GNU Backgammon Position ID: b28DAEB3bocAAA
Match ID : AQFgAXAAAAAE
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ O: gnubg (Cube: 2)
| O O O O O | | O | 7 points
| O O O O O | | | On roll
| O O O O | | |
| | | |
| | | |
| |BAR| |^ 11 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: axel
Pip counts: O 59, X 63

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On 2/9/2023 1:42 AM, Axel Reichert wrote:

GNU Backgammon Position ID: b28DAEB3bocAAA
Match ID : AQFgAXAAAAAE
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ O: gnubg (Cube: 2)
| O O O O O | | O | 7 points
| O O O O O | | | On roll
| O O O O | | |
| | | |
| | | |
| |BAR| |^ 11 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: axel
Pip counts: O 59, X 63

Coincidentally, I faced a similar cube decision yesterday.
The score was exactly the same as it is here; X needs about
6/57, or a little over 10%, to take. (Stick, perhaps, calls
this the "live" cube takepoint, whatever that means.) If X
were closed out then it would be a huge pass, but it's not
so easy for O to complete the closeout, so X has some persistent
chances of hitting a shot or even just winning the race. Hard
to judge, but I'd guess that X has between 10% and 15% chances
of winning, so I'd take.

---
Tim Chow

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On Thursday, February 9, 2023 at 9:21:11 AM UTC-5, Timothy Chow wrote:

On 2/9/2023 1:42 AM, Axel Reichert wrote:

GNU Backgammon Position ID: b28DAEB3bocAAA
Match ID : AQFgAXAAAAAE
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ O: gnubg (Cube: 2)
| O O O O O | | O | 7 points
| O O O O O | | | On roll
| O O O O | | |
| | | |
| | | |
| |BAR| |^ 11 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: axel
Pip counts: O 59, X 63

Coincidentally, I faced a similar cube decision yesterday.
The score was exactly the same as it is here; X needs about
6/57, or a little over 10%, to take. (Stick, perhaps, calls
this the "live" cube takepoint, whatever that means.) If X
were closed out then it would be a huge pass, but it's not
so easy for O to complete the closeout, so X has some persistent
chances of hitting a shot or even just winning the race. Hard
to judge, but I'd guess that X has between 10% and 15% chances
of winning, so I'd take.

---
Tim Chow

You know the dead cube take point in money games is 25% right? You know the live cube take point is a lot lower than that, generally accepted as ~22% but it fluctuated depending on how much use one might gain from cube ownership right? I don't
understand what you're not understanding. A lot of times we of course skip over saying *live cube take point* and simplify to *take point* which is fine but there are definitely times when the distinction needs to be made so I don't see what your
problem is with it.

Stick

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On 2/9/2023 1:42 AM, Axel Reichert wrote:

GNU Backgammon Position ID: b28DAEB3bocAAA
Match ID : AQFgAXAAAAAE
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ O: gnubg (Cube: 2)
| O O O O O | | O | 7 points
| O O O O O | | | On roll
| O O O O | | |
| | | |
| | | |
| |BAR| |^ 11 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: axel
Pip counts: O 59, X 63

I don't play very many 11 point matches, so 4a 11a is not a score that
I'm familiar with. But it seems to me that doubled gammons are fairly
valuable and since the cube is already turned to 2 and O has some (but
not many) gammon chances holding looks reasonable.

If O ships it, and X takes then the cube is going to 8. Can O risk that?
Yeah, I think so, and since the gammons are so few it looks correct.

Can X take? 2a 11a gives about a 6% MWC and with the race nearly even
and the open three point, looks like a take.

R/T for me. Without much confidence.

--
Ah....Clem
The future is fun, the future is fair.

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On 2/9/2023 2:52 PM, Stick Rice wrote:

You know the dead cube take point in money games is 25% right? You know the live cube take point is a lot lower than that, generally accepted as ~22% but it fluctuated depending on how much use one might gain from cube ownership right? I don't

understand what you're not understanding.

I don't understand why one would use the adjective "live cube"
to refer to a dead cube.

---
Tim Chow

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On Friday, February 10, 2023 at 2:29:32 PM UTC, Timothy Chow wrote:

On 2/9/2023 2:52 PM, Stick Rice wrote:

You know the dead cube take point in money games is 25% right? You know the live cube take point is a lot lower than that, generally accepted as ~22% but it fluctuated depending on how much use one might gain from cube ownership right? I don't

understand what you're not understanding.

I don't understand why one would use the adjective "live cube"
to refer to a dead cube.

I don't think the mandatory match redouble cubes are either live or dead.
This is how I would define these terms. (Of course, correct me if I'm wrong). A live cube means (to me) that the cube (if taken) stays with the opponent
for an indeterminate period of time and is an asset to the opponent.
(Hence the naive 25% take rule in money play (assuming no gammons) is an overestimate although it's a good first approximation to teach beginners.)
A dead cube means (to me) that, assuming competent play, doubling is
either pointless or illegal. So, for money play, in no-gammon situations
(like any interesting race), 25% is exactly the dead-cube take point.
Usually, a dead-cube take point functions as a theoretical construct,
I would think, as an aid to thinking about the live cube situation which is
far more common.

