Suppose you have access to an idealised perfect money player (XG with
no weaknesses perhaps). XG (or someone acting on behalf of XG) is
entitled to select any position at all. XG and you will play the position
from both sides, so the theoretical equity is zero.
The current cube value is defined to be 1, but it might not be centred.
How much would XG have to pay you upfront to take this prop?

Exactly the same question, but now the restriction is to races (no contact).
Surely in the race scenario, a good player could profitably accept this prop with only
a small upfront payment like 0.02 or so?

Paul

On 8/5/2022 9:49 AM, peps...@gmail.com wrote:
> Suppose you have access to an idealised perfect money player (XG with
> no weaknesses perhaps). XG (or someone acting on behalf of XG) is
> entitled to select any position at all. XG and you will play the position
> from both sides, so the theoretical equity is zero.
> The current cube value is defined to be 1, but it might not be centred.
> How much would XG have to pay you upfront to take this prop?

I had to read this four or five times before I arrived at an
interpretation that made some sense. Let me check my interpretation.

"Idealised perfect money player" and "XG with no weaknesses" and "XG"
are all synonymous in the above.

"Access to" doesn't mean that you can consult the idealised perfect
money player when making your decisions. It just means that the
idealised perfect money player has deigned to grant you an audience,
and offered to play you under certain circumstances.

You're going to play "duplicate backgammon," meaning that two copies
of the board will be set up, with sides reversed, and you'll play out
both games. Presumably, though, the dice are not duplicated. But you
didn't specify whether you can learn from watching your opponent play.
Suppose that the first roll of the dice is the same on both boards.
Can you wait to see how XG plays the dice and imitate the play on the
other board?

---
Tim Chow

On August 5, 2022 at 6:40:12 PM UTC-6, Tim Chow wrote:

> On 8/5/2022 9:49 AM, peps...@gmail.com wrote:

>> XG and you will play the position from both
>> sides, so the theoretical equity is zero.

Below, I'll propose a variant for a different purpose.
>> How much would XG have to pay you upfront
>> to take this prop?

I'll play if XG pays me our PR difference. Since my
PR isn't known upfront, it'll have to be calculated
after the games are played.

It must be due to my lack of experience in these
kinds of propositions that I don't understand the
goal here. What is to be earned or learned..?

> You're going to play "duplicate backgammon,"....
> Presumably, though, the dice are not duplicated.

Why do you presume this? I would say otherwise
that the dice needs to duplicted for fairness. For
an opponent who doesn't try to imitate the bot,
(i.e. me), seing how XG plays won't matter. In fact,
if the human player is required to move first, their
plays will diverge after a few obvious moves and it
won't matter if he gets to see how XG moves first.

Now, my proposition:

- Pick 2 from among your favorite gamblegammon
bots and make them play each other as above but
without any upfront payment.

- Let them play a large set of games, (i.e. 20,000)
from the same position(/s) using duplicated dice.

- Regardless of how the dice rolls are produced, (i.e.
from internal/external dll's, text files, online servers,
etc.), for 10,000 times let Bot-A produce them and
feed to Bot-B as manual dice rolls and for the other
10,000 let Bot-B produce them and feed to Bot-A as
manual dice rolls.

- Calculate the bots' PR's separately after each set
of 10,000 games twice: once by Bot-A and once by
Bot-B.

- Observe if each bot's all four PR's are the same or
substancially similar. Then observe if each bot's two
sets of two PR's are similarly consistent in pairs.

- Also observe if the actual games won/lost by each
bot is in line with their PR's first for each set, then
for each pair of sets and finally for all four sets.

- Report your findings to RGB. Let's see what kinds
of sick cheating shits which of your much worshipped
gamblegammon bots are...

Upfront, I bet that no such experiments will ever be
conducted, for fear of discovering somethings that
you have been comfortably in denial of thus far...

MK

On Saturday, August 6, 2022 at 1:40:12 AM UTC+1, Tim Chow wrote:
> On 8/5/2022 9:49 AM, peps...@gmail.com wrote:
> > Suppose you have access to an idealised perfect money player (XG with
> > no weaknesses perhaps). XG (or someone acting on behalf of XG) is
> > entitled to select any position at all. XG and you will play the position
> > from both sides, so the theoretical equity is zero.
> > The current cube value is defined to be 1, but it might not be centred.
> > How much would XG have to pay you upfront to take this prop?
> I had to read this four or five times before I arrived at an
> interpretation that made some sense. Let me check my interpretation.
>
> "Idealised perfect money player" and "XG with no weaknesses" and "XG"
> are all synonymous in the above.
>
> "Access to" doesn't mean that you can consult the idealised perfect
> money player when making your decisions. It just means that the
> idealised perfect money player has deigned to grant you an audience,
> and offered to play you under certain circumstances.
>
> You're going to play "duplicate backgammon," meaning that two copies
> of the board will be set up, with sides reversed, and you'll play out
> both games. Presumably, though, the dice are not duplicated. But you
> didn't specify whether you can learn from watching your opponent play.
> Suppose that the first roll of the dice is the same on both boards.
> Can you wait to see how XG plays the dice and imitate the play on the
> other board?

I'll reply according to the mental picture I had, rather than focusing on
interpreting my original text. After all, my surname is Epstein, not Scalia.

Where you assume something about what I meant, you are correct with only
the following (possible) exceptions:
The duplicate games do not take place simultaneously but sequentially.
XG gets to decide the order in which the two games are played.
Yes, you can learn from XG.

Paul