On May 19, 2022 at 7:40:31 AM UTC-6, Tim Chow wrote:

> On 5/19/2022 5:13 AM, MK wrote:

>> It wasn't obvious neither always nor to all and it still
>> isn't. Even to you, only in temporary/easy words but
>> not in essence or with any consequences. You just
>> make detached statements in order to save the day
>> and then continue from where you left off before that.

> No. I have always said this.

Okay, fine. No big deal. I'll just try to hold you to it.

> I don't draw the same conclusions that you do from
> this obvious fact, but the fact itself is obvious.

I don't expect you to call the cube skill bullshit. I am
doing it liberally, enough for all of us. ;) But you can't
avoid the implications of what you acknowledge. You
can't keep building more elaborate arguments on top
of inaccurate equities.

>> ..... try to be more useful by making a case for why a
>> converged "running total expected value" is needed
>> in addition to just adding up the wins and losses for
>> each player and leave it at that?

> Suppose I have a fair coin, and I gain $2 whenever .....
> I have to keep flipping it and see what value the answer
> settles down to (or "converges" to, to use the standard
> term).

You keep explaining what I already said I understand
but failed to answer my question. Read it again. I was
asking "what is the need, in real life gamblegammon,
for a running total expected value to converge"? I don't
know how else to word my question. Try to understand.

>> Of course, it does. It's puts an even more realistic limit
>> on the cube value than your artificial 1024, 4096, etc.

> Again, if the game *never* exceeded 20 rolls then you
> would be correct. But the *average* length can be 20 and
> the expected value could still be infinite (i.e., not exist).

So, I would be correct but not correct. You're making
conflicting statements but not of matter to dwell on.

> ..... Then the average length of a game will be 20 rolls.
>
> Now suppose that you win 4 points when the game .....
> Then the expected value will not exist.

Who cares? Why does it need to exist? Whatever points
each player wins or loses is the only thing that matters.

>> So then, the bots using the cube skill formulas should
>> be able to handle large cube values. Why don't they?

> Trouble does *not* automatically arise when the games
> go on arbitrarily long, but only when the game go on
> arbitrarily long *and* the cube value gets too high.

I'm okay with your clarification.

>> This example is also "artificial". It's not a legal position.

> You're not going to understand anything if you are focused
> on lobbing irrelevant objections instead of actually trying to
> learn something.

Same goes for you...

> The purpose of the example is to illustrate a point in a
> simple way. If you understand the simple example then
> you can see how to construct more complicated and
> realistic examples.

As you yourself said recently, what we are talking about
here is applied math to gamblegammon, not theoretical
math. Your using an example that can't arise in real life
is useless. Furthermore, it's not simple. If so, and since
you must necessarily understand your own simple artificial
example, I dare you to "construct more complicated and
realistic examples". Let's see how you will do...

But, my point wasn't even this at all. First you concocted
an illegal position. Then you did an XG rollout of it, which
produces some "inaccurate equity estimates". But you
didn't mind this and went on the disagree with the bot's
cube decision based on its "inaccurate equity estimates".

Then with your own "maths and mirrors" calculations, you
came up with different equities and different correct cube
decisions. Finally you conluded "Therefore "perfect play"
doesn't make sense in this position", meaning "this illegal,
artificial position. What have you accomplished? What are
the implications of your argument and conclusion? Sorry,
but I just don't get it. All I see is circular mathshit. :(

> In this case, the conclusion is exactly the conclusion that
> you want to draw...

Similar to mine but not exactly or even remotely the same.

> this is a position that proves your point that it makes no
> sense to talk about "cube skill" here if the cube is allowed
> to get arbitrarily high. Why are you complaining about this
> example when it's exactly the type of example that can be
> used to prove your point to other people?

Except that I use it to generalize and say that the entire cube
skill theory is bullshit. For me, it's either all valid or not at all.
You, Axel, etc. limit it to only certain positions and otherwise
call it good. That's where we diverge.

>> You never were able to make a case for cube skill except
>> by giving real life examples from positions at the last two
>> or three rolls in a game.

> You seem to think that my artificial example above is
> intended to prove the existence of cube skill. It's not.
> It's intended to prove *your* point, that cube skill makes
> no sense.

I should be elated to hear this but I'm not because I know
that you don't mean it. It's just another temporary, detached
statement from you that you won't hold yourself to. You'll
just go back making your old arguments as though you've
never said this.

> Any by the way, I did make a case for cube skill by solving
> Hypestgammon. Again, you never took the time to study
> the results I got. Probably because it proved you wrong and
> you refuse to understand anything that reveals your errors.

I had looked at the results and had responded to it, although
with a long delay, because of our misunderstanding. What
you did was through the same calculations used for equities
that you acknowledged as "inaccurate by unknown amounts".

You need to do a real life experiment by a "cubeful training"
of a bot and see if you and that bot would come up with the
same equities. Then you will have proven that you solved it.

> You know that your argument is silly here. Cube skill theory
> is completely fine in match play, because if the cube value
> goes higher than the match value, it does not increase the
> payoff, so there is effectively a maximum value that the
> cube can take.

Yes but you need that "cube skill" to know this, don't you? Or
else, a player can drop a theoretically allowed and correct
double past the game value because of lack of cube skill...

Anyway, you are right though that this isn't worth dwelling on.

>> Then the discussion strayed into undefined equities, etc.

> It "strayed" there because you asked for an explanation of
> SPP.

It strayed before I asked anything about it. SPP should have
never been mentioned durins the experiment. I continuously
objected that it didn't apply to gamblegammon.

And also, I didn't ask for "an explanation of SPP" which I had
sufficiently understood. What I asked was how Axel and you
were using it in relation to gamblegammon becaus it doen't
exist in gamblegammon. Only some rare similar sequences
occur within games that don't amount to SPP by any definition.

> See the example above. The *average* length of a game is 20
> but there is no limit on the cube value because *sometimes*
> the game lasts arbitrarily long.

For the purpose that I had suggested the experiment, it doesn't
matter. Especially in "real life" which I keep stressing. In fact,
during Axel's first 5,000+3,000+3,000 games everything was
fine in the cube value stats that he had posted.

Only when he started extrapolating with Markov chains that
things went berzerk, most likely because he made incorrect
assumptions. Then, since he couldn't post a tally of actual
cube values encountered, he switched to posting "average
game values" and started talking about SPP...

> That the maximum value is 6 is exactly why the example
> does not illustrate what can happen when the cube value
> gets arbitrarily large. A more complicated example is
> needed to illustrate that point.

It clearly says: ".....as n grows, the average will almost surely
converge to the expected value, a fact known as the strong
law of large numbers".

Okay, so the reader needs to at least know what "converge"
means, if not "strong law of large numbers" (which I can't
say that I know much about myself). In your example, you
were explaining that the value will conver until a very large
cube occurs, that if you keep playing it will converge again
until an even larger cube occurs, and so on... Isn't that the
weak law of large numbers? That it will repeatedly and
periodically converge to "some value"? If so, what's wrong
with accepting those "some values"?

Again, I was only after the actual points won or lost after
an only robotically possible large number of games and I
repeatedly expressed during the experiment that I didn't
"give a shit about SPP". For my purpose, expected value's
converging didn't matter. (Neither could you offer a valid
argument as to why should it matter.)

On the other side, after Axel became obsessed with SPP,
he started saying that he only cared about SPP from that
point on. But that's okay because at least the experiment
was done, even if not quite correctly, and we all can use
the results for our own arguments.

MK