10-12-2003 18:54									#61
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AWESOME!

Thankyouthankyouthankyou!

	10-12-2003 19:13									#62
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{BOLD}
{SIZE=15}



{/SIZE}
{/BOLD}

I know that it didn't work, it just to emphasize the thought.

	10-12-2003 19:16									#63
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I did some maths...

If I'm not wrong, in a combat where with the old system was a 70% possibilities of lossing the combat, now will be a 86% or 88% of possibilities of lossing the combat (86% if ties are resolved with 1 combat, 88% if ties are resolved with 4 combats again).

This systems increments the advantage of the most powerful unit - in every single combat. For defense and offense. True, it will be more difficult that a tank lost against a Spearmen, but many other results (in units from the same age, for instance) will also change.

In Civ2 we had the Firepower/Hit Points system that gives advantage to units from a moder age compared to ancient units. In Civ3, with the new system, this advantage is not given to units of modern age, but to any unit that is more powerful, even if only a little more, than its enemy unit.

	10-12-2003 19:23									#64
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Um... okay, forgive the English teacher here, but someone tell me what the math just became on, say:

a warrior beating a spear in a town without walls?

Correct me if I'm wrong, but the warrior may have just become a completely useless unit (spare the "it already was" talk - in MP, jagrushes and chasquirushes are not uncommon) in any form.

In fact, this mechanic change makes defense (typically easier due to all the defensive bonuses) much easier, and vastly increases the need for lots of artillery beforehand.

I'm not certain this is a good change *at all.*

That's if I understand this right, which I'm not sure I do.

(Everything else is great, just this one has me rather worried.)

	10-12-2003 19:28									#65
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Umm... okay, forgive my bad english, teacher

Any combat that was "easy" in the old system (easy means that you won more time that you lost; or, in other word, it was more likely to win that to lost) is now "easier".

I don't know Civ3 (I'm a Civ2 guy) enough to tell you if defense is easier that offense in Civ3, but it is was, now it is even more "easier".

What was "unlikely" in the past, is now more unlikely. What was likely, is now likely.

IMHO that is great for some unlikely results (like ancients units beating mordern units) but not for some other results

	10-12-2003 19:36									#66
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I updated the combat calculator for the patch.
See the effect of the change for yourselves.

Attachment: c3c combat.zip
This has been downloaded 34 time(s).

	10-12-2003 19:44									#67
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please correct me if i'm wrong...
but aren't the odds the same as before, just the standard deviation changed?
it's still a bell-curve, just a lot "tighter".

another effect of this combat system: speed is even more important because you could need to retreat a lot more than before.

	10-12-2003 19:59									#68
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Well that's true for identical attack and defend values. But as soon as they differ altering the standard deviation for both distributions changes the odds of winning.

To see the point think of 2 normal distributions with mean 2, and any standard deviation. Changing the sd wont affect the probability of a random draw from one distribution being greater than a random draw from the other.

But make the second distribution have a mean of 3 (ie swords versus unfortified spear with no bonus) then the effect of decreasing the sd of both distibutions most definitely does alter the probability of a random draw from the second distribution being greater than a draw from the first.

That's not exactly how the Civ3 combat model works, and there are hitpoint distinctions of course. But it should show you how decreased sd does change the odds of winning a battle.

	10-12-2003 20:50									#69
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quote: Originally posted by JesseSmith Combat System "Less Streaky" The Change was having the random number generator (rng) calculate the Results 4 times instead of 1. Possible Outcomes: AttackerLoses, AttackerWins If there is a tie, it retries. This forces the combat system to be more accurate and less "streaky"

reposted from my message to civfanatics-

[Summary of the mathematical results below: This change does not eliminate 'streakiness' except as a side-effect...]

If the probability of a 'w' is q where q lies on the interval [0,1], and the probability of an 'l' is 1-q, then:
(a) the probability of 4 w's is ,
(a) the probability of 3 w's and an l is ,
(a) the probability of 2 w's and 2 l's is ,
(a) the probability of 1 w and 3 l's is and
(a) the probability of 4 l's is .

Therefore, if the probability of a win in this new system of odds is p (where a win requires at least 3 w's out of 4), then obviously

and solving for p, .

Clearly this transformation from q to p changes the distribution. Plotted below (courtesy of Mathematica ) is q vs. p:



What this does not do is eliminate the streakiness of the results, except as a side-effect.

Mathematically, the only real way to eliminate streakiness is to use a better pseudo-random number generator. In particular, a good choice of a very fast random number generator with extremely low periodicity is the Mersenne Twister: Mersenne Twister web page (with code).

Even with the best pseudo-random number generator, streaks will occur with proper statistical frequency. This statistical frequency may seem higher than "common sense" might suggest, merely because the human mind notices streaks more than non-streaks and tends to note them, distorting the "observational frequency"...

