I can't figure out how to Google this, so I'm hoping someone here is better at math than I am.
If my opponent is adding X troops per turn, and I am adding Y troops per turn (where Y > X), how long will it take before I have 3 times my opponent's troop number?
Re: Math question: adding troops
Posted: Fri Feb 20, 2015 2:41 pm
by sempaispellcheck
Let's say at the time you start adding troops, you have A troops and your opponent has B troops. After C turns, you will have (C x Y) + A troops, and your opponent will have (C x X) + B troops. You want C such that: (C x Y) + A = 3((C x X) + B) (C x Y) + A = (C x 3X) + 3B C x Y = (C x 3X) + 3B - A Y = 3X + (3B/C) - (A/C) (3B - A)/C = Y - 3X C = (3B - A)/(Y - 3X) Now you simply plug in your values for A, B, X, and Y and solve.
sempai
Re: Math question: adding troops
Posted: Fri Feb 20, 2015 2:43 pm
by owenshooter
sempaispellcheck wrote:Let's say at the time you start adding troops, you have A troops and your opponent has B troops. After C turns, you will have (C x Y) + A troops, and your opponent will have (C x X) + B troops. You want C such that: (C x Y) + A = 3((C x X) + B) (C x Y) + A = (C x 3X) + 3B C x Y = (C x 3X) + 3B - A Y = 3X + (3B/C) - (A/C) (3B - A)/C = Y - 3X C = (3B - A)/(Y - 3X) Now you simply plug in your values for A, B, X, and Y and solve.
sempai
seriously... i wouldn't have even bothered my 5th grader for this answer... jeez...-Jésus noir
Re: Math question: adding troops
Posted: Fri Feb 20, 2015 4:02 pm
by nietzsche
a= your opponent's starting troop number b= your starting troop number A = total opponent troops B = your total troops X= your opponent's troops per turn Y= your troops per turn T = turns
ok sempai beat me to it but it's fun to solve it nonetheless.
Re: Math question: adding troops
Posted: Fri Feb 20, 2015 4:59 pm
by Metsfanmax
nietzsche wrote:This equation will only work when Y > 3X.
Which means that you can only ever get to three times your opponent's troops if you're earning more than three times as many troops as him. Possibly non-intuitive; naively it seems like if you're out-trooping your opponent then your relative strength over them should grow without bound. But it doesn't; asymptotically you can never amass more relative troops than that implied by the number you each get per turn.
Re: Math question: adding troops
Posted: Fri Feb 20, 2015 6:00 pm
by nietzsche
Metsfanmax wrote:
nietzsche wrote:This equation will only work when Y > 3X.
Which means that you can only ever get to three times your opponent's troops if you're earning more than three times as many troops as him. Possibly non-intuitive;
Yes, it did take me a second when I tried to corroborate it with values of 2 to 1.
Re: Math question: adding troops
Posted: Fri Feb 20, 2015 8:22 pm
by AyeTrain
You guys are scholars and gentlemen! Much obliged.
...looks like I might have to settle for smaller odds.
Re: Math question: adding troops
Posted: Sat Feb 21, 2015 9:22 pm
by Ragnars Wolves
I am NO math genius to be sure....but if you get out of strictly math and DO get into the game as the post started out....it will depend on where you are located, if you are playing while accumulating troops, and bonus's you get not to mention the troops you AND your opponent lose.
Anything other than that in this game isn't worth the effort seems to me.
Re: Math question: adding troops
Posted: Sun Feb 22, 2015 3:41 pm
by JPlo64
Using nietzsche notation, as T -> infinity, B/A -> Y/X
Re: Math question: adding troops
Posted: Sun Feb 22, 2015 3:44 pm
by JPlo64
AyeTrain wrote:You guys are scholars and gentlemen! Much obliged.
...looks like I might have to settle for smaller odds.
But even though the troop proportion doesn't really change, your odds do continue to improve as the troop count goes up b/c of attacking dice advantage.
Re: Math question: adding troops
Posted: Tue Feb 24, 2015 9:13 am
by macbone
Without knowing the situation, 3x your opponent's troops on a single tert is way more than enough. 2x is a safe margin, 1.5x is generally enough, and in a simple 1v1 situation, even having one more troop than the other player gives you an advantage, particularly the more you each have on the tert.
If your opponent has more territories, though, you'll need more troops of your own, generally +1 for each territory your opponent owns.
Re: Math question: adding troops
Posted: Tue Feb 24, 2015 9:39 am
by owenshooter
the black jesus has spoken, let's shut this baby down...-Jésus noir
Re: Math question: adding troops
Posted: Tue Feb 24, 2015 12:30 pm
by Dukasaur
owenshooter wrote:the black jesus has spoken, let's shut this baby down...-Jésus noir
Re: Math question: adding troops
Posted: Tue Feb 24, 2015 12:57 pm
by owenshooter
Dukasaur wrote:
owenshooter wrote:the black jesus has spoken, let's shut this baby down...-Jésus noir
come on... get a little more contemporary!!-Jésus noir
Posted: Fri Feb 20, 2015 1:47 pm