It's hard for me to know my PR particularly precisely.
I'm definitely worse than 5 but a performance of 7 really
disappoints me. Let's say I'm a 6.

Suppose I play a match with XG. I think most people would think
that, provided the match is long enough, XG can get a winning
probability of at least 95%.

However, I now think this is wrong. Here is what I could do to
guarantee myself a > 5% probability. Suppose I reach a bad position
but with solid 10% game-wining chances. I could then double XG
and we could keep doubling and redoubling each other until the cube
value was more than the length of the match. My probability of winning
the match then becomes 10%. The doubling and redoubling ad infinitum
suits both sides -- XG because it is wrongly assuming an optimal opponent,
and myself because I'm only looking for > 5% MWC.

Paul

On 10/11/2022 9:01 AM, peps...@gmail.com wrote:
> However, I now think this is wrong. Here is what I could do to
> guarantee myself a > 5% probability. Suppose I reach a bad position
> but with solid 10% game-wining chances. I could then double XG
> and we could keep doubling and redoubling each other until the cube
> value was more than the length of the match. My probability of winning
> the match then becomes 10%. The doubling and redoubling ad infinitum
> suits both sides -- XG because it is wrongly assuming an optimal opponent,
> and myself because I'm only looking for > 5% MWC.

Hey, you've rediscovered what Murat has been preaching all
these decades!

Whether your numbers are correct, I don't know, but the principle
is sound. This is why Murat was trying so hard, at one point in time,
to get people to take his bet that he could outperform what the
"standard formulas" for winning chances (based on PR) predicted. He
thought that a successful performance would finally demonstrate to
people that PR is nonsense.

I told him that people already understood this principle and so he
wouldn't be proving anything people didn't already know. I suggested
that he instead bet that he could beat XG more than 50% of the time
in short matches (say, 7 points). Of course he got angry, because he
knew he couldn't do that, but didn't want to come out and admit it.

---
Tim Chow

On Tuesday, October 11, 2022 at 2:15:14 PM UTC+1, Tim Chow wrote:
> On 10/11/2022 9:01 AM, peps...@gmail.com wrote:
> > However, I now think this is wrong. Here is what I could do to
> > guarantee myself a > 5% probability. Suppose I reach a bad position
> > but with solid 10% game-wining chances. I could then double XG
> > and we could keep doubling and redoubling each other until the cube
> > value was more than the length of the match. My probability of winning
> > the match then becomes 10%. The doubling and redoubling ad infinitum
> > suits both sides -- XG because it is wrongly assuming an optimal opponent,
> > and myself because I'm only looking for > 5% MWC.
> Hey, you've rediscovered what Murat has been preaching all
> these decades!
>
> Whether your numbers are correct, I don't know, but the principle
> is sound. This is why Murat was trying so hard, at one point in time,
> to get people to take his bet that he could outperform what the
> "standard formulas" for winning chances (based on PR) predicted. He
> thought that a successful performance would finally demonstrate to
> people that PR is nonsense.
>
> I told him that people already understood this principle and so he
> wouldn't be proving anything people didn't already know. I suggested
> that he instead bet that he could beat XG more than 50% of the time
> in short matches (say, 7 points). Of course he got angry, because he
> knew he couldn't do that, but didn't want to come out and admit it.

Ok, but I think I can add interesting substance to the discussion.
Assuming my PR is 6, and assuming a match of more than 1000 is impractical,
what is the largest p such that some match length <= 1000 exists such that my probability
of losing to XG is at least p?
(My argument shows that p < 95%).
Well, "shows" might be a bit strong, but I think so.
This question must be intractable, but it might be interesting to speculate how such a question
could be tackled.
What would your estimate for p be? I'll go with 80% but it's just a wild guess.

Paul

On October 11, 2022 at 7:30:12 AM UTC-6, peps...@gmail.com wrote:

>On October 11, 2022 at 2:15:14 PM UTC+1, Tim Chow wrote:

>>On 10/11/2022 9:01 AM, peps...@gmail.com wrote:

>>> However, I now think this is wrong. Here is what I could do to
>>> guarantee myself a >5% probability. Suppose I reach a bad
>>> position but with solid 10% game-wining chances. I could then
>>> double XG and we could keep doubling and redoubling each
>>> other until the cube value was more than the length of the
>>> match. My probability of winning the match then becomes 10%.

Contrary to Tim's misunderstanding it, this is not the same as my
arguments about the inaccuracy of ELO and PR (PR also implies
inaccuracy of cubing points, i.e. "cube skill", which is in turn based
on inaccurate equity calculations).

But it's still interesting that you came to see how you can exploit
situational differences between PR and MWC, even though you
are not questioning the accuracy of either number as calculated
for your consumption by the bot.