Here, we don't have a dead cube or a live cube in my opinion.
This follows the general rule: When two adults are arguing with each
other, the most usual thing is that there's a degree of right and wrong
on both sides. Most of the Stick/Tim debates are like that, in my
judgment, despite Stick's much greater bg abilities and reputation.

Paul

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On 2/11/2023 9:54 AM, [email protected] wrote:

Here, we don't have a dead cube or a live cube in my opinion.
This follows the general rule: When two adults are arguing with each
other, the most usual thing is that there's a degree of right and wrong
on both sides. Most of the Stick/Tim debates are like that, in my
judgment, despite Stick's much greater bg abilities and reputation.

The issue under debate wasn't the term "live cube" itself, but the
term "live cube take point."

I don't mind using the term "live cube" in certain situations; it's
an informal term, and useful just like any other informal term.

The term "live cube take point," on the other hand, conveys the
impression that it's something quantitative that can be calculated,
and that depends only on the match score and cube location. For
starters, as you say, there are match scores and cube locations in
which calling the cube "live" makes very little sense. A fortiori,
"live cube take point" makes very little sense in such situations.
You can always assign the phrase some meaning, but why would you?
It just causes confusion.

But even setting that aside, the fundamental problem is that when
there really is (arguably) a "live cube," any attempt to define a
"live cube take point" must take into account recube vig, and the
key point is that *recube vig depends on the specific position*.
If you insist on defining "live cube take point" anyway, then you
have one of two choices:

1. Make the "live cube take point" depend on the specific position
and not just on the match score and cube location.

2. Choose some figure for "recube vig" that you apply indiscriminately
to all positions at that match score and cube location.

Option 1 flies in the face of how the term "take point" is normally
used, and I don't think anyone selects this option. Option 2 is thus
the only real option, but it suffers from several problems. First and foremost, rarely if ever does anybody explain clearly how the recube
vig is calculated. If I go into XG's menu about cube information,
nowhere is recube vig even mentioned. The "dead cube take point" can
be calculated from the match equity table, so the user is given the
impression that the "live cube take point" should be as well, and is
left confused. The second problem is, given that recube vig varies
from position to position, I think it makes far more sense to give a
range of values, rather than just assume a single value once and for
all. The terminology "live cube take point" just reinforces the
impression that recube vig is a fixed quantity, which is simply not
true.

As a compromise, I'd be okay with the terminology "average take point"
instead of "live cube take point." That terminology at least prompts
the user to ask, "average over what?" (with the answer being "average
over different values of the recube vig) and encourages understanding,
rather than blind faith in bot numbers.

---
Tim Chow

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Axel Reichert <[email protected]> writes:

GNU Backgammon Position ID: b28DAEB3bocAAA
Match ID : AQFgAXAAAAAE
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ O: gnubg (Cube: 2)
| O O O O O | | O | 7 points
| O O O O O | | | On roll
| O O O O | | |
| | | |
| | | |
| |BAR| |^ 11 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: axel
Pip counts: O 59, X 63

The subject line was referring to METs for skewed player skills. This
rollout is for the "standard" Kazaross XG 2 MET:

Rollout cubeless equity +0.842 (Money: +0.845)

Cubeful equities:
1. Double, pass +1.000
2. Double, take +1.194 (+0.194)
3. No double +0.975 (-0.025)
Proper cube action: Redouble, pass

Rollout details:
Player gnubg owns 2-cube:
0.916 0.013 0.000 - 0.084 0.000 0.000 CL +0.842 CF +0.975
[0.001 0.000 0.000 - 0.001 0.000 0.000 CL 0.002 CF 0.002]
Player axel owns 4-cube:
0.920 0.013 0.000 - 0.080 0.000 0.000 CL +1.482 CF +1.194
[0.001 0.000 0.000 - 0.001 0.000 0.000 CL 0.005 CF 0.010]
Truncated cubeful rollout (depth 6) with variance reduction
139 games, Mersenne Twister dice gen. with seed 449002682 and quasi-random dice
Stop when std.errs. are small enough: limit 0.0100 (min. 36 games)
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]
Different evaluations after 2 plies:
Play: 1-ply cubeful
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Cube: 2-ply cubeful prune [world class]

And now for the player on roll (gnubg) having a 100 ELO advantage
(probably overestimating my skill):

Rollout cubeless equity +0.841 (Money: +0.847)

Cubeful equities:
1. No double +0.934
2. Double, pass +1.000 (+0.066)
3. Double, take +0.887 (-0.047)
Proper cube action: No redouble, take (41.7%)

Rollout details:
Player gnubg owns 2-cube:
0.917 0.013 0.000 - 0.083 0.000 0.000 CL +0.841 CF +0.934
[0.001 0.000 0.000 - 0.001 0.000 0.000 CL 0.002 CF 0.002]
Player axel owns 4-cube:
0.920 0.014 0.000 - 0.080 0.000 0.000 CL +1.291 CF +0.887
[0.001 0.000 0.000 - 0.001 0.000 0.000 CL 0.004 CF 0.010]
Truncated cubeful rollout (depth 6) with variance reduction
175 games, Mersenne Twister dice gen. with seed 449002682 and quasi-random dice
Stop when std.errs. are small enough: limit 0.0100 (min. 36 games)
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]
Different evaluations after 2 plies:
Play: 1-ply cubeful
keep the first 0 0-ply moves and up to 8 more moves within equity 0.16
Cube: 2-ply cubeful prune [world class]

In my opinion METs are the elephant in the room: Even for club buddies I
know for years I have only a vague idea who is the better player, and if
so, by how much (50 ELO, -100 ELO?). As this example shows, that is
easily the difference between doubling being almost a whopper and taking
being a double whopper.

