I gave it a try.
1. Checker play: Do what GNU Backgammon does with checker
play set to "Expert" level.
2. Cube decisions:
a) Double with more than 50 percent cubeless winning chances
b) Take or pass according to GNU Backgammon's assessment
("World Class")
c) Raccoon if beavered ("higher order" rodents forbidden)
I hope this is more or less what Murat politely suggests us to do to
become better backgammon players, supposedly on "alpha" level.
The score after 1000 games (money session, Jacoby) is
This is larger than 6600 (GNU Backgammon's net result), so the jury
is still out. I will continue the run and keep you posted.
In the mean time, statistical advice is very welcome.
In the mean time, statistical advice is very welcome.
The score after 1000 games (money session, Jacoby) is
GNU Backgammon: 14182 (564 wins)
Murat Mutant: 7582 (436 wins)
This is larger than 6600 (GNU Backgammon's net result), so the jury is
still out. I will continue the run and keep you posted. In the mean
time, statistical advice is very welcome.
.... Then just play enough games so that even the rarer
outcomes are achieved more than a handful of times.
How long did the 1000 games take?
Can you set it to the highest level from now on?
Can we run this using both cybeless and cubeful winning chances?
And also cubeless winning chances calculated by other bots for at
least the opening and reply rolls?
Did your mutant double immediately after gnubg opened with 63 and
took the beaver?
can we make this based on more than 50 percent
c) Raccoon if beavered ("higher order" rodents forbidden)
Again can you run this either way?
Can you explain why the limitation? How would it help the experiment?
I never use Jacoby myself. Can you turn it off
plot a histogram of the results
MK <mu...@compuplus.net> writes:
How long did the 1000 games take?
Over night.
Did your mutant double immediately after gnubg opened
with 63 and took the beaver?
No. According to "World Class", after GNU Backgammon splits with
62 and 63 or runs with 64 (which is was "Expert" checker play does)
the mutant is a slight underdog. Hence no double. But there are other "Expert" plays where "World Class" thinks the replier is favourite:
can we make this based on more than 50 percent
Perhaps I am willing to do a test with 0.618 (golden ratio, to throw
in esoterics for good measure), which is between 0.6 and 0.625
Again can you run this either way?
No. I never play with Raccoons, and in our club we had discussions
of banning Beavers as well (they tend to attract the "wrong" players).
Can you explain why the limitation? How would it help the experiment?More on this in a different thread.
I never use Jacoby myself. Can you turn it off
I always use Jacoby. This is crucial in chouettes, because without
Jacoby the team might be bored to death while the captain, having
slept during the cube decisions, tries to squeeze out a Gammon.
My gut feeling says that this is almost certainly not because your
doubling strategy is competitive, but rather due to the St Peterburg Paradoxon. More of my thoughts on this in a different thread.
Out of curiosity I tested some other doubling "strategies" (all with
Jacoby and without Beavers, Null hypothesis as before):
- Double with 50 % winning chances, always take
- Always double if legal, take according to GNU Backgammon "World
Class"
- Always double if legal, always take
This could be rejected after 200 games.
Note that even this last, maniac strategy needed 200 games to get
rejected with 95 % certainty! This means that you should be extremely suspicious regarding results from a mere 100 games, especially if the strategy tends to drive the cube up, up and away.
That's it, I will not spend more time on things like this
On November 4, 2021 at 12:29:29 PM UTC-6, Axel Reichert wrote:
No. According to "World Class", after GNU Backgammon splits with 62
and 63 or runs with 64 (which is was "Expert" checker play does) the
mutant is a slight underdog. Hence no double. But there are other
"Expert" plays where "World Class" thinks the replier is favourite:
This one is important and that's why I asked if you could use opening
equity calculations by other bots (like TD-Gammon). I thought the
opening book was user editable, no? Also, bots like XG++ split the 64
and slot the 21. If you want to imitate Murat's experiments, you need
to do these. Otherwise, it's an experiment of your own and has nothing
to do with what I had suggested (as the thread title implies).
any arbitrary and/or calculated constants used by the bots should be
made user selectable variables in the settings or in a editable config
file. I will be curiously waiting to see what you come up with 0.618,
etc...
No. I never play with Raccoons, and in our club we had discussions of
banning Beavers as well (they tend to attract the "wrong" players).