>>> The doubling and redoubling ad infinitum suits both sides --
>>> XG because it is wrongly assuming an optimal opponent,
>>> and myself because I'm only looking for >5% MWC.

It doesn't suit the bot at all. Apparently you only half-understand
how it suits you, i.e. "you are forcing the bot to play your game".

Surely you don't mean that the bot would drop your doubles if
it new that you weren't an "optimal opponent", do you..?

>> Hey, you've rediscovered what Murat has been preaching all
>> these decades!

Not quite so but still a "discovery" for him, in a different way.

>> Whether your numbers are correct, I don't know, but the principle
>> is sound. This is why Murat was trying so hard, at one point in
>> time, to get people to take his bet that he could outperform what
>> the "standard formulas" for winning chances (based on PR)
>> predicted. He thought that a successful performance would
>> finally demonstrate to people that PR is nonsense.

Yes, of course, it would and I still maintain my position on this, with
the clarification again that I argued ELO and "cube skill" also were
bullshit, based on grossly inaccurate cubeful equities and somewhat
inaccurate cubeless equities.

However, here Paul is not questioning the accuracy of any of theese.

>> I told him that people already understood this principle and so
>> he wouldn't be proving anything people didn't already know.

You made that claim without offering any evidence for it, solely to
steal away the originality of my arguments from me. If you want to
substantiate it, it's not too late for you to provide proof for any
statements made by anyone, in any forum or media, before I first
argued that PR, ELO, "cube skill", equity, etc. calculations were all
either totally or partially bullshit.

What is rather fascinating is that you or anyone else who admits
that those are all bulshits to varying degrees, none of you can
face the implications of what you are admitting. You still go on
with your daily bott-kissings as usual... :(

>> I suggested that he instead bet that he could beat XG more than
>> 50% of the time in short matches (say, 7 points).

Beating XG more than 50% nor playing matches instead of money
sessions were not/are not necessary, (i.e. it would be much more
than what would be enough), to prove my above arguments.

>> Of course he got angry,

Hah hah! I wasn't just angry. I was steaming mad! :) Keep trying... ;)

> because he knew he couldn't do that, but didn't want to come out
> and admit it.

This is not true but you just can't help yourself being a scumbag liar,
can you..? :(

Anyone who doesn't already know (or the seniles who have since
forgotten) the full story about this subject, should read the thread:
"Murat Ali vs. XGR++ or Gnubg?" from 2020.

https://groups.google.com/g/rec.games.backgammon/c/yDs7m_lpUpA/m/9Psv0O7LAwAJ

Just read Tim's, Paul's, Dmitry's and my comments and skip others
that are not relevant but needlessly distracting from the main topic.

If you want to go at least one step further back on the same topic,
you can read my discussion with Dmitry: "Murat vs XG" from 2017.

https://groups.google.com/g/rec.games.backgammon/c/x59DXAOCyeQ/m/ZPGgwtOmCgAJ

In order to maximize my winnings that I could extract from the bet,
I first wanted to bet that I could beat the bot more than predicted,
i.e. expected MWC based on my PR, because then I could raise the
bet that I could beat the bot more than 50% also.

But if I were to first bet that I could beat the bot more than 50%,
then the other bet would become moot.

Dmitry seemed he never understood this. Tim either also didn't or
he so pretended in order to keep being his slimy self.

As I really wanted the bets to happen, in the end I compromised
and offered a combined bet, i.e. that I would bet half of my money
on beating the bot more than predicted by my PR and bet the other
half on beating the bot more than 50% (see the above two threads).

I never retracted my offer. You all can still take me up on it anytime.

> Assuming my PR is 6, and assuming a match of more than 1000 is
> impractical, what is the largest p such that some match length <=
> 1000 exists such that my probability of losing to XG is at least p?
> What would your estimate for p be? I'll go with 80% but it's just a
> wild guess.

You better hang on to your wild guess. ;) I don't think Tim is capable
of unswering such questions. In fact, just recently, he asked a similar
question himself for Axel to answer. You can also try your luck asking
Axel also but I don't think he will be capable of answering it either. :(

MK

On 10/14/2022 1:46 AM, MK wrote:
>>> I told him that people already understood this principle and so
>>> he wouldn't be proving anything people didn't already know.
>
> You made that claim without offering any evidence for it, solely to
> steal away the originality of my arguments from me.

The evidence is that as soon as people understood what you were
offering to bet, they recognized that you would be a favorite, and
so they declined.

---
Tim Chow

On Friday, 14 October 2022 at 06:46:18 UTC+1, MK wrote:

> You better hang on to your wild guess. ;) I don't think Tim is capable
> of answering such questions.
>
> MK

Tim isn't even capable of seeing that GnuDung bellyaching about not landing an 11-in-36 shot and marking it as unlucky is a crock.

He is spending way too much time hawking fast cars on YouTube and not nearly enough time on backgammon.