Races are easy to play, hence match equity calculations make sense
there.

Best regards

Axel

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On 2/15/2023 2:56 AM, Axel Reichert wrote:

Races are easy to play, hence match equity calculations make sense
there.

Nice example. I agree that races are probably the type of position
where a fish MET is the most instructive. But there's still a lot
of handwaving, even if you have accurate Elo estimates. In particular,
while the checker play in a race is usually easy, the cube action is
not. So really, one should factor in some estimate of how likely the
player is to make correct cube decisions in subsequent play. This can
be difficult.

---
Tim Chow

--- SoupGate-Win32 v1.05
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On Thursday, February 16, 2023 at 3:02:19 PM UTC, Timothy Chow wrote:

On 2/15/2023 2:56 AM, Axel Reichert wrote:

Races are easy to play, hence match equity calculations make sense
there.

Nice example. I agree that races are probably the type of position
where a fish MET is the most instructive. But there's still a lot
of handwaving, even if you have accurate Elo estimates. In particular,
while the checker play in a race is usually easy, the cube action is
not. So really, one should factor in some estimate of how likely the
player is to make correct cube decisions in subsequent play. This can
be difficult.

I'd like to clarify that. Optimal checker play in a race is actually incredibly
difficult. Plays that look equivalent will differ in equity by 0.0001 (for example)
and no one will know why. The easy thing is playing your checkers in a race so that you never make an error that is worse than 0.01.

Paul

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On 2/24/2023 5:12 PM, [email protected] wrote:

On Thursday, February 16, 2023 at 3:02:19 PM UTC, Timothy Chow wrote:

On 2/15/2023 2:56 AM, Axel Reichert wrote:

Races are easy to play, hence match equity calculations make sense
there.

Nice example. I agree that races are probably the type of position
where a fish MET is the most instructive. But there's still a lot
of handwaving, even if you have accurate Elo estimates. In particular,
while the checker play in a race is usually easy, the cube action is
not. So really, one should factor in some estimate of how likely the
player is to make correct cube decisions in subsequent play. This can
be difficult.

I'd like to clarify that. Optimal checker play in a race is actually incredibly
difficult. Plays that look equivalent will differ in equity by 0.0001 (for example)
and no one will know why. The easy thing is playing your checkers in a race so
that you never make an error that is worse than 0.01.

Yes, I agree, with the caveat that it's certainly not uncommon to
see people botch plays like the one below.

XGID=-HCB--A--A---------cbcaba-:1:-1:1:21:0:0:0:0:10

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 | +---+
| | | O O O O | | 2 |
| | | O O | +---+
| | | |
| | | |
| |BAR| |
| | | 8 |
| | | X |
| | | X X |
| | | X X X |
| X | | X X X X |
+12-11-10--9--8--7-------6--5--4--3--2--1-+
Pip count X: 35 O: 48 X-O: 0-0
Cube: 2, O own cube
X to play 21

1. Rollout¹ 9/8 6/4 eq:-0.762
Player: 27.33% (G:0.00% B:0.00%)
Opponent: 72.67% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.766..-0.759) - [100.0%]

2. Rollout¹ 9/7 6/5 eq:-0.850 (-0.088)
Player: 25.47% (G:0.00% B:0.00%)
Opponent: 74.53% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.853..-0.847) - [0.0%]

3. Rollout¹ 6/3 eq:-0.887 (-0.125)
Player: 24.67% (G:0.00% B:0.00%)
Opponent: 75.33% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.890..-0.884) - [0.0%]

4. Rollout¹ 6/4 3/2 eq:-0.890 (-0.128)
Player: 24.61% (G:0.00% B:0.00%)
Opponent: 75.39% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.893..-0.887) - [0.0%]

5. Rollout¹ 6/4 2/1 eq:-0.917 (-0.155)
Player: 24.05% (G:0.00% B:0.00%)
Opponent: 75.95% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.920..-0.914) - [0.0%]

6. Rollout¹ 9/6 eq:-0.963 (-0.201)
Player: 23.02% (G:0.00% B:0.00%)
Opponent: 76.98% (G:0.00% B:0.00%)
Confidence: ±0.003 (-0.966..-0.960) - [0.0%]

¹ 1296 Games rolled with Variance Reduction.
Dice Seed: 271828
Moves and cube decisions: 4-ply

eXtreme Gammon Version: 2.19.211.pre-release

---
Tim Chow

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