But aren't Raccoons, Rats, Bats, Cats, etc. all part of what you all
call "cube skill"...?
- Double with 50 % winning chances, always take
Should be at least 51%
Why are you even wasting time with these??
Note that even this last, maniac strategy needed 200 games to get
rejected with 95 % certainty! This means that you should be extremely
suspicious regarding results from a mere 100 games, especially if the
strategy tends to drive the cube up, up and away.
If you are referring to my 100 games, I can't very well play 1000
games in one night and that's exactly why we are making bots
to play "long enough" sessions.
Sounds like the results went against your expectations?
To my knowledge, GNU Backgammon has no opening book
.....
According to XG's opening book
the replier has an advantage only after 41S
(with or without Jacoby).
My understanding is that you double after all 6x splits and
maybe for other opening rolls, I don't know.
My mutant doubles after 1x splits and 43Z. In all these cases
the winning chances of the replier should be between and
49.48 % and 50.16 %.
So in my opinion it does not matter in which of these cases
you raise the stakes, it is too early anyway, because you are
foregoing the possibility to double your opponent out.
Which is also "arbitrary". If you start to come up with ideas about
gammonish positions and "play left in the game" I should start to
get worried, because then you would reinvent the (mathematical)
concepts of equity and volatility. (-;
But aren't Raccoons, Rats, Bats, Cats, etc. all part of what you all
call "cube skill"...?
The interesting question I try to research here is not any "maniac"
cube strategy, but whether a Petersburg Paradoxon occurs in
backgammon with unlimited cube
... If yes, I think we will have an interesting (but mostly philosophical)
discussion about skill.
Should be at least 51%
Why not 50.000001 %?
Why are you even wasting time with these??
See above. My interest is the Peterburg Paradoxon, not the cube
strategy.
On November 6, 2021 at 3:23:08 AM UTC-6, Axel Reichert wrote:
How about we go by the Gnubg rollouts
I don't understand the S's, Z's, etc. after the rolls
I don't understand why the 49.48% to 50.16% range
I thought the common teaching of "cube skill" was that it was better
used to maximize your winning and not necessarity to double your
opponent out.
not because I want to reinvent any such "mathematical concepts", but
to debunk them alltogether.
not do I mind your calling my or any other strategy "maniac" as long
at it results in winning more.
And I have no idea what Petersburg Paradox has anything to do with the subject
winning the opening roll gives an advantage (according to the link
above +.0393 on average).
Checker+cube skills being equal, the player who will win more opening
rolls will win more.
What I'm interested in is to find out if luck+checker skills are equal,
how much does the so called "cube skill" matter after 4 billion games?
I don't expect to convince anyone that the cube has a value
https://plus.maths.org/content/os/issue15/features/doubling/index
very convincing
MK <mu...@compuplus.net> writes:
How about we go by the Gnubg rollouts
As I wrote, this will not matter. Your thinking seems to be
that as soon as you are even a tiny favourite, you should
raise the stakes. This is correct if you cannot get redoubled.
.....
So it does not matter whether you have 49.89 % according to
bot A or 50.03 % according to bot B
since this difference will be dwarfed by the difference between
having access to the cube or not.
I don't understand the S's, Z's, etc. after the rolls
https://bkgm.com/articles/Keith/nactation.html
I don't understand why the 49.48% to 50.16% range
These are the winning chances after said rolls according to ...
I thought the common teaching of "cube skill" was that it was
better used to maximize your winning and not necessarity to
double your opponent out.
Precisely. And because you give away the powerful weapon of
the cube you should not double to early, even if you are a favourite.
Please read https://bkgm.com/articles/Kleinman/FootballFields
not because I want to reinvent any such "mathematical concepts",
but to debunk them alltogether.
I know. But it won't be easy. (-:
And I have no idea what Petersburg Paradox has anything to do with
the subject
See below.
winning the opening roll gives an advantage (according to the link
above +.0393 on average).
Sure, but this is not enough to give the weapon away.
What I'm interested in is to find out if luck+checker skills are equal,
how much does the so called "cube skill" matter after 4 billion games?
This can be answered as long as you can put numbers on the value
of a position. If you run into a Petersburg Paradox you cannot do this
any more, so at that point discussions about the pros and cons of
particular cube strategies become meaningless, because there are no
numbers to compare. Now if your cube strategy turns backgammon
into a Petersburg Paradox than you can neither claim that your cubing
is better than the bot's nor could someone else claim that it is worse
than the bot's. It cannot be proven any more.
