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**Paddy** · December 28, 2003, 08:03

I like your stats...

**MrWhereItsAt** · December 28, 2003, 08:35

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.

**sprudl** · December 28, 2003, 08:55

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...

**MrWhereItsAt** · December 28, 2003, 09:13

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.

**sprudl** · December 28, 2003, 09:50

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

**Epistax** · December 28, 2003, 10:23

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..?

**sprudl** · December 28, 2003, 10:57

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...

**BigFurryMonster** · December 28, 2003, 12:36

Nice statistic work! You should join the Inter Site Demo Game and help me out in the Area X (Secret Service; Intelligence) department.

**Epistax** · December 28, 2003, 22:41

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?

**sprudl** · December 29, 2003, 06:43

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

**MrWhereItsAt** · December 30, 2003, 10:23

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

**BigFree** · December 30, 2003, 19:48

I like to use this site for calculating multiple units against multiple units.

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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.

**joncnunn** · January 3, 2004, 17:54

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?

**EnduringBlue** · January 6, 2004, 16:05

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?

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