	10-12-2003 21:01									#70
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quote: Originally posted by eliliang Even with the best pseudo-random number generator, streaks will occur with proper statistical frequency. This statistical frequency may seem higher than "common sense" might suggest, merely because the human mind notices streaks more than non-streaks and tends to note them, distorting the "observational frequency"...

* Dominae bookmarks this quote for use in arguments against those who think streaks are not part of randomness, and that the human mind is intuitively a great judge of the probabilty of random events.

	10-12-2003 21:17									#71
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Here's a chart showing what new a/d ratio you need to get the same odds for victory as you used to get with a given a/d ratio.

You need about 2.1 times the defender to get the same odds as you used to get with a tank against a fortified spearman. So Cavalry now is more effective against Spearmen than Tanks used to be!

Attachment: combat1.jpg
This has been downloaded 280 time(s).

Last edited by alexman on 10-12-2003 at 21:27

	10-12-2003 21:42									#72
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Thanks for the plot alexman. It takes a minute to figure out, but makes a lot of sense after that.

What I'm getting from it is that:

1. If the attacker and defender are more or less evenly matched, there is little difference between the new combat and the old combat (same odds for Archers versus Spearmen, Knights versus Pikemen, etc.).

2. As eliliang points out, this does nothing to address "streaky" results, except indirectly (perhaps this is why Jesse put this in quotations in his post). The real question is therefore: how long are the "streaks" that are generated by the Civ3 RNG? Whatever the number is, it's now divided by four. Does this solve the streakiness problem many players complain about?

I suppose my real question is: does that alter combat that drastically? Personally I'm not seeing this as the big revolution that everyone is making it out to be. It's a welcome tweak, but not game-altering IMO.


Dominae

	10-12-2003 21:47									#73
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Some speculations:

Technology is now even more important. You better not run into fortified Riflemen in cities with your Cavalry.

Swordsmen are now better than Horsemen.

A single Immortal Army (attack=6) will conquer the world.

Harder difficulty levels will become even harder, and easier ones even easier.

	10-12-2003 21:56									#74
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quote: Originally posted by alexman Swordsmen are now better than Horsemen.

Maybe I'm reading your graph wrong.

From what I can tell, the difference in combat odds between the Swordsmen:Spearmen and Horsemen:Spearmen before and after the change are minimal (like, less than 5%). So while Swordsmen may in fact be better now, it's nothing to write home about.

Of course, this assumes the Swordsmen/Horsemen are up against fortified Spearmen; if it's against Warriors, you're right that Swordsmen are noticeably more kick-butt than Horsemen now.


Dominae

	10-12-2003 21:58									#75
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quote: Originally posted by Dominae Thanks for the plot alexman. It takes a minute to figure out, but makes a lot of sense after that. What I'm getting from it is that: 1. If the attacker and defender are more or less evenly matched, there is little difference between the new combat and the old combat (same odds for Archers versus Spearmen, Knights versus Pikemen, etc.). 2. As eliliang points out, this does nothing to address "streaky" results, except indirectly (perhaps this is why Jesse put this in quotations in his post). The real question is therefore: how long are the "streaks" that are generated by the Civ3 RNG? Whatever the number is, it's now divided by four. Does this solve the streakiness problem many players complain about? I suppose my real question is: does that alter combat that drastically? Personally I'm not seeing this as the big revolution that everyone is making it out to be. It's a welcome tweak, but not game-altering IMO. Dominae

As I said in my post above with identical attack and defend values there is no difference between the two models.

However with any difference between the 2 numbers the new model amplifies the chance of the highest number winning. Now, I'm sure no one will bemoan spears having a much lower chance of beating tanks. However, even 'normal' examples like swords versus spears give markedly differently results.

I am not saying it is bad, but it will certainly be different.

	10-12-2003 22:01									#76
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Will the new calculations slow down combat noticeably? Or will it slow down ancient pcs but not new ones (I have a middle of the road 1.7ghz 784rdram)

	10-12-2003 22:02									#77
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My impression is that the streakiness involved is nothing more than a matter of probability theory. For example, getting "heads" five times in a row when flipping a coin is unlikely, but if you run the experiment thirty-two times, on average you'll get "heads" five times in a row once. Given the sheer number of combats in a Civ game, and especially across multiple games for those who play frequently, it is a statistical certainty that strange things will happen to us every now and then. Since human nature is such that we notice and remember strange results a lot more than we do expected results, combat looks "streaky" even though the streaks occur neither more nor less often than the laws of probability say they should.

I hope someone from Firaxis will correct me if I'm wrong.

	10-12-2003 22:04									#78
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By the way, cool avatar DrSpike (love that show!).

	10-12-2003 22:05									#79
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quote: Originally posted by Dominae Maybe I'm reading your graph wrong.

I don't think my chart is a good way to judge Swordsmen vs Horsemen.

Old way (assuming no retreat):
Horsemen defeat fortified Spearman 34% of the time
Swordsmen defeat fortified Spearman 56% of the time

New way (assuming no retreat):
Horsemen defeat fortified Spearman 16% of the time
Swordsmen defeat fortified Spearman 63% of the time

	10-12-2003 22:22									#80
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I am for anything that makes outcomes more predictable. You can adjust your play if that alters things, but at least you can plan more accurately.

