1.29 and PTW: Closer but still not great

[Coracle]

Originally posted by Destroyer
I thought the original post made some excellent points. While I love civ3, it should not have had civ2s better features stripped out.

Scenario building is the thing which has etched civ2 into legend.

And kept it going for over five years.

It was nothing less than a ripoff that Civ 3 was marketed without that vital aspect of Civ 2.

[Theseus]

Originally posted by N. Machiavelli
Only one small problem with their 'Civulator'. It doesn't take into account building and individual citizen bonuses when calculating the defense value of a unit in a city. The number of citizens and buildings are calculated when coming up with the defense bonus. I do not have the editor here at work, but it's something like +1% per citizen and +4% per building or something like that. These bonuses account for alot of 'odd' results when attacking a city, like a modern armour losing against a fortified pikeman in a city.

For the odds guys:

Is what Nic saying correct? Are there others defense factors when in cities that are not included by the Civulator?

I'll tell you what's wrong with that thing... it won't do calculations for ARMIES!!! Want a real mind-bender? Try doing the combinatorial odds for a mixed-unit Army, on either defense or offense, against multiple units...

[Excelsior84]

Originally posted by Theseus
Is what Nic saying correct? Are there others defense factors when in cities that are not included by the Civulator?

I don't *know* that this is not the case, but I've never heard of it. I think he may be mis-interpreting the "citizen" and "building" fields under "Defensive Bonuses" (under "General Settings") as being a per-citizen/building bonus to unit defense. According to the help, however, this value is used to determine population and building resistance to bombardment. i.e., 4 defensive bonus means a bombardment with 4 damage has a 50% chance of killing a citizen.

[vondrack]

Originally posted by Excelsior84
Yes! I got it!

The probability is (sorry for the formatting, as it looks hideous):

((5!)/((3!)((5-3)!)) * ((.25)^3)((.75)^2)) + ((5!)/((4!)((5-4)!)) * ((.25)^4)((.75)^2)) + ((5!)/((5!)((5-5)!)) * ((.25)^5)((.75)^1)) = 90/1024 + 15/1024 + 1/1024 = 106/1024 = 0.103515625...

Or, in words, the combination of 5 taken 3 at a time times success probability of .25 to the 3rd power times the failure rate of .75 squared plus 5 taken 4 at a time times success probability of .25 to the 4th power times the failure rate of .75 plus 5 taken 5 at a time times success probability of .25 to the 5th power times the failure rate of .75 to the 0th power (1).

Ex, the formula is not correct - you forgot that the combination involving the last round won by the swordsman must be taken out. However, your formula helped me to recall that little bit of math I needed. It is like this:

[Excelsior84]

Urm...no, I think that formula isn't right. Mine, at least gives the right answer. Hold on, I'll write mine up where it can actually be read.

[F18fett]

I miss the days when an army of tanks could wipe out a stupid civ that didn't know to build defense units better than musketeers.

[Excelsior84]

This is it:

[vondrack]

Originally posted by Excelsior84
Urm...no, I think that formula isn't right. Mine, at least gives the right answer. Hold on, I'll write mine up where it can actually be read.

Well, it is interesting... your formula actually does produce the right result, although I have no idea what the numbers in it represent... especially having (1/4)^5 puzzles me - what does that stand for? It would be the probability of the archer winning five consecutive rounds...?! Even the 5!/(5!(5-5)!) would correspond to that... but then, there is no such situation possible...

BTW - try enumerating my formula. You will get the same result! Math is fun, isn't it?

Wait... I am looking into your formula and... I begin to understand it. Your formula expresses the probability that the archer will win at least three out of five consecutive rounds. But that is something a bit different from what we are trying to express... the combat will end after his third victorious round, so considering five victorious rounds is incorrect. I find it interesting that the result is exactly the same, even if the formula expresses something different... is that a coincidence?

So, I still insist on that my formula is correct, even though yours gives the same result...

[vondrack]

I must say that I enjoy this math discussion much more than my Hitler discussion yesterday...

[The_Aussie_Lurker]

For my part, I'd say that Dom Pedro is NOT a whiner, because he makes realistic, constructive criticisms!! Coracle, on the other hand, is a Whiner-not only because his criticisms are NOT constructive, but because they are REPETATIVE!!! If he hates this game so much, he should just go back, play Civ2 and leave the rest of us ALONE!!
I'd agree with DP that the editor patch, though excellent overall, does leave some vital elements out. For me the absence of events scripting, pooled editor flags for units and buildings and the ongoing presence of Hardcoded values for things like movement on enemy roads/Railroads and points for Cultural Victory are major issues, but ones which I hope Firaxis will deal with in time (and I believe they will, as well)!!
I also hope that, one day, they will re-examine the issues of trade routes (perhaps making them visible, like those in CtP!) and resource disappearance ratios! It seems to me that it would fairly easy to code for a "Disappearance Ratio/city" value, based on the resources "Rarity" and "Deposit Size", so that the chance of your resource actually disappearing would be connected to the size of your empire. I also feel that all units which require a resource as fuel (such as coal or oil) should start to suffer 1hp damage every turn they are cut off from that resource (eg. as in an embargo). I do feel, though, that just the presence of strategic resources in the game, and their importance in building units and improvements, shows how the game has evolved from it's Civ1/2 roots! As for bringing back spies and caravans-yech!!! All that did was provide opportunities for tedium, and was the major thing that put me off playing Civ2 on a regular basis! The trade and espionage systems do need to be improved, but I prefer the abstracted method!
Anyway, I'm sure this will simply get me a "Fanboy" label from Coracle but...WHO CARES!!!

