29-04-2003 21:26									#1
	Combat odds for large stacks Support Apolyton, pre-order Civilization IV

I've just finished a combat calculator for large stacks of units (as per the current situation), and think it is working more of less correctly now. Currently it doesn't deal with bombard units on attack or defense, but that's something I can work on.

Relevant results for the moment:

Stack on Arashi 2 attacks Arashi:

average no. of GS casulaties: 1.56, with 1.52 promotions and 0.029 great leaders (that's a 3% chance of a great leader, more or less). Average no. of Vox casulaties: 5.44, with 0.45 promotions.

No of Vox survivors with probability (and cumulative probability)
0 18.8% 18.8%
1 33.7% 52.5%
2 27.6% 80.0%
3 13.9% 93.9%
4 4.8% 98.7%
5 1.1% 99.8%
6 0.2% 100.0%
7 0.01% 100.0%

I like those odds - 80% chance that we have 2 or fewer units to mop up after they attack.

EDIT: Had written Gow, changed to Vox - thanks Shiber

Last edited by vulture on 29-04-2003 at 21:36

	29-04-2003 21:34									#2
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Great work Vulture! This could also come in very handy when we change to assault mode.
Typo: GoW instead of Vox.

	29-04-2003 21:35									#3
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Next set of results: Arashi 2 attacks Tempest

Average GS casualties 2.32, with 1.36 promotions and 2.6% chance of GL.
Average Vox casulaties 4.68, with 0.68 promotions.

No of Vox survivors with probability and cumulative probability
0 8.6% 8.6%
1 22.1% 30.7%
2 27.6% 58.3%
3 22.2% 80.5%
4 12.2% 92.72%
5 4.9% 97.6%
6 2.1% 99.7%
7 0.3% 100.0%

So we are actually running a 0.32% chance of losing Tempest (ignoring the effect of defensive catapults) if they attack with everything on Arashi 2 this turn. Ooh, scary! But in either case they are likely to lose most of their units, leaving just 2 or so injured immortals to kill.

EDIT: changed Gow to Vox again - was getting ahead of myself

	29-04-2003 21:44									#4
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Oh, ought to mention that I've assumed all units in the cities are fortified - I suspect this isn't actually the case, but it isn't going to make a huge difference. IIRC Arashi is on a hill, with walls (size 4), for a total of +100% defensive bonus (+125% if fortified) and Tempest is on a hill with no walls (size 6), for a +75% / +100% bonus (unfortified / fortified). I've used the lists of units from the Turn 99 thread (page 5 for our defenders, in Arrian's post, the screenshot on page 1 for the Vox stack), so I hope those are correct.

In reality, average losses for both sides will be slightly lower since there will be sequences in which Vox stop the attack without fighting to the last man (if they lose 4 immortals in a row without scratching a defender for instance, I'd expect them to cut their losses and give up).

	29-04-2003 21:44									#5
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Comforting stuff, vulture

the only question left is how psychology will play a role. Will vox throw everything at one city, or will it cut its losses after a few routs. Either way, we win, just will take a bit longer.

	29-04-2003 21:47									#6
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DISCLAIMER: I may just discover a huge bug in the program next time I look at it, which would make all these results useless....

	29-04-2003 22:05									#7
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It's also comforting to know that these numbers don't take our catapults into consideration. The odds should be even greatly in our favor.
The end of 590BC screenshot show that Tempest does have walls, btw.

Asleepatthewheel: good point. We'll only know for sure next turn, though.
I actually think that Vox will move its stack 2 down the mountains or 6 heading for Sandstorm, either after they lose many units and see that they don't have a chance against Arashi or Tempest, or without going to battle at all, hoping that we won't be able to react to their move in time.

	29-04-2003 22:15									#8
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The assumption of fortification (which in the case of several of our pikemen is incorrect) and the missing effect of the catapults probably comes close to balancing out.

Anyway, we're looking at good odds on defense.

-Arrian

	29-04-2003 22:16									#9
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vulture,

Here is how Nathan arranged our forces:

quote: Tempest: Four pikes, two regular medieval infantry, a 2/4 WC, and a 2/5 WC. Worst case: the 2/4 WC gets killed and the 2/5 WC keeps Vox from entering the city. Arashi: Three pikes, a healthy veteran medieval infantry, a 3/4 medieval infantry, a 2/3 medieval infantry, a healthy WC, and two 3/5 WCs, all fortified except for one pike

-Arrian

	29-04-2003 22:31									#10
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We did rush Walls in Tempest, so once you've got the bug figured out make sure to include them.

Great job, btw, very cool.

