11-12-2003 00:07									#91
	Put an end to popups!

Clarity from Mike ... thanx

And thank heavens my spearmen can still go "Gates of Fire" a la spartans ... once in a while

	11-12-2003 00:15									#92
	Extra Rolls Lose 30 kilos (of popups)

Mike,

Won't all that extra rolling eventually slow the game down, especially if you are playing a bunch of civs in the game.

	11-12-2003 00:22									#93
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MORE BEER FOR MIKE!!

	11-12-2003 00:35									#94
	Re: Combat Help yourself to an AD-FREE life

quote: Originally posted by Mike Breitkreutz FIRAXIS 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.

What you are doing is effectively changing the PRNG. By averaging a number of rolls, you have changed the statistical distribution of results. This effectively changes the relative probability of discrete events (wins vs. losses).

Let me show this more graphically by exaggerating your example. Think of the attacker rolling a 10 sided dice with sides numbered from 1 to 10. Say that the defender has a defense value of 4. So as in your example, if the number rolled is greater than or equal to 4, the attacker hits, otherwise the defender hits. In this scenario, with one roll, the attacker hits 7 out of 10 times or 7/10 probability of the attacker hitting. Your example might be that we roll the dice 4 times and take the average. Well lets take this to an extreme so that I can graphically show you the effect of this change in distribution. Let's say that we roll the dice a TRILLION times and take the average of these rolls. What is the result? Intuitively, you should sense that the average will tend to stay close to the mean, or 5 1/2. Well 5 1/2 is greater than 4. Even without computing the exact odds, I think you would agree that in this case, the odds that the average are greater than or equal to 4 is much greater than 7/10 now.

So you see, this algorithm does change the resulting probabilities in much the same way as Tavis's original description.

Describe exactly how you are doing this (how many rolls, etc.) and we can calculate mathematically the exact effect.

BTW, I don't feel this is the right way to remove even the "perception" of streakiness, nor would I agree that removing the "perception" of streakiness is what should even be done if all it is, is a perception and not a reality.

	11-12-2003 00:38									#95
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quote: Originally posted by alexman 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.

Exactly. It does affect the odds even if only two 'die rolls' are averaged. Exactly how much the odds change depend on how many 'die rolls' go into the average.

	11-12-2003 00:43									#96
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::Mourns the fall of horsemen::

I don't like this *AT ALL.* Horsemen have been relegated to the category of the chariot, and chariots are an even bigger joke than ever before.

You might as well ignore the horse resource altogether now until chivalry! How very disappointing.

	11-12-2003 00:46									#97
	Full PM-box? Change here!

Yes Mike, don't tease us!

The statistical distribution certainly changes, but (and it is hard to say for sure with the limited info) it is not quite in the way imagined earlier.

	11-12-2003 00:47									#98
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wow, thank you Firaxis for this clever move -- a beta patch will be great for all of us!

As for the combat results imbroglio , I just don't care.

(No offense to all those dedicated civvers who love to deal with this calculations)

	11-12-2003 00:47									#99
	Increase the size of your Attachments

If you are looking to change the randomness of the results but not the actual probabilities of success, why not just generate the 4 random numbers and then take the 4th as the result. That should cut those unnatural "uberunit" streaks to 1/4 the size they would have been. Alternately you could take each roll, but perform some kind of transform on a subset of them. (For example, for a 0-1 random number, take 1 minus the number for every other roll. So, if there are a bunch of high numbers in a row, they would be changed to alternate high/low/high/low.....

Edit:

I just had a thought. If you add 4 uniformly distributed random numbers 0-1 together and then just look at the decimal part, you should get a uniformly distributed random number from 0-1. Maybe that's what Mike means when he says "average the rolls" In this case the probabilities would not change, but unnatural streaks would get averaged out.

Last edited by Gyromancer on 11-12-2003 at 00:56

	11-12-2003 00:50									#100
	Avatar Enlargement: We've got the solution

quote: Originally posted by Gyromancer If you are looking to change the randomness of the results but not the actual probabilities of success, why not just generate the 4 random numbers and then take the 4th as the result. That should cut those unnatural "uberunit" streaks to 1/4 the size they would have been. Alternately you could take each roll, but perform some kind of transform on a subset of them. (For example, for a 0-1 random number, take 1-the number for every other roll. So, if there are a bunch of high numbers in a row, they would be changed to alternate high/low/hig/low.....

You are presuming to know the behavior of the PRNG being used in Civ3 without ever seeing the algorithm. As such, such hacks will most likely fail since it is just as likely that a change as you are suggesting could make streaking even worse. This is because your suggestion is yet another transformation on the PRNG.

