Excuse me but I am unable to set up positions easily, so I'm going
to describe some positions in words.
If anyone prefers diagrams, they can provide them themselves.

Suppose I have two checkers on my deuce point, and two checkers on my
ace point. Akiko has one checker on her 5 point and one checker on her
two point. It's my roll, we're playing for money, and I own the cube.

Although it might seem impossible that such a weak player as myself
could beat a world-class player like Akiko, I am clearly a favourite.
My 5 out shots are more significant than her 19/36 to 17/36 edge
when she gets to roll.
So should I double?
Call the current cube value 1. If I don't double, my equity is 5/36 from
my immediate wins. My normal numbers lead to an equity of
31/36 * (17/36 - 19/36). So my equity is 5/36 - 31/36 * 1/18 = 59/648.
And if I do double: Then she usually redoubles and we get
2 * 5/36 - 4 * 31/36 * 1/18 = 56/648. So holding is better by 1/216.

Now let's see what happens if everything's the same but all my four
checkers are on my acepoint. Then holding gives 1/6 - 5/6 * 1/18 = 13/108. Doubling gives 2 * 1/6 - 4 * 5/6 * 1/18 = 16/108. So, with this slightly better
position, doubling is better by 1/36.

The above is in the style of Mochy, who gave some endgame analysis
on youtube re some positions that are variants of standard positions
and can be calculated exactly.

I was thinking about this a bit in the taxi today, doing all the computations in my head, and getting them right. As far as I can remember, I didn't
analyse either of these positions before or see anyone else analyse them.

Paul

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On 8/21/2022 1:53 PM, peps...@gmail.com wrote:

Suppose I have two checkers on my deuce point, and two checkers on my
ace point. Akiko has one checker on her 5 point and one checker on her
two point. It's my roll, we're playing for money, and I own the cube.

Although it might seem impossible that such a weak player as myself
could beat a world-class player like Akiko, I am clearly a favourite.
My 5 out shots are more significant than her 19/36 to 17/36 edge
when she gets to roll.
So should I double?

[...]

I was thinking about this a bit in the taxi today, doing all the computations in my head, and getting them right. As far as I can remember, I didn't analyse either of these positions before or see anyone else analyse them.

Another natural question, if you like these sorts of calculations,
is whether it would be a double with a centered cube.

---
Tim Chow

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On Sunday, August 21, 2022 at 10:51:11 PM UTC+1, Tim Chow wrote:

On 8/21/2022 1:53 PM, peps...@gmail.com wrote:

Suppose I have two checkers on my deuce point, and two checkers on my
ace point. Akiko has one checker on her 5 point and one checker on her
two point. It's my roll, we're playing for money, and I own the cube.

Although it might seem impossible that such a weak player as myself
could beat a world-class player like Akiko, I am clearly a favourite.
My 5 out shots are more significant than her 19/36 to 17/36 edge
when she gets to roll.
So should I double?

[...]

I was thinking about this a bit in the taxi today, doing all the computations
in my head, and getting them right. As far as I can remember, I didn't analyse either of these positions before or see anyone else analyse them.

Another natural question, if you like these sorts of calculations,
is whether it would be a double with a centered cube.

It might be a "natural" question but it's too elementary a question for the regulars here.
Clearly we double a centered cube because we have an edge.
In these scenarios, doubling is obviously and clearly equivalent to just multiplying our edge by 2.
The only case for holding in similar positions is that it prevents the opponent doubling.

So these are obvious doubles with a centered cube.
But are they doubles with a centred cube?

The answer is no, because Brits aren't gamblers and willingly sacrifice equity to keep the stakes low.
So a double with a centered cube, but a hold with a centred cube is my answer.

Paul

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On 8/21/2022 6:14 PM, peps...@gmail.com wrote:

So these are obvious doubles with a centered cube.
But are they doubles with a centred cube?

The answer is no, because Brits aren't gamblers and willingly sacrifice equity to keep the stakes low.
So a double with a centered cube, but a hold with a centred cube is my answer.

You've lost me. Can I buy a vowel?


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

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On 8/21/2022 1:53 PM, peps...@gmail.com wrote:

Suppose I have two checkers on my deuce point, and two checkers on my
ace point. Akiko has one checker on her 5 point and one checker on her
two point. It's my roll, we're playing for money, and I own the cube.

Here's the position:

XGID=-BB-----------------a--a--:1:1:1:00:0:0:3:0:10

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

The short answer is that you don't cube since you have to eat an 8 cube
when you roll one of the 31 numbers that don't win immediately, and
you're not favored to win.

It's close though and a good practical double against a human since some
will pass. But not Akiko.


