Re: Tech Progression Formula?
 

Jimbob, that will work in some but not all situations.

If you have only 6 levels of propulsion, thats what the other player will receive.

If you have 12 levels and he has 5, he will receive levels 6, 7, 8, 9, 10 and 11 !! You are giving him 6 levels that he doesn't have.

Best to know exactly what each other has before making the trade.

I once made this trade with the AI. Can't remember what I gave, but he gave me two levels of fighters. Like this:

fighters
fighters

I only received one level because that was all he had! (Naturally I had to declare war and wipe him out. http://forum.shrapnelgames.com/images/icons/icon12.gif )

Re: Tech Progression Formula?
 

<font size="2" face="Verdana, Helvetica, sans-serif">I think I got it... one more question. Suppose I have level 5 Existentialism and he has level 1 Existentialism, and then I offer:

Existentialism
Existentialism

Will he get levels 2 & 3? Or will he get all the way up to level 5 (even though I only 'gave' two levels in the trade)? It seems he should just get levels 2 & 3. But if he had level 2 to start, he would get levels 3 & 4.

Yes?

Re: Tech Progression Formula?
 

Yes. It appears you have it now Jimbob.

Re: Tech Progression Formula?
 

<font size="2" face="Verdana, Helvetica, sans-serif">Well, DavidG's formulas are mathematically equivalent to Andrés' formulas (yeah, I'm a geek; I did a quick arithmetic proof). DavidG's formulas are just the recursive form (i.e., the total cost is the previous level's cost plus the difference calculated from his formulae), while Andrés' formulas are the absolute form (i.e., you just need to know the level cost and the level being researched to find the total cost).

For those who are interested, the proof involves taking the "absolute" formula for level "L" and subtracting the formula for level "L-1", then reducing algebraically to come up with the difference between each level.

Full proof follows:

Low tech cost: absolute formula is LC*L

LC*L - LC*(L-1) = LC*L - LC*L + LC = LC

Therefore, the difference in cost for each level is equal to the level cost.

-----------------------------------
Medium tech cost: absolute formula is LC*(L²/2)

LC*(L²/2) - LC*[(L-1)²/2] = LC*[L²/2 - (L²/2 - 2L/2 + 1/2)] = LC*[2L/2 - 1/2] = LC*(L - 0.5)

Therefore, the difference in cost for each level is equal to the level cost times "Level - 0.5"

-----------------------------------
High tech cost: absolute formula is LC*(L²)

LC*(L²) - LC*(L-1)² = LC*[L² - (L² - 2*L + 1)] = LC*(2L - 1) = 2*LC*(L - 1/2)

Therefore, the difference in cost for each level is equal to the level cost times 2, times "Level - 0.5"

[ July 23, 2002, 17:18: Message edited by: DirectorTsaarx ]

Re: Tech Progression Formula?
 

Awesome work DirectorT. Really! http://forum.shrapnelgames.com/images/icons/shock.gif

I am a bit of a math dweeb myself, but not at your level apparently. I did test a few levels of DavidG's method (Can't bring myself to call it a "formula" http://forum.shrapnelgames.com/images/icons/icon12.gif ) and I did see that it worked for every one I tested. So I assumed it would be correct forever. I figured there was a way to mathematically prove it, but my brain started hurting when I tried, so I quit. http://forum.shrapnelgames.com/images/icons/icon7.gif

Geoschmo

Re: Tech Progression Formula?
 

<font size="2" face="Verdana, Helvetica, sans-serif">Well, if you really were curious (and I certainly hope you're not), my semi-versed eye wants to say that proving this should probably involve mathmatical induction, and the principle thereof. 'Course, the Last "math" course I took was Analysis of Algorithms, and said principle was my main tool therein...

E. Albright

"When all you have is a hammer, everthing starts to look like a nail."

Re: Tech Progression Formula?
 

Well, I did learn one thing... how to successfully bait math geeks. And to think how many of you were passed on the starring role in "A Beautiful Mind."

http://forum.shrapnelgames.com/images/icons/icon12.gif

Well, needless to say I found this info valuable, but as a pragmatist I bailed out mentally when arithmetic proofs popped up. OUCH! http://forum.shrapnelgames.com/images/icons/blush.gif

What I'm trying to say is thanks, especially to Andres, for his quick response.

I think most PBW players will find this info quite pertinent. It should limit the amount of stumbling around when figuring out trade values.