If, on the other hand your cube strategy does not turn backgammon
into a Petersburg Paradox (e.g., because it is too timid for this, or
because it is prevented by rules, be it match play, a cap on the cube
in money sessions, forbidding beavers, ...), then there exists a number
for the value of a position, and so immediately one can debunk one
strategy or the other, even if it takes lots of games.
This would mean that the mutant strategy can be debunked in the
beavers-only case by spending more CPU time....
If so, there is an easy explanation for your success against the
bot's in a particular session of only 100 games
(not your mistake, of course, I do understand the reasons).
Frank Berger <bgbl...@googlemail.com> writes:
I don't expect to convince anyone that the cube has a value
All this is certainly more or less trivial for you, but as you
can see from this thread I still have not given up explaining.
Even elementary cube theory is not intuitive for beginners
(as can be seen when trying to teach them the 25 % take
point for the dead cube).
So one could characterize my mutant's doubling "strategy"
as treating himself the cube as dead but hoping that the
opponent treats it as very much alive. (-;
In your experiment, the mutant plays normally after the first cube. In
my proposal, the mutant never drops except when it has no chance of
winning.
How do you know? Have you tested and verified how much is the weapon
worth?
On November 13, 2021 at 3:02:18 AM UTC-7, Axel Reichert wrote:
Frank Berger <bgbl...@googlemail.com> writes:
The feeling of frustration is mutual. To me, you guys soundI don't expect to convince anyone that the cube has a valueAll this is certainly more or less trivial for you, but as you
can see from this thread I still have not given up explaining.
like pre-Copernican astronomers showing me all kinds of
elaborate formulas and trying to impress me with how so
exactly you can predict retrograde movements of planets.
And I still have not given up explaining to you guys that your
calculations have no value applicable to reality because
planets don't travel backwards.
Interesting how you validate each other so eagerly. I guess
misery likes company...
Even elementary cube theory is not intuitive for beginnersMaybe it's just difficult to "teach" (convince of) something
(as can be seen when trying to teach them the 25 % take
point for the dead cube).
that doesn't add up..?
Also, your "cube hypothesis" must have self-verified itself
into "cube theory" without the use of any empirical data,
test or experiment. Convincing a small number of mentally
ill gamblers that they will win more by doubling/taking at
certain calculated equities, and then "observing" that they
all try to play like that but only the ones most capable of
it (i.e. achieving low PR's) win more, is not enough to make
your cube hypothesis a cube theory.
So one could characterize my mutant's doubling "strategy"Well enough with the clarification that it is "your" mutant
as treating himself the cube as dead but hoping that the
opponent treats it as very much alive. (-;
alone and not mine nor anyone else's. So, yes, you should
be given full credit for "your mutant's" silly doubling strategy.
MK
... the chances of GnuDung rolling a 4-5 are 2-in-36......but the
chances of rolling a 4-5 when it's *exactly* the roll it needs is.....?
MK <mu...@compuplus.net> writes:
In your experiment, the mutant plays normally after the first cube. In
my proposal, the mutant never drops except when it has no chance of
winning.
So you always double with winning chances > 50 % and always take with
winning chances > 0 %?
How do you know? Have you tested and verified how much is the weapon
worth?
Would about this proposition?
https://www.bkgm.com/rgb/rgb.cgi?view+838
On November 14, 2021 at 4:32:49 AM UTC-7, Axel Reichert wrote:
You double and take as long as you still have "hope of winning". At
the start of the game your hopes are high (d/t point is low), towards
the end of the game your hopes are low (d/t point is high).
If I understand it correctly, this is similar to the difference
between live and dead cube points(??) but more precise.
Since we can't change the numbers 2, 4, 8... on the cube
"how much checker play is still left in the game". Since I'm not a
math phd tempted to nail everything with a math hammer, I would gladly
settle for being a simple potato counter
In the "cube market" of backgammon, however, you can manipulate the
market by checker play, which is "the other weapon"...
MK <mu...@compuplus.net> writes:
You double and take as long as you still have "hope of winning". At
the start of the game your hopes are high (d/t point is low), towards
the end of the game your hopes are low (d/t point is high).
