Combat odds for large stacks

[vulture]

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

[Shiber]

Great work Vulture! This could also come in very handy when we change to assault mode.
Typo: GoW instead of Vox.

[vulture]

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

[vulture]

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).

[asleepathewheel]

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.

[vulture]

DISCLAIMER: I may just discover a huge bug in the program next time I look at it, which would make all these results useless....

[Shiber]

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.

[Arrian]

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

[Arrian]

vulture,

Here is how Nathan arranged our forces:

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

[Theseus]

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.

[nbarclay]

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.)

[Shiber]

Vulture, when you calculated the odds for promotions for Vox, did you take into account the fact that their civ is militaristic?

[nbarclay]

Persia is NOT militaristic. It is scientific/industrious.

[vulture]

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.

[Shiber]