Err.. 2/3 + 1/2 + 1/6 > 1...
No Maths scholar, but here's what I remember from my high school lessons
Ok, let's assume you spread your army 1/4 : 1/4 : 1/2 is A,B,C
You win A if your opponent's army there is <= 1/4
You win B if your opponent's army there is <= 1/4
You win C if your opponent's army there is <= 1/2
So...the probability that you win A & B is the probability that your opponent's army at A <= 1/4 and B <=1/4
Since your opponent is random, the probability of each combination he chooses is equal...that is the probability of him setting his army 1/4:1/4:1/2 is the same as the probability of 1/3:1/3:1/3. In other words, 1/(total possible combinations). From there you should be able to calculate the total combinations where A <= 1/4 and B <= 1/4. And from there, the probabilities
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Thread: How do you think through this?

05132010, 10:03 PM #314w5, Fi>Ne>Ti>Si>Ni>Fe>Te>Se, sp > so > sx
appreciates being appreciated, conflicted over conflicts, afraid of being afraid, bad at being bad, predictably unpredictable, consistently inconsistent, remarkably unremarkable...
I may not agree with what you are feeling, but I will defend to death your right to have a good cry over it
The whole problem with the world is that fools & fanatics are always so certain of themselves, and wiser people so full of doubts. ~ Bertrand Russell

05132010, 10:18 PM #32
Haha, yah i saw that after I saw my original answer on top. I was thinking you have to win 2/3 of the time and wrote that instead of 1/3 . Damn, I don't even remember what I did in math in high school.
Ok I get where your coming from now, the equation kind of confused me. Domo arigato gozaimasu.This post grammatical errors had been intentionally left uncorrected.

05132010, 10:26 PM #33
Haven't done any calculations, but my gut feel is that 0:1/2:1/2 would give the best results...
4w5, Fi>Ne>Ti>Si>Ni>Fe>Te>Se, sp > so > sx
appreciates being appreciated, conflicted over conflicts, afraid of being afraid, bad at being bad, predictably unpredictable, consistently inconsistent, remarkably unremarkable...
I may not agree with what you are feeling, but I will defend to death your right to have a good cry over it
The whole problem with the world is that fools & fanatics are always so certain of themselves, and wiser people so full of doubts. ~ Bertrand Russell

05132010, 11:39 PM #34
Alright, so I've spent some time running this puzzle through my mind, and I've found a definite, 100%, win/win scenario.
Firstly, let's review the errors in logic:
 THE ERROR OF 'NOT REALLY INFINITY BUT STILL KINDA LIKE IT'
a) The first error and most obvious error, is found in the OPs use of the term 'essentially infinite'.
 Infinite numbers cannot be divided, otherwise the number divided will be infinite as well.
 It is impossible to subtract anything from infinity and come to something less than infinity; e.g., if you take one banana away from an infinite number of bananas, the number of remaining bananas is infinite.
>>> Thus, dividing a certain amount of troops to conquer and having all of your troops killed is logically impossible; all possibilities result in an infinite battle. Of course, the OP tried to correct the flaw, but it failed harder than Bill Clinton on his wedding night.
b) It's motherfucking infinite.
 It's infinite, motherfucker.
 THE ERROR OF RANDONIMOTYINOMITY
The opposing general uses no strategy and distributes his troops randomly.
 How did this dumbshit of a warlord come into power?
 How does he keep the economy and people under his control?
 Where do they live, as the universe might not be able to contain an infinte amount of people.
 Etc.

Yet, EVEN IN THE MIDST OF SUCH OVERWHELMING ODDS I've arrived at a DEFINITE CONCLUSION:
IT'S MOTHERFUCKING DELICIOUS!!!!INTJ  5w4  Sp/Sx/So  54(9/1)  RLoEI  MelancholicCholeric  Johari & Nohari
This will not end well...
But it will at least be poetic, I suppose...
Hmm... But what if it does end well?
Then I suppose it will be a different sort of poetry, a preferable sort...
A sort I could become accustomed to...

