All tapped out for strategies? Is it Game Over?

[Jennifer]

@rjclayton:

@Jennifer:

And RJ:  Yes.  According to Newton and the modern mathematical community, 6 decimal places for a single variable equation is considered accurate.  More is nice, but it is not necessary to be considered accurate in a single variable equation such as percentage of infantry units that hit on attack or percentage of fighter units that hit on attack.

But aren’t your examples 8 decimal places?

No.

I’ve averaged 32.476215% accurate with Infantry on attack; 12.978248% accurate with attacking fighters over the past 9 games so far.

There are two integers followed by six decimal places.  Thousands, Hundreds, Tens and Ones are not decimal places.  Thousandths, Hundredths, Tenths are decimal places.

[rjclayton]

But the probability that you have calculated is .32476215 for Infantry on attack and .12978248 for fighters on attack.  8 decimal places.  That you chose to display them as a percentage does not change the fact that the probability is to 8 decimal places.

@Jennifer:

BTW, for the record, in Math we consider 6 decimal places to be accurate. It’s a Newton thing.

So, you wouldn’t happen to be referring to Newton’s Method, would you?  A guess and check method for calculating the root?  Because I don’t see what this calculation has to do at all with calculating the average number of hits with your infantry?

http://tutorial.math.lamar.edu/AllBrowsers/2413/NewtonsMethod.asp

[newpaintbrush]

@ncscswitch:

Chess has 32 pieces and 64 spaces.

A&A has a LOT more pieces, and more spaces.
A&A adds pieces.
And A&A has dice.

Yes, there are a finite number of moves…
Call it Chess to the Google power (for thsoe who know the meaning of google instead of just the online service).

That same complexity makes it simpler.

[newpaintbrush]

The nice thing about Axis and Allies is that it’s so predictable.

My thought is that people like games because they’re predictable.

Unlike in real life, when NAKED PEOPLE STREAK PAST THE WINDOW SCREAMING.

The unshaved ones quite put you off your morning croissant and latte.

[rjclayton]

I see you found your crack pipe again!

[Baghdaddy]

@Jennifer:

@rjclayton:

But aren’t your examples 8 decimal places?

No.

I’ve averaged 32.476215% accurate with Infantry on attack; 12.978248% accurate with attacking fighters over the past 9 games so far.

There are two integers followed by six decimal places.  Thousands, Hundreds, Tens and Ones are not decimal places.  Thousandths, Hundredths, Tenths are decimal places.

If Thousands, Hundreds, Tens and Ones are not decimal places, what are they?

http://www.factmonster.com/ipka/A0881929.html
http://www.gomath.com/htdocs/lesson/decimal_lesson1.htm
http://www.mathleague.com/help/decwholeexp/decwholeexp.htm
http://en.wikipedia.org/wiki/Decimal

I guess they could be Vigesimals, Duodecimals, Octals or even (my personal favorite) Sexagesimals….

But then I don’t thing we are counting things up quite the same way any more.

[Baghdaddy]

@rjclayton:

I see you found your crack pipe again!

He also seems to be sharing it with the resident MILF…

[Jennifer]

@rjclayton:

But the probability that you have calculated is .32476215 for Infantry on attack and .12978248 for fighters on attack.  8 decimal places.  That you chose to display them as a percentage does not change the fact that the probability is to 8 decimal places.

It’s two integers with 6 decimals.  You could make it a fraction too, does that mean there are NO decimals now?  After all, 32.476215% is just 32476215/100000000 and that is NO decimals.

Hmm……

So yes, decimal places are counted by the number of places filled to the RIGHT of the decimal and not the integers to the LEFT of teh decimal.

I should know, after all, I only TEACH this stuff and have passed numerous state certifications to teach this stuff and classes in learning this stuff.  You can twist it and turn it, but I can just reverse the twists and turns and twist and turn it to the same degree in the other direction.  But it all boils down to 6 decimals (AKA the number of integers to the right of the decimal) is what mathematicians generally consider to be an accurate number.  Does that mean 8 decimals is less accurate?  No.  8 decimals are obviously MORE accurate.  But no one is going to calculate 8 decimals by hand.

[newpaintbrush]

@Jennifer:

@rjclayton:

But the probability that you have calculated is .32476215 for Infantry on attack and .12978248 for fighters on attack.  8 decimal places.  That you chose to display them as a percentage does not change the fact that the probability is to 8 decimal places.

It’s two integers with 6 decimals.  You could make it a fraction too, does that mean there are NO decimals now?  After all, 32.476215% is just 32476215/100000000 and that is NO decimals.

Hmm……

So yes, decimal places are counted by the number of places filled to the RIGHT of the decimal and not the integers to the LEFT of teh decimal.

I should know, after all, I only TEACH this stuff and have passed numerous state certifications to teach this stuff and classes in learning this stuff.  You can twist it and turn it, but I can just reverse the twists and turns and twist and turn it to the same degree in the other direction.  But it all boils down to 6 decimals (AKA the number of integers to the right of the decimal) is what mathematicians generally consider to be an accurate number.  Does that mean 8 decimals is less accurate?  No.  8 decimals are obviously MORE accurate.  But no one is going to calculate 8 decimals by hand.

Oo, I am invited to “twist it and turn it”.  Innuendo aside, is that implied support for state certifications, and thereby, the system upon which state certifications are based?

Who are these mathematicians that consider six decimal places to be accurate?  Obviously those that are constrained by others to limit the precision with which those calculations can be reported.  As such, those mathematicians can no longer really be considered “mathematicians” in the pure sense, can they?