	11-12-2003 00:52									#101
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quote: Originally posted by alexman You can see for yourself. All the tools you need are in this thread.

I was not questioning your analysis, I was pointing out that I did not crunch the numbers myself. Halving the potency of Horsemen against their standard opponents seems wrong to me, and I'm trying to figure out why it is so (without doing any work!).


Dominae

	11-12-2003 00:58									#102
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quote: Originally posted by Dominae I was not questioning your analysis, I was pointing out that I did not crunch the numbers myself. Halving the potency of Horsemen against their standard opponents seems wrong to me, and I'm trying to figure out why it is so (without doing any work!). Dominae

I get the impression the earlier results are not true, although they were valid for the situation we believed to be the case earlier.

	11-12-2003 01:03									#103
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quote: Originally posted by eliliang You are presuming to know the behavior of the PRNG being used in Civ3 without ever seeing the algorithm. As such, such hacks will most likely fail since it is just as likely that a change as you are suggesting could make streaking even worse. This is because your suggestion is yet another transformation on the PRNG.

I wouldn't say "just as likely." Obviously such a change wouldn't create a truely random number. It would be meant to create one that a human with a limited time window and limited powers of observation (except maybe for Alexman... ) does not perceive as being nonrandom.

Anyway, my solution was really meant as an example of how such a transformation would work to avoid changing the underlying probabilities. I'm sure there are better transforms out there that would suit the internal workings of the game better.

	11-12-2003 01:03									#104
	Lose 30 kilos (of popups)

Here's a random idea (ha!) that intuitively could solve the problem a little better:

1. Use the old system for calculating combats.
2. Do each combat 5 times.
3. Award the win to the unit that wins the most combats.

So, instead of messing with things on the HP level, it's now on the combat level. This is no more work than the current solution (on average it should actually be less).

Now, I'm not really sure: does this introduce a bias or not, like the current system does?


Dominae

	11-12-2003 01:05									#105
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Yes, any averaging will introduce a bias towards the unit that has a better chance of winning.

	11-12-2003 01:06									#106
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quote: Originally posted by Dominae Here's a random idea (ha!) that intuitively could solve the problem a little better: 1. Use the old system for calculating combats. 2. Do each combat 5 times. 3. Award the win to the unit that wins the most combats. So, instead of messing with things on the HP level, it's now on the combat level. This is no more work than the current solution (on average it should actually be less). Now, I'm not really sure: does this introduce a bias or not, like the current system does? Dominae

The bias is still there. Also, how do you decide how wounded the survivor will be?

	11-12-2003 01:12									#107
	Avatar Enlargement: We've got the solution

Ok, bad idea.

	11-12-2003 01:12									#108
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So much for ultra-early rushes!!

And Muskets and Rifles just got *much* more important.

	11-12-2003 01:16									#109
	Avatar Enlargement: We've got the solution

The more I think about it, the more drastically I think this effects strategy.

Can we say "arms race"?

	11-12-2003 01:17									#110
	Avatar Enlargement: We've got the solution

Can we say "offense sells tickets but defense wins championships"?

	11-12-2003 01:22									#111
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quote: Originally posted by Gyromancer I wouldn't say "just as likely." Obviously such a change wouldn't create a truely random number. It would be meant to create one that a human with a limited time window and limited powers of observation (except maybe for Alexman... ) does not perceive as being nonrandom.

No. Because what I meant when I said that you don't know anything about the PRNG is that you don't know that your transformation wouldn't actually create a less random one from the perspective of "a human with a limited time window and limited powers of observation". This is because inherent in your approach is an assumption that after you apply your transform, randomness is enhanced in some perceptible way, when this could be even the opposite of true. I'll give a stupid example. Take a sequence: 1 8 8 4 2 5 7 3 5 10 6

Seems a bit random. But maybe not. What if we start with the first number and take every third afterwards to "enhance randomness"?: 1 ... 4 ... 7 ... 10 ...

oops. From my "perception", things have gotten worse.

See, you didn't know anything at all about my sequence, so taking every 3rd, 4th, etc. doesn't solve any problem. In fact, it might make things worse.

If you don't know anything about the PRNG, you can't apply a transform to it, especially a linear one, and expect things to "improve".

quote: Originally posted by Gyromancer Anyway, my solution was really meant as an example of how such a transformation would work to avoid changing the underlying probabilities. I'm sure there are better transforms out there that would suit the internal workings of the game better.

