If you've really got absolutely nothing better to do, you might like to
think about all three possible symmetric races where:
1) The on-roll player has the cube.
2) The pip count for each player is 7.
3) Each player has exactly two checkers.

If the checkers are on the points 6 and 1, it's a pass.
Otherwise it's a take.
With the checkers on 5 and 2, it's a bigger take than with
the checkers on 4 and 3. Note that with the checkers on 5 and 2,
it's a redouble whenever the on-roll player doesn't immediately bearoff.
All positions need 3 rolls to bear off iff the first two rolls are 21,
1 roll to bear off if the player immediately bears off (duh!)
and 2 rolls to bear off otherwise.
This means that the EPC depends only on the number of out shots.
There are 19 outshots in the 5, 2 position, 17 in the 4, 3 position
and 15 in the 6, 1 position.
So the higher the EPC, the worse for the off-roll player.

This seems paradoxical to me but I recently had a croissant and two
fried eggs for breakfast and used the croissant to mop up the left over yolk,
so I may not be a reliable source of info.

Paradoxical because in a symmetrical position, a person might naively
expect that the longer the race, the more chances the underdog has.
But these three positions go in exactly the other direction.

Thanks for listening. And thank you just as much if you didn't listen at all.

Paul

On October 14, 2023 at 6:08:18 PM UTC-6, peps...@gmail.com wrote:

> Thanks for listening. And thank you
> just as much if you didn't listen at all.

In either case, you must be thanking
"a certain Tim" for listening or not, as
your subject title infers that everyone
else are lesser players who might not
be interested, just like I wasn't ;).

And I have this hunch that "your Tim"
is the one with a math PHD; "RGB's
infamous Tim The Math-Giver" who
gave us "The 21^7 < 2^32 < 21^8"... :)

If that's the case, then I have a strange
suspicion that you intended to give him
a private math lesson by discouraging
everyone else as lesser players, (which
adds injury to insult), but you sent your
email to RGB by mistake... ;)

MK

On Sunday, October 15, 2023 at 5:18:48 AM UTC+1, MK wrote:
> On October 14, 2023 at 6:08:18 PM UTC-6, peps...@gmail.com wrote:
>
> > Thanks for listening. And thank you
> > just as much if you didn't listen at all.
> In either case, you must be thanking
> "a certain Tim" for listening or not, as
> your subject title infers that everyone
> else are lesser players who might not
> be interested, just like I wasn't ;).
>
> And I have this hunch that "your Tim"
> is the one with a math PHD; "RGB's
> infamous Tim The Math-Giver" who
> gave us "The 21^7 < 2^32 < 21^8"... :)
>
> If that's the case, then I have a strange
> suspicion that you intended to give him
> a private math lesson by discouraging
> everyone else as lesser players, (which
> adds injury to insult), but you sent your
> email to RGB by mistake... ;)
>
> MK
Thanks for your feedback.
I didn't mean what you thought I meant.

I will change the title of the thread.

Paul

On Sunday, October 15, 2023 at 1:08:18 AM UTC+1, peps...@gmail.com wrote:
> If you've really got absolutely nothing better to do, you might like to
> think about all three possible symmetric races where:
> 1) The on-roll player has the cube.
> 2) The pip count for each player is 7.
> 3) Each player has exactly two checkers.
>
> If the checkers are on the points 6 and 1, it's a pass.
> Otherwise it's a take.
> With the checkers on 5 and 2, it's a bigger take than with
> the checkers on 4 and 3. Note that with the checkers on 5 and 2,
> it's a redouble whenever the on-roll player doesn't immediately bearoff.
> All positions need 3 rolls to bear off iff the first two rolls are 21,
> 1 roll to bear off if the player immediately bears off (duh!)
> and 2 rolls to bear off otherwise.
> This means that the EPC depends only on the number of out shots.
> There are 19 outshots in the 5, 2 position, 17 in the 4, 3 position
> and 15 in the 6, 1 position.
> So the higher the EPC, the worse for the off-roll player.
>
> This seems paradoxical to me but I recently had a croissant and two
> fried eggs for breakfast and used the croissant to mop up the left over yolk,
> so I may not be a reliable source of info.
>
> Paradoxical because in a symmetrical position, a person might naively
> expect that the longer the race, the more chances the underdog has.
> But these three positions go in exactly the other direction.
>
> Thanks for listening. And thank you just as much if you didn't listen at all.
>
> Paul

