28-12-2003 16:03									#1
	Military chances Put an end to popups!

I 've done some quick calculations for taking Madrid using the screenshot from when we founded the embassy in Madrid.

Using a combat calcuator I found that 1 veteran archer has 50.9% of beating one of the regular spears in Madrid. To beat 5 we'd need a lot more.

If I'm right, this is a binomial distirbution (it's been a while since I've done any statistical stuff), so these would be our chances:

• 5 vet archers -> 3.4% chance for victory
  
• 6 vet archers -> 11.8%
  
• 7 vet archers -> 24.2%
  
• 8 vet archers -> 38.3%
  
• 9 vet archers -> 52.2%
  
• 10 vet archers -> 65.5%
  

Last edited by sprudl on 28-12-2003 at 17:55

	28-12-2003 17:03									#2
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I like your stats...

	28-12-2003 17:35									#3
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SprudL - yes, as far as I can tell it would be a binomial distribution.

I can't find the formula, yet I think you have made some mistake somewhere with the chances of winning with only five Archers. The probability of beating 5 Spears with 5 Archers is the probability of One Archer beating One Spear to the power of 5 (5 battles). This is (.509)^5 = .034, a 3.4% chance, yet your results say 6.8%.


Doesn't make much real difference to us, especially since I get close to the same values as you using a table where the chance of victory is 0.5, but I am a perfectionist in these things.

Archers are quick to build, and New Asgard is on 10spt right now. It needs to build a settler to reduce pop so it doesn't riot, but it should be easy to get it back to this spt again for 2 turn Archers or 3 turn Galleys. Building 10 Archers is not a problem. Building 10 Archers + more for the assaults on OTHER cities, with Spears, and most of all the Galleys needed for this will be tricky.

	28-12-2003 17:55									#4
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You're right, WIA. I copied the wrong value for 5 archers. The right chance is 3.4%. But I doubt anyone would consider taking on 5 spears with only 5 archers
I'm ignoring increase/decrease in hitpoint between battles, so this is just an approximation.

If anyone's interested, I used these sites to do the dirty work/calculations:
Combat calculator
Binomial probabilty

I tried putting the binomial calculation in a spreadsheet, but I can't find the right formula in OpenOffice.

There's a chance there will be less than 5 spears defending Madrid. Or there could be more...

	28-12-2003 18:13									#5
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quote: Originally posted by sprudl I'm ignoring increase/decrease in hitpoint between battles, so this is just an approximation.

Actually I think the probabilities take account of everything. Remember that the Civ3 Combat Calculator accounts for each combination of hp left to either side after the battle, and does so using the probability of each permutation as well as the end result (eg Prob of Win Win Loss Win + Prob of Loss Win Win Win are both part of the chance to win with 3hp left percentage), and the Binomial calculation takes account of the different permutations of Archer victory vs Spear victory as well (eg Win for Spear Archer Archer Archer Archer is added to the chance for win of Archer Spear Archer Archer Archer).

IOW, these probabilities should be perfect.

	28-12-2003 18:50									#6
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I'm still trying to decode your post, WIA You're right that the order of wins and loss doesn't matter.

But a binomial distribution is for events that don't influence each other. In this case this isn't entirely true. A spear can defeat the archer and but lose 2 HP at the same time. The next archer would then have a much better chance to win.

In the binomial formula each battle is supposed to occur in the exact same circumstances. A spear should win and stay at 3hp or lose. What happens to the archer doesn't matter until the next turn.

But then again, I think this is a good enough approximation

	28-12-2003 19:23									#7
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Hold on there a sec. The enemy is in a town, we are in enemy territory. Won't any surviving units on their side get health where our side won't? I started a sentence and ended it with the same strange word. Plus their defense is likely to increase in size if we fail on the first turn, whereas or offense is not. What I propose is we add some more numbers:

% Chance we will win * Multiplier for how positive the outcome will be (how good is it to own madrid).

compared to

% Change we will lose * Multiplier for how negative the outcome will be (all archers die, spain attacks back, etc).