Standard cube theory has the concepts of dead/life cube and
volatility for this.
If I understand it correctly, this is similar to the difference
between live and dead cube points(??) but more precise.
Less. Quantify hope. (-:
But your thinking reminds me on a player in our club who was
eager to take the most desperate positions if only the volatility
was sky-high.
Since we can't change the numbers 2, 4, 8... on the cube
This is what
https://bkgm.com/rgb/rgb.cgi?view+429
is about.
Imagine a tripling cube (3, 9, 27, ...) and you end up with a
Petersburg paradox. Which is why I am so eager to find out
whether aggressive cube strategy, beavers, or raccoons have
the same effect as the tripling cube.
And because of the high volatility this cannot be done by just
running long sessions with the bot (they would be too long),
but we need to have a surrogate model (Markov chains), which is
fed with the data from shorter sessions with the bot. The surrogate
model can then easily be run a billion times. This is what I am doing.
"how much checker play is still left in the game". Since I'm not a
math phd tempted to nail everything with a math hammer, I would
gladly settle for being a simple potato counter
How would this potato counter look like? We need to quantify things,
not because we like our math hammer, but because otherwise we
cannot test hypotheses.
In the "cube market" of backgammon, however, you can manipulate
the market by checker play, which is "the other weapon"...
With both sides playing their checkers like the bot, this weapon is
cancelled with the argument from symmetry. So my experiment
leaves just the cube skill in the game, as desired.
On November 15, 2021 at 12:29:18 PM UTC-7, Axel Reichert wrote:
Were you curious enough to look up the RGB thread that it was
extracted from? I did. And wow! Hundreds of long and detailed articles written by perhaps 40-50 different participants, many of the
apparently mathematicians.
what will the result of your experiment mean
And because of the high volatility this cannot be done by just
running long sessions with the bot (they would be too long),
I don't understand what high volatility has to do with it
just run long enough sessions
did you mean that you can test hypotheses by quantifying things with
math?
If raccoons turn out to end up as Petersburg paradox, it would just be an incentive for some clubs (mine, for example) to have them forbidden in
order to keep backgammon a mind sport, not a gambling amusement. Same
for beavers (if Petersburg kicks in there as well). If not, then maniac
cube strategies (contradicting standard cube theory) can be dismissed by investing CPU time, be it "real" sessions or Markov chain runs.
MK <mu...@compuplus.net> writes:
Were you curious enough to look up the RGB thread that it was
extracted from? I did. And wow! Hundreds of long and detailed
articles written by perhaps 40-50 different participants, many
of the apparently mathematicians.
Thanks for the hint, I might take a look.
what will the result of your experiment mean
If raccoons turn out to end up as Petersburg paradox, it would
just be an incentive for some clubs (mine, for example) to have
them forbidden in order to keep backgammon a mind sport, not
a gambling amusement.
Same for beavers (if Petersburg kicks in there as well). If not, then
maniac cube strategies (contradicting standard cube theory) can
be dismissed by investing CPU time, be it "real" sessions or Markov
chain runs.
By the way, in 10000 games with 1 beaver allowed, double > 0.5
and take > 0.0 the mutant lost 62117 against gnubg's 84870.
In one game the cube reached 4096 (gnubg's limit), so I checked
this game manually from the session file. In fact gnubg held the
cube after beavering the mutant's redouble to 2048.... blah blah
But before declaring victory over the mutant's strategy, I need to
ensure that the expectation settles, of which I was not yet sure
after 5 billion games (Markov chain runs).
I don't understand what high volatility has to do with it
The higher the volatility (the one of the whole process, not the
volatility of an individual position), the longer it takes until the
law of large numbers kicks in.
just run long enough sessions
From my Markov chain runs it is quite certain that even several
million games are not enough.
I will not spent half a year of CPU time if smart surrogate
methods yield a robust result much quicker.
"There nothing more practical than a good theory."
did you mean that you can test hypotheses by quantifying
things with math?
Sure. This is called simulation, my field of expertise for 25 years.
The positions with undefined equity already demonstrate that the
paradox arises with ordinary backgammon, but apparently that does not dissuade your club from allowing money games. So why would showing
that the paradox arises with raccoons dissuade your club from allowing raccoons?
On November 17, 2021 at 12:10:38 PM UTC-7, Axel Reichert wrote:
If raccoons turn out to end up as Petersburg paradox [...]