On Sunday, October 15, 2023 at 12:09:40 PM UTC+1, peps...@gmail.com wrote:
> On Sunday, October 15, 2023 at 1:08:18 AM UTC+1, peps...@gmail.com wrote:
> > If you've really got absolutely nothing better to do, you might like to
> > think about all three possible symmetric races where:
> > 1) The on-roll player has the cube.
> > 2) The pip count for each player is 7.
> > 3) Each player has exactly two checkers.
> >
> > If the checkers are on the points 6 and 1, it's a pass.
> > Otherwise it's a take.
> > With the checkers on 5 and 2, it's a bigger take than with
> > the checkers on 4 and 3. Note that with the checkers on 5 and 2,
> > it's a redouble whenever the on-roll player doesn't immediately bearoff..
> > All positions need 3 rolls to bear off iff the first two rolls are 21,
> > 1 roll to bear off if the player immediately bears off (duh!)
> > and 2 rolls to bear off otherwise.
> > This means that the EPC depends only on the number of out shots.
> > There are 19 outshots in the 5, 2 position, 17 in the 4, 3 position
> > and 15 in the 6, 1 position.
> > So the higher the EPC, the worse for the off-roll player.
> >
> > This seems paradoxical to me but I recently had a croissant and two
> > fried eggs for breakfast and used the croissant to mop up the left over yolk,
> > so I may not be a reliable source of info.
> >
> > Paradoxical because in a symmetrical position, a person might naively
> > expect that the longer the race, the more chances the underdog has.
> > But these three positions go in exactly the other direction.
> >
> > Thanks for listening. And thank you just as much if you didn't listen at all.
> >
> > Paul

Above, I tried to change the title of the thread to "Three Symmetrical Races".

Not sure if it worked.

BTW "might not be interested" means the same (to me) as "might be interested".
After all, if something might happen, then it also might not happen (and vice versa).
It's intended as a logical/mathematical joke.

Paul

On October 15, 2023 at 5:07:31 AM UTC-6, peps...@gmail.com wrote:

> On October 15, 2023 at 5:18:48 AM UTC+1, MK wrote:

>> On October 14, 2023 at 6:08:18 PM UTC-6, peps...@gmail.com wrote:

>>> Thanks for listening. And thank you
>>> just as much if you didn't listen at all.

>> And I have this hunch that "your Tim"
>> is the one with a math PHD; "RGB's
>> infamous Tim The Math-Giver" who
>> gave us "The 21^7 < 2^32 < 21^8"... :)

>> If that's the case, then I have a strange
>> suspicion that you intended to give him
>> a private math lesson by discouraging
>> everyone else as lesser players, (which
>> adds injury to insult), but you sent your
>> email to RGB by mistake... ;)

> Thanks for your feedback.
> I didn't mean what you thought I meant.
> I will change the title of the thread.

It's too late. Your good deed is already
done even if unintentionally, as it often
happens... :)

I had complained many times in the past
that you start very interesting threads but
that you don't pursue them to fruition and
one of my frustrations with you is thay you
are not adverserial enough with the likes
of Tim, Axel, etc... :(

It may be because of your shit-licking dog
personality towards the members of your
pack of ilks, whom you will nibble at but
not bite, even though I consider you more
capable of analytical and logical thinking
than them half-brained PHD math-shitters.

Despite my being snide in my previous post,
I did indeed find your symmetrical examples
interesting. Ever since I stuffed our "Tim The
Math-Giver" into donkey's ass, I doubt that
you will hear from him even though you were
serviently reaching out to him specifically. :(

But I think you yourself will be capable of
developing further on what you posted. So,
I will encourage you to do that by asking you
whether the numbers you gave were based
on Botsight or Isight..??

Since I never considered anything to know
about, I know nothing about Isight and I
would more specifically like to hear what
Isight says about your examples...??