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

--- SoupGate-Win32 v1.05
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On 8/21/2022 7:45 PM, ah....Clem wrote:

On 8/21/2022 6:14 PM, peps...@gmail.com wrote:

So these are obvious doubles with a centered cube.
But are they doubles with a centred cube?

The answer is no, because Brits aren't gamblers and willingly
sacrifice equity to keep the stakes low.
So a double with a centered cube, but a hold with a centred cube is my
answer.

You've lost me. Can I buy a vowel?

Only if you pay in pounds.

---
Tim Chow

--- SoupGate-Win32 v1.05
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On Monday, August 22, 2022 at 12:57:54 AM UTC+1, ah....Clem wrote:

On 8/21/2022 1:53 PM, peps...@gmail.com wrote:

Suppose I have two checkers on my deuce point, and two checkers on my
ace point. Akiko has one checker on her 5 point and one checker on her
two point. It's my roll, we're playing for money, and I own the cube.

Here's the position:

XGID=-BB-----------------a--a--:1:1:1:00:0:0:3:0:10

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

The short answer is that you don't cube since you have to eat an 8 cube
when you roll one of the 31 numbers that don't win immediately, and
you're not favored to win.

It's close though and a good practical double against a human since some
will pass. But not Akiko.

You don't cube but you have to actually do the calculations (like I did) to conclude this. You do cube with all four on the acepoint even though there's the same basic characteristic of you being an underdog unless you roll a major joker.

It's a good practical double for a completely different reason. Of course, no one will
pass. I mean they may but it's extremely unlikely. It's much too obvious a take.

The good practical point is very different: Your opponent might not redouble when you don't
roll one of your 5 jokers (for example, they might be intimidated by the stakes). Just for fun, let's
work out what your opponent's no-redouble probability needs to be for you to have a cube.
Let this no-redouble probability be s (for sailing which Walt loves).
The hold equity is 59/648. The cubing equity is 2 * 5/36 - 31/36 (4 * (1 - s) + 2s) * 1/18 =
5/18 - 31/162 + 31s/324. As a sanity check, when s = 0, we get 56/648 which I calculated earlier.
It's a double if 31s/324 > 1/216 which is the same as s > 324/(216 * 31) = 3/62 which is slightly less
than 5%. I think s is at least this in practice. (The opponent might not bother doubling because they're
in a rush as they're desperately eager to go sailing as soon as the game finishes.)

Paul

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"peps...@gmail.com" <pepstein5@gmail.com> writes:

Suppose I have two checkers on my deuce point, and two checkers on my
ace point. Akiko has one checker on her 5 point and one checker on her
two point. It's my roll, we're playing for money, and I own the cube.

To my (slight) surprise, my Isight method gives a RD/T for this, which
is wrong by 0.005, but correct if there is an 0.5 % chance that the
opponent will pass.

Now let's see what happens if everything's the same but all my four
checkers are on my acepoint.

Here, my Isight method gives a D/T, but no RD/T. To hold the cube is
wrong by 0.028. I can live with this size of errors, the small size of
which were the reason for my surprise, since non'ana;ytical methods
break down considerably for sub-10-length races. But see section 5.4,
"Comments on Cub-offs", which might be very relevant for non-worldclass
mental calculators, especially when the clock is ticking.

Best regards

Axel

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On Sunday, August 28, 2022 at 10:38:16 AM UTC+1, Axel Reichert wrote:

"peps...@gmail.com" <peps...@gmail.com> writes:

Suppose I have two checkers on my deuce point, and two checkers on my
ace point. Akiko has one checker on her 5 point and one checker on her
two point. It's my roll, we're playing for money, and I own the cube.

To my (slight) surprise, my Isight method gives a RD/T for this, which
is wrong by 0.005, but correct if there is an 0.5 % chance that the
opponent will pass.

Now let's see what happens if everything's the same but all my four checkers are on my acepoint.

Here, my Isight method gives a D/T, but no RD/T. To hold the cube is
wrong by 0.028. I can live with this size of errors, the small size of
which were the reason for my surprise, since non'ana;ytical methods
break down considerably for sub-10-length races. But see section 5.4, "Comments on Cub-offs", which might be very relevant for non-worldclass mental calculators, especially when the clock is ticking.

Best regards

Axel

Interesting thoughts.
As I said earlier, the practical reason for doubling these positions where the hold is correct,
isn't that the opponent might pass.
The more relevant probability is the probability that the opponent fails to correctly redouble.
This is a more realistic failure on the part of the opponent, particularly when you bear in
mind the tendency for people to play for more than they can really afford.
This probability also needs only to be very small to justify a practical double. (I do the exact
calculation above).

Paul

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