Civ III: Conquests Patch Notice

[ThaddeusAlexander]

Clarity from Mike ... thanx

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

[b_ramsdell]

Extra Rolls

Mike,

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

[Theseus]

MORE BEER FOR MIKE!!

[eliliang]

Re: Combat

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.

[eliliang]

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.

[Fried-Psitalon]

::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.

[DrSpike]

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.

[Alex]

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)

[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 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.

[eliliang]

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.

[Dominae]

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

[DrSpike]

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.

[Gyromancer]

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.

[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

[alexman]

Yes, any averaging will introduce a bias towards the unit that has a better chance of winning.