Can you reword that in terms of what it means about "cube skill"?
By the way, in 10000 games with 1 beaver allowed, double > 0.5 and
take > 0.0 the mutant lost 62117 against gnubg's 84870.
What's important here is how that compares to what would be
expected. Did you use your high math to calculate a prediction before
you started? Would you have expected that the mutant would lose by ten
fold, twenty fold, etc...? You haven't.
And the above numbers are incredibly good towards proving that the
so-called "cube skill" is bullshit.
When you refine your doubling and especially taking points from >0 to
more logical/practical one (such as deriving from my tests), you will
see the the mutant will decimate gnubg...
gnubg held the cube after beavering the mutant's redouble to 2048
Was gnubg wrong to hold the cube?
But before declaring victory over the mutant's strategy, I need to
ensure that the expectation settles, of which I was not yet sure
after 5 billion games (Markov chain runs).
Take your time, I've got the beer chilling... ;)
"There nothing more practical than a good theory."
Is that a quote from the bible?
Like David Ullrich. Personally, I kind of liked quite a few of the
things that he wrote in RGB. You can't find a single reference
to him in bkgm.com or bgonline.org. You should ask why??
MK <mu...@compuplus.net> writes:
Can you reword that in terms of what it means about "cube skill"?
I have tried to explain this before. Without existing expected value I
do not think there is a way to quantify the difference between cube strategies (Big O notation, anyone?). As long as you have an expected
value, it is possible to dismiss particular cube strategies as inferior.
By the way, in 10000 games with 1 beaver allowed, double > 0.5
and take > 0.0 the mutant lost 62117 against gnubg's 84870.
What's important here is how that compares to what would be
expected. Did you use your high math to calculate a prediction
before you started? Would you have expected that the mutant
would lose by ten fold, twenty fold, etc...? You haven't.
As in my other trials the Null hypothesis was that the mutant cubes
as good as gnubg. Assuming a normal distribution of the cube value
(which is not quite correct, since it should be closer to a geometrical distribution) the lead should be between -13296 and +13296 with 95 % probability. However, gnubg's lead was nearly twice as high. But see
below.
And the above numbers are incredibly good towards proving that
the so-called "cube skill" is bullshit.
Why so? I am eagerly waiting for your irrefutable reasons.
When you refine your doubling and especially taking points from
0 to more logical/practical one (such as deriving from my tests),you will see the the mutant will decimate gnubg...
Show the results once you have them. I am eagerly waiting for your statistically significant experiments.
gnubg held the cube after beavering the mutant's redouble to 2048
Was gnubg wrong to hold the cube?
With "held" I meant "was possessing". It could not redouble any
more. Like I wrote, without the hard-wired limit of 4096,
it would have redoubled a couple of rolls later according to standard
cube theory.
... My interpretation of all this is that you have successfully entered Petersburg country, so your cube strategy cannot be dismissed
easily (big O notation, anyone? Perhaps this could be applied in this context), because no expected value exists.
However, with all due respect, you will almost certainly not be
able to back your strategy with cash in a real money session,
since the highest cube I encountered was roughly 500e9. Even
at a modest stake of 1 Euro/point this is a fairly ambitious
amount of money.
"There nothing more practical than a good theory."
Is that a quote from the bible?
No. https://en.wikiquote.org/wiki/Kurt_Lewin
On 11/18/2021 5:20 AM, MK wrote:
Like David Ullrich. Personally, I kind of liked quite a few of the
things that he wrote in RGB. You can't find a single reference
to him in bkgm.com or bgonline.org. You should ask why??
He is mentioned on bkgm.com a few times. https://www.bkgm.com/rgb/rgb.cgi?view+983 https://www.bkgm.com/rgb/rgb.cgi?view+1254 https://bkgm.com/rgb/rgb.cgi?view+1310 https://bkgm.com/articles/Zare/UndefinedEquity/index.html
Show the results once you have them. I am eagerly
waiting for your statistically significant experiments.
accepting XG's raccons
On November 18, 2021 at 1:51:16 PM UTC-7, Axel Reichert wrote:
I can't speak your language and was asking to reworded in simpler
English but maybe it's not easy for you to do either.
If you ran sessions with different "cube strategies" [...], can you
compare if some do better than others?