	29-04-2003 22:52									#11
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We have walls in Tempest (actually not rushed; just completed normally in place of a pike), but none of the units there except the WCs are fortified. In Arashi, all the units are fortified except for one pike. Note that if Vox targets Arashi, they have a regular immortal on Arashi 9 that can attack in addition to the main stack. (They also have a 3/4 spearman on Arashi 9, which they might conceivably attack with if by some miracle they win all the other battles.)

	29-04-2003 23:40									#12
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Vulture, when you calculated the odds for promotions for Vox, did you take into account the fact that their civ is militaristic?

	29-04-2003 23:53									#13
	Increase the size of your Attachments

Persia is NOT militaristic. It is scientific/industrious.

	30-04-2003 00:37									#14
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I initially thought that Persia was sci/ind, but then read somewhereon 'poly today that they were militaristic, so I put them down as that. Doesn't affect the combat odds, but since they are non-mil, halve their promotions.

What is the bombard defense of a unit on a mountain? Is it just their combat strength with terrain modifier, as normal, or is it something weird. Defensive bombard always seems to do better than I'd expect somehow.

	30-04-2003 00:44									#16
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quote: Originally posted by vulture What is the bombard defense of a unit on a mountain? Is it just their combat strength with terrain modifier, as normal, or is it something weird. Defensive bombard always seems to do better than I'd expect somehow.

That's a good question.
I have absolutely no idea how defensive bombardment is calculated. I've only seen threads about experiments being made with attack bombardment. I've even seen a very comprehensive study on CFC recently and it didn't have anything on defensive bombardment either.

	30-04-2003 00:53									#17
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If you're talking about the shots our cats will get if Vox attacks our cities, I don't know either, but I strongly suspect that it's the cat's bombard power (4?) versus either the Immortals' attack power (4) or defense power (2). Not sure which. I very much doubt that the terrain matters at all.

My experience with cats on defense has been limited to watching the effect AI cats have on my attacking troops in the ancient/medieval eras. My horsemen almost always get hit. My knights get hit fairly often. My Cav sometimes get hit by cats...

I think it's probably the attack strength that matters. So that would give our cats a 50/50 shot at attacking Immortals.

Total guesswork, though.

-Arrian

	30-04-2003 16:21									#18
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Updated odds, get them while they're hot!

Still no catapult data as such, but I've done two cases, one with no catapults, and one assuming all catapults hit. On average we will end up about halfway between the two, but it shows the range of difference the catapults can make.

Stacks on Arashi 2 and Arashi 9 attack Arashi (and attack with everything, which probably isn't realistic, as before - how often are they going to attack with a spearman or 1 hp immortal).

First column, number of Vox survivors (aka no. of Vox victories), second is prob, 3rd cumulative prob, both ignoring catapults. 4th and 5th are prob and cumulative prob with maximum benefit from 3 catapults.

0 || 8.5% 8.5% || 14.4% 14.4%
1 || 20.4% 29.0% || 27.2% 41.6%
2 || 25.4% 54.4% || 26.6% 68.2%
3 || 21.4% 75.7% || 17.7% 85.9%
4 || 13.6% 89.3% || 8.9% 94.8%
5 || 7.0% 96.3% || 3.7% 98.5%
6 || 2.8% 99.1% || 1.2% 99.7%
7 || 0.7% 99.8% || 0.2% 100.0%
8 || 0.1% 100.0% || 0.03% 100.0%
9 || 0.01% 100.0% || 0.0% 100.0%

Averages without catapults (and with catapults):

Vox: dead 6.52 (7.03), promoted 0.40 (0.33), leaders 0.0 (0.0)
GS: dead 2.48 (1.97), promoted 1.86 (2.03), leaders 0.050 (0.060).

On average the presence of leaders increases our leader odds from 5% to around 5.5%, which is nice. Leader odds are probably overstated, since I suspect quite a lot of them come from a spearman attacking an elite pikeman, which is something that just wouldn't happen in a real game, so the 3% from the previous tables is more realistic.

	30-04-2003 16:31									#19
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And for the Arashi 2 stack attacking Tempest (columns as before):

0 || 11.5% 11.5% || 19.2% 19.2%
1 || 26.7% 38.2% || 33.3% 52.4%
2 || 28.7% 66.9% || 26.9% 79.4%
3 || 19.8% 86.7% || 14.1% 93.4%
4 || 9.6% 96.3% || 5.2% 98.6%
5 || 3.0% 99.3% || 1.2% 99.8%
6 || 0.6% 99.9% || 0.2% 100.0%
7 || 0.1% 100.0% || 0.03% 100.0%

Averages (with catapults):

Vox: dead 4.99 (5.43), promoted 0.30 (0.24), leaders 0.0 (0.0)
GS: dead 2.01 (1.57), promoted 1.44 (1.59), leaders 0.027 (0.032).

	30-04-2003 18:22									#20
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I searched poly and CFC for hours... still no idea how defensive bombardment works.
Vulture: great job!