Higher value wins out. The value for the 'multiplier' is somewhat difficult, however words such as propinquity (sp?) help us out here. Which psychologist did this..?

	28-12-2003 19:57									#8
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Those are valid points, Epistax. What's the propinquity thing you're refering to?

However, my entire reasoning is based on taking Madrid in 1 turn in its current situation. How many defenders there would be by the time we get there will most likely be different. The SMC will have to come up with a strategy for more than 1 city as well.

This is just to wake up the government to get them to make troops if they're serious about invading Spain

Owning Madrid is good for two things. We would get the Lighthouse. Secondly, Spain would no longer have it It is one of their best cities...

	28-12-2003 21:36									#9
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Nice statistic work! You should join the Inter Site Demo Game and help me out in the Area X (Secret Service; Intelligence) department.

	29-12-2003 07:41									#10
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I believe propinquity refers to the chance that similiar events will spawn because of this event.

Anyway what I'm getting to is this: Sure we can push our chances above 50%, but is the value of winning the fight worth the cost of losing it? I see Madrid has the great lighthouse. Would our plans for the future be greatly helped by this?

	29-12-2003 15:43									#11
	Avatar Enlargement: We've got the solution

So propinquity is synonymous to bad RNG

The GL is always a nice thing on a map like this. But to me that not even the most important reason.

We need to expand and we need resources. Egypt and Persia are too strong for us. Jaen on the southern island is close to horses and there's iron near Seville.

Taking Madrid would give us a good foothold on their land, but we'd need to take a lot more. We should also take Jaen right away.

Oh. And Egypt is at war with Spain. They've destroyed a city near Santiago. We want a part of the cake

	30-12-2003 19:23									#12
	Avatar Enlargement: We've got the solution

quote: Originally posted by Epistax I believe propinquity refers to the chance that similiar events will spawn because of this event. Anyway what I'm getting to is this: Sure we can push our chances above 50%, but is the value of winning the fight worth the cost of losing it? I see Madrid has the great lighthouse. Would our plans for the future be greatly helped by this?

Perhaps Madrid may not be worth, it, but war with Spain means we should be able to take the Horses in the Sth Isle at the least. And with the GL not only do we gain the ability to move in sea, we can set up trade routes through sea as well. This could prove very useful to us where we would otherwise need a clear coastal route to the target trading civ.

SprudL - you are right there - I forgot about the idea that we could lose a battle but weaken a Spear. Also, we could lose a battle and the Spear gains an extra hp in promotion! However, the odds calculated above are if the Spear is of all its hp in EVERY battle, which is on the unlucky end of things for us. The only worse situation is where we lose an Archer without causing any hp loss to the Spear, AND it is promoted! As this will hopefully be pretty rare, any adjustment for promotions and hp loss to Spears in earlier battles will give us a HIGHER overall probability of success with more than 5 Archers. I hope this makes sense. Admittedly my last post was a little dense, and it WAS 3am when I wrote it

	31-12-2003 04:48									#13
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I like to use this site for calculating multiple units against multiple units.

http://www.zachriel.com/BattleCivulation.asp

It says the we need at least 10 reg archer to have a greater than 50% chance at defeating 5 reg spearmen that are fortified in a town without walls.

We do need to consider that holding the city once taking it will become a priority. The AI is not likely to let us sue for peace so soon.

	04-01-2004 02:54									#14
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Well, the probability of killing the first five spearmen in the same turn with five archmen if there were no possibility of a flawless victory by a spearmen that resulted in a promotion of the spearmen.

It's not until the 6th combat in that turn that how we did previously starts to matter.

Maybe there's a softer target than Madrid?

	07-01-2004 01:05									#15
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Is there a general consensus that the production priorities for the next couple centuries should aim toward full war with Spain / expanding into its territory or terr it would have taken, with taking the GL and getting the Sth Island's horses the specific goals? Or is this just step 1 in oscillating war, with protracted war with spain just a temporary goal?