I shouldn't have said things like "more logical/practical take points
than > 0" because I am the one arguing against a "certain cube skill"
I already said no human can live long enough to satisfy you guy's
requirement for statistically significant.
My interpretation of all this is that you have successfully entered
Petersburg country, so your cube strategy cannot be dismissed easily
(big O notation, anyone? Perhaps this could be applied in this
context), because no expected value exists.
I suppose this is good news for my argument even if the experiment
wasn't exactly what I had proposed?
by now I also have ideas what to do in the cases where we end up with
a Petersburg paradox
In Petersburg country we need to employ other techniques (big O
notation, analytical approaches) to dismiss foolish strategies.
More to come!
MK <mu...@compuplus.net> writes:
accepting XG's raccons
So this means you beavered XG's doubles. According
(roughly) to what criterion? Being above (estimated)
40 % winning chances? Or always?
MK <mu...@compuplus.net> writes:
... If you think this foolish, then apparently you believe in cube skill. (-;
I already said no human can live long enough to satisfy you guy's
requirement for statistically significant.
Of course you can. But the length of the trial depends on the volatility. Once we are "in Petersburg country", a more or less trivial strategy is
to get the cube to a high level, win one of these games and protect the
lead from then on by passing.
I suppose this is good news for my argument even if the experiment
wasn't exactly what I had proposed?
Not too fast. Let us put it this way: In Petersburg country we need to
employ other techniques (big O notation, analytical approaches) to
dismiss foolish strategies. I might have a 66 in my dice cup ...
E(n = 2k-1) = p(n = 2k-1) * c(n = 2k-1)
= 0.3745 * 0.1739^(k-1) * 3.5350 * 5.8026^(k-1)
= 1.3239 * 1.0092^(k-1)
E(n = 2k) = p(n = 2k) * c(n = 2k)
= 0.3118 * 0.1739^(k-1) * 7.0700 * 5.8026^(k-1)
= 2.2044 * 1.0092^(k-1)
This is a geometrical series, and a divergent one, since
1.0092 >= 1
With 0 beavers allowed, we get 0.6957. No Petersburg paradox.
With 1 beaver allowed, we get 1.0092. Close, but still Petersburg.
With 2 beavers allowed, we get 1.6363. Clearly Petersburg.
So my next task will be to use these numbers to calculate the
expected value including gammons and backgammon. This
will need some distinctions between the various cases (cube
ownership, even/odd number of cubings, ...), but most likely I
will have time for these in the next couple of days.
Stay tuned!
So my next task will be to use these numbers to calculate the
expected value including gammons and backgammon. This
will need some distinctions between the various cases (cube
ownership, even/odd number of cubings, ...), but most likely I
will have time for these in the next couple of days.
Stay tuned!
On November 22, 2021 at 3:21:45 PM UTC-7, Axel Reichert wrote:
So my next task will be to use these numbers to calculate the
expected value including gammons and backgammon. This
will need some distinctions between the various cases (cube
ownership, even/odd number of cubings, ...), but most likely I
will have time for these in the next couple of days.
Stay tuned!
It has been 10 or "a couple of 5" days since... I hope you are
still intending to do or working on this. I don't know about the
others but I'm all ears, impatiently waiting to hear about it.
MK <mu...@compuplus.net> writes:
It has been 10 or "a couple of 5" days since... I hope you are
still intending to do or working on this. I don't know about the
others but I'm all ears, impatiently waiting to hear about it.
Yes, I am making progress and think my approach works.
Even as I asked for it twice, you never offered any predictions nor
committed to what will your results mean either way.
MK <mu...@compuplus.net> writes:
Even as I asked for it twice, you never offered any predictions
nor committed to what will your results mean either way.
Mathematical proofs are different in nature from statistical
hypothesis testing. Pythagoras did not need to state a
hypothesis about the sides of a triangle before testing it,
Since my approach is analytical, there is no need for
hypothesizing either. If it works, fine, if not, the jury is still out.
So my next task will be to use these numbers to calculate the expected
value including gammons and backgammon. This will need some
distinctions between the various cases (cube ownership, even/odd
number of cubings, ...)
Axel Reichert <ma...@axel-reichert.de> writes:
Case closed.
My prediction is that we won't hear a peep from any
of them, for the reasons even you should be able to guess, but I
will patiently wait a to see... (Before slapping you some more ;)
MK
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