Without knowledge of the PRNG algorithm, no.

	11-12-2003 01:28									#112
	Remove this text

It seems to me that what is being bemoaned is the likelihood of unlikely events taking place... at one extreme, Spear versus Tank, and at the other Horses attacking fortified Spears/Pikes... and that the general community reaction is that the curve might be off on the latter.

In other words, units of equal or near strength should be more likely to stray from absolute results, not the reverse.

	11-12-2003 01:36									#113
	Remove this text

So, disparities in effective A and D values become more definitive with regard to likely overall combat outcome.

Would seem to make for some pretty drastic changes to the game, rippling well beyond combat itself. Does beelining for Navigiation, with the chance to sew up overseas trades for C3C's scarcer resources before others have a chance to trade for them, still make sense when you could beeline for Cavs and take on AI pikes?

Without actually having played with the thing, leads me to speculate that techs that offer combat unit upgrades just became a lot more powerful seducers of one's research budget.

Catt

	11-12-2003 01:39									#114
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quote: Originally posted by nbarclay 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.

While this change scares me a bit(as any change scares any human), I think it might be fun.

I've always thought it would be neat to actually have to lay seige to strong(strategically placed as well as well-defended) cities instead of just throwing more grunts at it.

This change could actually make bombardment much more important, but as has been shown in the past, the AI just doesn't get it. Which means this might do more to harm the AI than any good that could come of trying to eliminate the Uber Spearman. Besides, when I encountered old Uber S, I just assumed he was some sort of wicked smart MacGyver-type. It made losing a Tank to a guy with a pointy stick a lot easier to swallow.

Besides, if the AI still has spears when I have tanks, a couple of unlucky rolls isn't _that_ big a deal, to me.


Anyway, it'll be interesting to see if this makes catapults-arty more necessary, and if so, how the AI copes.

	11-12-2003 01:40									#115
	Remove this text

quote: Originally posted by alexman Can we say "offense sells tickets but defense wins championships"?

Yeah, but there's no league rules here... warfare in Civ has ALWAYS been about attacking at the point of relative advantage... now, the aggressor will 1) not attack with number of units advantage in the face of stronger defenders, 2) need, um, 50%? more units when faced with equal defense due to defense modifiers, and 3) go INSANE upon reaching an attack strength advantage.

UUs need to be discussed at length, btw, in light of this.

It changes the game a LOT... I am not sure if for good or bad though, especially when considered from a Seven Pillars standpoint. I could argue it either way: a) attack strength advantage becomes so powerful that game balance is thrown off, and winning the arms race is pretty much the game over strategy (shades of Vel's complaints), or b) stronger defense in general allows for other game-winning strategies.

	11-12-2003 01:43									#116
	Lose 30 kilos (of popups)

So if one of my allies runs into my submarine with an ironclad... they will still declare war, but their chances of sinking the sub have been increased?

	11-12-2003 01:44									#117
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Right, it would appear the principal problem is that in order to kill 'streaks', the probability of an nearly equal combat is skewed heavily toward the 'better' unit. So a horseman attacking a city is screwed badly with statisitical 50% reduction. Sure it is good that those spearmen will be slaughtered by a tank; whoever is still using them deserves it. But those spearmen will now slaughter your horses. This is not I would hope the intended change. We would have to see how this is exactly being implemented to be certain of the whole problem. The civ2 solution of FP seems more accurate at solving the problem of a godlike spear unit.

The biggest problem with this change if its used is that the computer does not seem as effective as a person in artillery implementation. This sort of change would require alot more bombardment on a targeted city (since city combats are generally the heaviest on D%) A MP game you'll see all those shells falling and should know where to mass your defense. Killing the 1 rated units into total uselessness isn't necessarily the best thing to come out either. No early rushes.

	11-12-2003 01:49									#118
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Uh, I just realized a real problem here... the change in distribution of strategic resources.

In each era, all civs now have access to resource free attacker and defender slowmovers of more or less equal strength... those civs WITHOUT resources are now screwed.

	11-12-2003 01:53									#119
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One of the changes modders have made to deal with the problem of unlikely outcomes is to increase the number of hit points. If Firaxis would do that internally and round off the results (for example, doubling the number of hit points internally at the start of the battle and showing a hit point lost on the screen each time two are lost internally), that would push the outcomes toward the average without fundamentally upsetting the balance of power.

	11-12-2003 01:54									#120
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quote: Originally posted by Stuie So if one of my allies runs into my submarine with an ironclad... they will still declare war, but their chances of sinking the sub have been increased?