[Jennifer]

@rjclayton:

So, you wouldn’t happen to be referring to Newton’s Method, would you?  A guess and check method for calculating the root?  Because I don’t see what this calculation has to do at all with calculating the average number of hits with your infantry?

The only part of newton I was referring too is the standard practice of using 6 decimals in your result as a standard of accuracy.

[Jennifer]

@newpaintbrush:

…is that implied support for state certifications, and thereby, the system upon which state certifications are based?

Who are these mathematicians that consider six decimal places to be accurate?  Obviously those that are constrained by others to limit the precision with which those calculations can be reported.  As such, those mathematicians can no longer really be considered “mathematicians” in the pure sense, can they?

No, but unfortunately, we live in an ever increasing socialist regime in the United States and if you WANT to have a job, THEN you have to pass the state exams to have the privalege to have the job.  What’s worse is you have to muzzle your freedom of thought and expression to an even greater degree then you do as a soldier or end up jobless.  (Unless you’re a liberal, then feel free to shove your gay, gun hating, freedom hating, hate spewing opinion down everyone’s throat, as long as you don’t recoginize any divine power over your own, you’re okay.  Or so it seems.)

Anyway, the mathematicians that consider six decimal places to be accurate ENOUGH are basically the mathematical community.  No one is stipulating that more accuracy is bad, just that it’s no longer a significant enough contributing factor to the problem.  Obviously, if you can have a team of super computers working in series on your problem taking it to the nth degree that’s more accurate then a single math professor with a pencil and paper.

But is there really a significant difference between 32.118795 and 32.11789500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004?

Most mathematicians don’t think so.  I am one of those.  But we all recognize that there is a difference, just thta it is not significant enough to worry about.

[rjclayton]

@Jennifer:

But is there really a significant difference between 32.118795 and 32.11789500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004?

Yes, there is a significant difference between the two.  Practically, the additional accuracy may or may not be important, it is entirely dependent on the application.  Which is why this “6 decimals are standard” thing is so absurd; it completely depends on the application.  You may just want to leave this one to the engineers Jen.  :roll:

[Jennifer]

Engineers are not mathematicians.  Neither are scientists.  On a macro scale there may be a very significant difference, there may not be.  That’s why science developed the policy of significant figures.  (ie, if you start with two decimal places, you end with two decimal places rounded up or down as needed.)

Math is different.  Pure math has the consensus, the general rule, that answers are significantly accurate at six decimal places.  This stems from Newton’s assertations when he was developing his theories and laws.  Thus, the square root of 3 is accurately described as 1.732051 with the last 808 rounded up.

Now, if your specific engineering instance demands a higher degree of certainty, that does not mean that the mathematical accuracy is wrong, it means you, personally, need more accuracy.  No one is stipulating that 1.732050808 is less accurate or of the same accuracy.  Mathematicians just stipulate that, for the purposes of pure math, 1.732051 is accurate enough, or 6 decimal places are the limit of significance we need to continue on to the next step of the problem.

Trust me, just leave the mathematical theory to the mathemeticians and stick to doing your own job.  Build something with the formulas, laws and theorems we give you.

[Guest]

Back on topic (and mathematical nuances of significant digits are NOT the subject of this thread)

[General_D.Fox]

I was beginning to get worried this was going to turn into Math 432.  And I thought Matrices were tough in Math 210, sheesh. I frankly don’t break out a calculator when I play this game.  It’s called my brain, and if I have more guys than him and am attacking at roughly the same or more than him on attack numbers, then I’m in business.  And since I’ve only played this game for a year and a bit, I’m sure there’s tons of strats for me to think of and break out and attempt and put into action.  What’s a little losing when you have fun and learn at the same time.

[losttribe04]

GEN Fox,

So scenarios like “you have a TRN leaving the DC Navel yard at two spaces per turn heading for Berlin. Germany has a TRN leaving Berlin at the rate of two spaces per turn heading for the DC Navel yard. The US TRN left one turn earlier then Germany’s. How long will it take till they both collide?” just don’t interest you? (he he  :lol:)

-LT04

[newpaintbrush]

@losttribe04:

GEN Fox,

So scenarios like “you have a TRN leaving the DC Navel yard at two spaces per turn heading for Berlin. Germany has a TRN leaving Berlin at the rate of two spaces per turn heading for the DC Navel yard. The US TRN left one turn earlier then Germany’s. How long will it take till they both collide?” just don’t interest you? (he he  :lol:)

-LT04

Fascinating.

Spockbrow!

[Jennifer]

@ncscswitch:

Back on topic (and mathematical nuances of significant digits are NOT the subject of this thread)

Awe, and I was about to break into some high level, esoteric sh*t too. :P

How about this, I’ll give you even odds your transport shoots down two of my transports and damages my battleship, surviving the engagement and forcing my battleship to withdraw to lick her wounds. :P

[General_D.Fox]

Jenn, I’ll take those odds.  I’ve seen 4 transports all get blown up by a lone bomber, and I’ve seen 3 transports blow up 2 bombers wihtout dying.  I may not have seen everything, but I’ve seen alot!  8-)

And PaintBrush, how much wood can a woodchuck chuck if a woodchuck could chuck wood?  Yeah, if given time I’d probably figure out that problem.  But for the rest of those numbers everyone’s breaking out…WHOOSH, over my head!

[Jennifer]

Yea, that happened to me against Djensen.