Yours,
The_Aussie_Lurker.

[Excelsior84]

Originally posted by vondrack
Wait... I am looking into your formula and... I begin to understand it. Your formula expresses the probability that the archer will win at least three out of five consecutive rounds. But that is something a bit different from what we are trying to express... the combat will end after his third victorious round, so considering five victorious rounds is incorrect. I find it interesting that the result is exactly the same, even if the formula expresses something different... is that a coincidence?

So, I still insist on that my formula is correct, even though yours gives the same result...

That's correct, it is the odds that it will win exactly 3 rounds + the odds that it will win exactly 4 rounds + the odds it will win exactly 5 rounds. The reason we have to include the odds for 4 and 5 rounds, even though the combat stops after 3 rounds, is that you can't simply throw away the cases where it wins all 5 (or 4) rounds. If it wins all 5, it will show up as 3 consecutive wins in combat, same as winning the first three and losing 1 of the next 2, and the same as winning the first 3 rounds, and losing the next two. These cases make up the probability of winning the first three rounds without a scratch.

i.e.,
odds of Vic-Vic-Vic-Fail-Fail = 9/1024
odds of Vic-Vic-Vic-Vic-Fail = 3/1024
odds of Vic-Vic-Vic-Fail-Vic = 3/1024
odds of Vic-Vic-Vic-Vic-Vic = 1/1024
The sum of those probabilities is 16/1024 = 1/64, the same as a simple Vic-Vic-Vic (because that's what it is)

EDIT: And to clarify, this same reasoning can be applied to instances such Vic-Vic-Fail-Vic-Vic, where it wins 4 of 5, yet it stops after the 4th.

Does that make sense?

[vondrack]

Originally posted by Excelsior84
That's correct, it is the odds that it will win exactly 3 rounds + the odds that it will win exactly 4 rounds + the odds it will win exactly 5 rounds. The reason we have to include the odds for 4 and 5 rounds, even though the combat stops after 3 rounds, is that you can't simply throw away the cases where it wins all 5 (or 4) rounds. If it wins all 5, it will show up as 3 consecutive wins in combat, same as winning the first three and losing 1 of the next 2, and the same as winning the first 3 rounds, and losing the next two. These cases make up the probability of winning the first three rounds without a scratch.

i.e.,
odds of Vic-Vic-Vic-Fail-Fail = 9/1024
odds of Vic-Vic-Vic-Vic-Fail = 3/1024
odds of Vic-Vic-Vic-Fail-Vic = 3/1024
odds of Vic-Vic-Vic-Vic-Vic = 1/1024
The sum of those probabilities is 16/1024 = 1/64, the same as a simple Vic-Vic-Vic (because that's what it is)

EDIT: And to clarify, this same reasoning can be applied to instances such Vic-Vic-Fail-Vic-Vic, where it wins 4 of 5, yet it stops after the 4th.

Does that make sense?

Yep, it does. I have realized that, too, only after submitting my last post. The difference between our formulas is that mine is a very close rewrite of the simple formulas I wrote in the very beginning, expressing exactly what happens (=is possible) in Civ3, while yours uses a smart trick of considering even "impossible" cases (which do not affect the result we seek) to get rid of the variable "length" of the combinations. Both are mathematically correct and provable (is there a word like that?), that is right. Just two ways to the same end.

[Excelsior84]

Good, then we agree.

[N. Machiavelli]

I'm glad we all agree.

[IthacaMike]

Originally posted by DrFell


Sorry to be nitpicky, but this is actually wrong... it should be 1/64 (1/4*1/4*1/4) for two regular units. 1 in 64 losses for the swordsman doesn't exactly seem like an unrealistic value for a swordsman attacking an archer. Maybe next time you should bring along more units, no?

No, he is close to right. The swordsman could win the first two rounds and then lose three in a row (3/4*3/4*1/4*1/4*1/4) or the swordsman could lose win one and then lose the next three, or...

I just ran a sim and it looks like the defending archer should win about 1 time in 10 (swordsman won 90.8% of the time in my sim).

Mike