	07-01-2004 14:27									#16
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Deciding right now for a full-out war with Spain is a little premature perhaps, as we are nowhere near ready for such an encounter. Until we are, we have to plan for building up to a level that we can take at least the colony(ies) they put on the Southern Island. At the same time we will be exploring in the hope of getting Iron and linking up to a Horse resource. I think Spain is the likely best target for a number of reasons (I can find the posts if you like), and we know we will have to fight SOMEone soonish.

So for the time being, we should be building our military, as we need to do this before striking at anyone and we have to do so before either a limited conflict or a full-scale war.

	07-01-2004 20:24									#17
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I agree Spain is the best target for a military solution (but my alignment is Builder so I would wait)...their territory is a mess and I'm glad we don't have their starting position. Unfortunately (for us) spanish territory is a bullseye with our future swordsmen at the center. unless we luck out with iron in the balance of the south island.

Before we start cranking out military units, I think it would make sense to fill up the rest of the south island with cities. I don't even think we have ten turns before that shore is littered with foreign settlers otherwise.

	08-01-2004 17:07									#18
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quote: Originally posted by EnduringBlue I agree Spain is the best target for a military solution (but my alignment is Builder so I would wait)...their territory is a mess and I'm glad we don't have their starting position. Unfortunately (for us) spanish territory is a bullseye with our future swordsmen at the center. unless we luck out with iron in the balance of the south island. Before we start cranking out military units, I think it would make sense to fill up the rest of the south island with cities. I don't even think we have ten turns before that shore is littered with foreign settlers otherwise.

Do you really feel that they will flood the area by then?

	08-01-2004 21:56									#19
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The map is naturally seafaring, and in my experience at this level, a heathen settler/galley combo you see is almost never the first or only one out there. The Spanish in particular can't cross a street within their own territory without using a boat. The other civs have probably traded world maps to each other recently, and they all have proof that there is unsettled land in our direction.

I would consider it a distinct possibility they've already run up against AI island chains or ocean on their combined northern front.

If we wait much longer, we may have to fight mountain barbies to the SE for more territory in the near future, or be restricted to disproportionately tundra terrain on the south island, if it's larger than it looks.

A second concentration of cities would also be nice for FP, too. we need more of an industrial base to fund the military campaign to get us beyond this cul-de-sac, unless someone's mapped out a turtle strategy i haven't read anything about.

	09-01-2004 14:27									#20
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a well stated case, thanks for that

	10-01-2004 21:11									#21
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Agreed about the need for us to settle the rest of the south island first.

Much cheaper than pumping out sufficent warriors to block the coastline.

	11-01-2004 01:14									#22
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I think we need to settle our land while maintaining a suffcient military force to deter any other Civs from decalring war on us while we are REXing. We simply do not have the strength needed to take on any one Civ right now.

	11-01-2004 03:20									#23
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We should fill up the remaining easy-to-colonize space while building extra military units. I don't think we'll be able to initiate a war in the immediate future, but once REX is done having archers and galleys in hand will make sense.

What about diving into the center of Spain and seizing that iron? It would be time consuming to transport troops, but it might be as valuable a target as the GL.

We'll need better units to fend off the immortals which will eventually knock on our door.

	12-01-2004 12:23									#24
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We have a couple of cities with fantastic food production, and they can be used with some care to quickly build settlers, whilst the others can build Archers. We can meet both settlement and defense needs simultaneously, IMO. We must give up on landing something to cut off Persia's Iron for the time being (it would not be worth the trouble right now) and send that Galley to check out the island to our west!

	13-01-2004 00:46									#25
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quote: Originally posted by BigFree I think we need to settle our land while maintaining a suffcient military force to deter any other Civs from decalring war on us while we are REXing. We simply do not have the strength needed to take on any one Civ right now.

That's pretty much my opinion right now as well.