	10-12-2003 22:25									#81
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quote: Originally posted by alexman Old way (assuming no retreat): Horsemen defeat fortified Spearman 34% of the time New way (assuming no retreat): Horsemen defeat fortified Spearman 16% of the time

Whoa! Horsemen are now half as effective against Spearmen as they used to be? That's bad (if your analysis is correct).

Edit: What was here made no sense.


Dominae

	10-12-2003 22:48									#82
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quote: Originally posted by JesseSmith * Fixed upgrade all bug (for units that do not have the upgrade ability but are part of the upgrade chain).

This is great news.
It's good to stomp this old bugs from vanilla civ.


Now, let me get strait.

This means that I could put Frigate and Privateer have upgrade path to Destroyer, but with upgrade flag removed, which would lead to just disabling these unit with Combustion tech (and no real upgrade).

Great add-on for moding community.

It could also be useful in base BIX rules too (same example).

	10-12-2003 22:54									#83
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I suspect that the combat change is going to get really nasty when defense modifiers start piling up - especially trying to take big cities on hills. Terrain modifiers, fortification modifiers, and so forth that were balanced well under the old combat system will tend to give the defender a much greater advantage under the new.

	10-12-2003 22:57									#84
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As NYE said, bombardment will be king.

quote: Originally posted by Dominae (if your analysis is correct).

You can see for yourself. All the tools you need are in this thread.

1) Old probability of victory of Horseman in single round of combat, q = 2/(2+2.7) = 0.426

2) From eliliang's analysis, new probability of victory in single round of combat, p = 0.327

3) Using the old combat system, you would need a unit with attack a = 2.7*p / (1-p) = 1.31 to get the same combat results as you get now with the new system. (because you want p = a/(a+2.7))

4) Use any old combat calculator to get the odds of a veteran 1.31 strong unit against a veteran 2.7 strong unit. These odds are 16%

Or you could just skip steps 1) to 4) above and use the combat calculator I attached above to get these new odds of Horse vs Spear directly.

5) Use any old combat calculator to get the odds of a veteran horse against a veteran fortified spear. These odds are 34%

	10-12-2003 23:02									#85
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Question: does the AI know about this change, or will it use horsemen to attack fortified spearmen on hills, thinking it will likely win (when in fact it has just 4% chance of winning)

	10-12-2003 23:15									#86
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Fix the damn running-into-a-submarine-causes-declaration-of-war bug!

[/broken record]

I'm not sure I like the idea of combat being too predictable. I guess I'll have to wait and see how it plays.

	10-12-2003 23:31									#87
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quote: Originally posted by alexman Question: does the AI know about this change, or will it use horsemen to attack fortified spearmen on hills, thinking it will likely win (when in fact it has just 4% chance of winning)

I think you mean "thinking it has a reasonable chance of winning" here, instead of "thinking it will likely win".

What we have been showing is that where something was likely before, it becomes even more likely in the new system, but where something was unlikely before, it becomes even less likely in the new system.

	10-12-2003 23:57									#88
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Here's some info on the "new" combat calculations. I didn't expect the change to even get any notice at all yet here I am reading post after post about it.

The combat calculations have not been made less streaky; they've been made to appear less streaky. The RNG itself has not been changed (the generator is working exactly as it should).

Think of each round of combat as the attacker rolling dice to see if they hit the defender. If the number rolled is greater than or equal to the defense value, the attacker hits; otherwise, the defender hits. The change we made was to the way the attacker rolls the dice. The attacker now rolls multiple times and the result is the average of all the rolls. This makes the combat results be more in line with what you'd expect them to be. It will reduce the luck factor because it eliminates most wild, "unnatural" runs. However, the luck is still present and it even makes lucky wins more meaningful since they are more rare. A single spearman can still beat a single tank but it's highly unlikely that a single spearman will be able to stand up to a stack of tanks (which is as it should be).

Again, though, this is a BETA patch (but several of us have been playing with it for a few months now) so things could change before the final release. I hope this info helps clear some things up .

P.S. I don't know where Jesse got the "rerolling for ties" thing because there are no ties.

P.P.S. One thing missing from the patch notes is that the '*' in the right-click menu used to denote elite units who have produced a great leader has been put back. I'm not sure where it went but it's back now.

	10-12-2003 23:59									#89
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quote: Originally posted by alexman A single Immortal Army (attack=6) will conquer the world.

And defense of min. 3.3, with min. 12 hps...

	11-12-2003 00:06									#90
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Thanks for the clarification Mike!

Now can you tell us how many times the 'die rolls' are averaged? It really does affect the odds of victory.

For example, if you average an infinite number of die rolls of 1-6, you will always get 3.5. If you need 4 or more for a victory, the odds of victory go from 33% (2 out of 6) to virtually zero.