MK

On October 17, 2023 at 1:07:09 AM UTC-6, MK wrote:

> I had complained many times in the past
> that you start very interesting threads but
> that you don't pursue them to fruition and
> one of my frustrations with you is thay you
> are not adverserial enough with the likes
> of Tim, Axel, etc... :(

> It may be because of your shit-licking dog
> personality towards the members of your
> pack of ilks, whom you will nibble at but
> not bite, even though I consider you more
> capable of analytical and logical thinking
> than them half-brained PHD math-shitters.
> Despite my being snide in my previous post,
> I did indeed find your symmetrical examples
> interesting. Ever since I stuffed our "Tim The
> Math-Giver" into donkey's ass, I doubt that
> you will hear from him even though you were
> serviently reaching out to him specifically. :(
> But I think you yourself will be capable of
> developing further on what you posted. So,
> I will encourage you to do that by asking you
> whether the numbers you gave were based
> on Botsight or Isight..??
> Since I never considered anything to know
> about, I know nothing about Isight and I
> would more specifically like to hear what
> Isight says about your examples...??

I'm not disappointed that Tim didn't respond
to you, since I had predicted that he wouldn't.

Perhaps he "gave you math" by private email
as it's very common practice among the sick
dog pack of the gamblegammon world.

I'm not disappointed that Axel didn't chime in
either about his Isight that I had asked about.

But I'm slightly disappointed that you didn't
respond to my question on a subject that you
initiated yourself... :(

So, let me do the dirty work and answer you all.

Noo-BG says:

43 EPC 12.502 Wastage 5.502 3 ply: 74.9 Double, take
52 EPC 12.048 Wastage 5.048 3 ply: 74.9 Double, take
61 EPC 12.956 Wastage 5.956 3 ply: 75.5 Double, pass

Quite obviously, you below paraphrased comments
were based on those numbers.

"19 outshots in the 5, 2
"17 outshots in the 4, 3
"15 outshots in the 6, 1 position.
"So the higher the EPC, the worse for the off-roll player.

Let me see if I can figure what Axel's Isight would say?

"To decide on cube action, start with a straight pip
"count for each player.

7 in all examples for both sides.

"Add 1 pip for each additional checker on the board
"compared to the opponent.

N/A in all examples for both sides.

"Add 2 pips for each checker more than 2 on point 1.

N/A in all examples for both sides.

"Add 1 pip for each checker more than 2 on point 2.

N/A in all examples for both sides.

"Add 1 pip for each checker more than 3 on point 3.

N/A in all examples for both sides.

"Add 1 pip for each empty space on points 4, 5, or 6
"(only if the other player has a checker on his
"corresponding point).

N/A in all examples for both sides.

"Add 1 pip for each additional crossover compared
"to the opponent.

N/A in all examples for both sides.

"The cube action for money is with your adjusted
"pip count L and your lead ∆L (can be negative),
"p = 80 − L / 3 + 2∆L is your approximated CPW.

L = 7
∆L = 0
p = 80 - 7 / 3 + 2 * 0 = 82.333

"The cube action for money is:
"p < 68 : No double, take.

N/A

"68 ≤ p < 70 : Double, take.

N/A

"70 ≤ p ≤ 76 : Redouble, take.

N/A

"p > 76 : Redouble, pass.

82.333 > 76: Redouble, pass in all 3 positions

Unless I misunderstand it, it looks like Axel's
Isight is a pile of horse-muffins...?

And the reason why nobody publicly followed
up to your original post, as well as the reason
why you haven't responded to my questions...?

MK

On November 7, 2023 at 2:50:11 AM UTC-7, MK wrote:

> 82.333 > 76: Redouble, pass in all 3 positions
> Unless I misunderstand it, it looks like Axel's
> Isight is a pile of horse-muffins...?

> And the reason why nobody publicly followed
> up to your original post, as well as the reason
> why you haven't responded to my questions...?

After three weeks since I posted the above,
nobody corrected my arithmetic either... :( ;)

We know that Tim, Axel, et al. are not really
mathematicians but not even arithmeticians?
Come on sick basses bite my bait so that I can
mount you on my wall...

In the alternative, you can all eat cow-pies and
horse-muffins and die...! :)

MK