X O | | 2 |
| X X X | | X X X O | +---+
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 127 O: 144 X-O: 0-0

Cube: 2, X own cube
X on roll, cube action

Analyzed in Rollout
No redouble

Player Winning Chances: 65.19% (G:26.50% B:1.02%)
Opponent Winning Chances: 34.81% (G:7.62% B:0.38%)
Redouble/Take
Player Winning Chances: 65.40% (G:26.01% B:1.04%)
Opponent Winning Chances: 34.60% (G:7.80% B:0.38%)

Cubeless Equities: No Double=+0.499, Double=+0.993

Cubeful Equities:
No redouble: +0.739
Redouble/Take: +0.706 (-0.033)
Redouble/Pass: +1.000 (+0.261)

Best Cube action: No redouble / Take
Percentage of wrong pass needed to make the double decision right: 10.0%

Rollout:
548 Games rolled with Variance Reduction.

Moves: 3-ply, cube decisions: XG Roller

Confidence No Double: ± 0.015 (+0.724..+0.753)
Confidence Double: ± 0.028 (+0.678..+0.734)

Double Decision confidence: 97.8%
Take Decision confidence: 100.0%

Duration: 2 minutes 39 seconds

eXtreme Gammon Version: 2.10


Cube in Center
---------------------------------

XGID=a--bBCCBAB------bbabbcA-A-:0:0:1:00:0:0:0:0:10

Score is X:0 O:0. Unlimited Game
+13-14-15-16-17-18------19-20-21-22-23-24-+

| O O O | | O O O X X |

| O O | | O O O |
| | | O |
| | | |
| | | |

| |BAR| |
| | O | |
| | | |
| | | X X |
| X X | | X X X O |
| X X X | | X X X O |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 127 O: 144 X-O: 0-0
Cube: 1

X on roll, cube action

Analyzed in Rollout
No double
Player Winning Chances: 65.17% (G:26.60% B:1.02%)
Opponent Winning Chances: 34.83% (G:7.60% B:0.37%)
Double/Take
Player Winning Chances: 65.31% (G:26.48% B:1.08%)
Opponent Winning Chances: 34.69% (G:7.73% B:0.37%)

Cubeless Equities: No Double=+0.500, Double=+1.002

Cubeful Equities:
No double: +0.687 (-0.033)
Double/Take: +0.720
Double/Pass: +1.000 (+0.280)

Best Cube action: Double / Take

Rollout:
1139 Games rolled with Variance Reduction.

Moves: 3-ply, cube decisions: XG Roller

Confidence No Double: ± 0.012 (+0.675..+0.698)
Confidence Double: ± 0.020 (+0.700..+0.739)

Double Decision confidence: 99.8%
Take Decision confidence: 100.0%

Duration: 5 minutes 56 seconds

eXtreme Gammon Version: 2.10

[peps...@gmail.com]

Thanks a lot for this.
So my attempt at an example doesn't work but it is only 0.04
away from working.

If the position is further changed by letting the underdog play two further aces from their six point to their 5 point,
then we may get a position that's an initial double only.

Paul

[peps...@gmail.com]

In my opinion, the only active poster here with any reasonable claim to expertise is Stick.
Sometimes I'm impressed by Tim's analyses but sometimes not.

If you own the cube, there are two things to consider:
1) How good is your position?
2) How much recube vig would the cube give the opponent (similar to your mention of volatility).

When you combine 1) and 2), you get a cube and the strengths of your position (the original position) have been explained
in detail here.
For an initial cube, the opponent has cube access anyway so there's less of a downside to cubing.
So the cubing is clearer in the initial case than the non-initial case but that doesn't mean that we
should be surprised that it's also a recube.

Your rollouts (for the new position) don't look extensive enough to reach a conclusion. I think it's a redouble despite your
preliminary results.

Paul

[Robert Zimmerman]

> Your rollouts (for the new position) don't look extensive enough to reach a conclusion. I think it's a redouble despite your
> preliminary results.
>
> Paul

People go for open heart surgery based on studies that accept 95% confidence intervals as solid evidence. And about 1% die of complications. The world is a safer place with me not working for NASA, but if I did I would want 10 studies with 99.999999999% confidence before launch. For purposes of illustrating a point in a board game, I can settle for 97.8%.
Bob