05142010, 12:00 AM #35
 Join Date
 Feb 2008
 MBTI
 INTJ
 Posts
 253
Aha! That's a sensible lad. Now, might I bring our attention to something much more meaningful to the mathematics, philosophy, and physics communities? This is the disjunction that infinity and quantitative distinction cannot be postulated to both exist at the same time in any objective sense; for the objective validity of the one would negate that of the other and vice versa. The sequence of reasoning is something like the following.
If the universe is infinitely expanding, then dividing it into quantitatively distinct parts is illusory for the same reason it makes little sense to divide troops if they are infinite. Since such an endeavor would preclude quanta from being discovered and distinguisheable, it follows that quanta is the necessary creation of a limited earthbound mind, which breaks the world up into discrete parts for convenience, but is not an accurate representation of the world as it is. If, on the other hand, quantitative distinctions of the universe are objective, then this necessitates that the universe is finite rather than infinite; for only in a finite world could quantity take on meaning. In that case, it is infinity that is necessarily created by the mind.
It is no small coincidence that maintaining that the universe is infinite lends to the Copenhagen Interpretation of quantum mechanics and its intense focus on the observeri.e. creator. For quantum mechanics without the observer means the universe is not infinite and that would contradict many of the longesteemed beliefs of our pop scientists.
Now, should quantum physicists get out of their dogmatic slumber and one day get it right by embracing Karl Popper's notion of quantum mechanics without the observer, and stop misconstruing Heisenberg's principle as precluding the possibility of measuring movement and position rather than as a statistical scatter, this, it seems, would not be entirely without consequence.

05142010, 12:07 AM #36
We got some physics going on in here!!! WOOT WOOT!
INTJ  5w4  Sp/Sx/So  54(9/1)  RLoEI  MelancholicCholeric  Johari & Nohari
This will not end well...
But it will at least be poetic, I suppose...
Hmm... But what if it does end well?
Then I suppose it will be a different sort of poetry, a preferable sort...
A sort I could become accustomed to...

05142010, 12:19 AM #37ReflecTcelfeRGuest
Throwing the first fight seems logical and then dividing into half your armies for the last two, because even if the opponent throws one opponent into the first fight you automatically win, but this is only strategically speaking, in other words... I agree with others before this post.

05142010, 02:11 AM #38
Infinity divided by infinity would equal to one, oh snap! Besides the concept of infinity in the problem is an inference which successfully caused MM's mind to asplode. We know that it's stating people and there is a limited amount of people in the world. So all we have to do is divide the total amount of people in the world in half (if it's odd, that unlucky soul would be first blood and would be used to rationalize the war) and use that number to compute the data. Unfortunately, that sounds like too much work. But, if you treat this problem like an abstract question, infinity would own your ass.
This post grammatical errors had been intentionally left uncorrected.

05142010, 02:44 AM #39
Infinity works a little bit different from numbers such as 3 or 4.
Check this out: WikiAnswers  Does infinity divided by infinity equalINTJ  5w4  Sp/Sx/So  54(9/1)  RLoEI  MelancholicCholeric  Johari & Nohari
This will not end well...
But it will at least be poetic, I suppose...
Hmm... But what if it does end well?
Then I suppose it will be a different sort of poetry, a preferable sort...
A sort I could become accustomed to...

05142010, 03:02 AM #40
Yes, I know what infinity stands for, obviously if you have infinite amount of people you would not even have a battle field to even work with. Infinity is an abstract idea in math. Trying to intergrate it in real life concept such as the probability question in this thread would give you no solution. However, it is used quite often in the concept of limits as a way to replace infinitesimal.
It is also the reason why I wonder how DC was able to reduce an infinite amount of universes in "Crisis on Infinite Earths" storyline to just 52 universes.
"You are the general of an army of essentially infinite numbers. The opposing general has an army equally as massive."
"Since infinity is not a set number, you cannot assume that infinity divided by infinity would equal one. Infinity could be 1 or it could be 9 trillion, the number is not set in stone."
This post grammatical errors had been intentionally left uncorrected.
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