06-03-2001 07:01									#31
	Support Apolyton buy from Amazon

DaveV: It's a nice little program, but it would be better still if it allowed you to enter ALL the modifiers (city walls, defensive terrain, fortified, etc). Kind of a shock seeing that old Win31 design again! I'm still holding out hope for a comprehensive Battle Odds spreadsheet (a standalone program would be ultra cool).

CyberChrist: So next time I'm launching an amphibious assault all I have to do is sail my carrier up next to the city and fire away with bombers? And his fighter defenses are toast? Sneaky, sneaky!!!

	06-03-2001 09:45									#33
	Put an end to popups!

I ran a number of combat tests to determine if the above formulas are correct. Since I ran each combat 200 times and averaged the damage sustained by the victor and the number of times each side won I can tell you that (a)/(a+d+0.125) only works when a=d. As soon as a and d diverge the odds become heavily weighted towards the unit with the higher stat.

After a little additional analysis I came up with this formula:

Odds= Max(2a-d,a)/(Max(2d-a,d)+Max(2a-d,a)+0.125)
When I apply this number to the binomial distribution formula the results come out right on the money including the damage numbers.

This amounts to giving the better unit an extra bonus equal to it's advantage over the weaker unit, for example a 6a attacking a 1d unit is really equivalent to an 11a unit attacking a 1d unit.

One of my tests had 15a,2f,2h attacking 9d,2f,2h and the 15a units were basically never loosing when they should have lost 15% of the time.

I tried the reverse with 2a,1f,1h attacking 4d,1f,1h and the 4d were also doing much better than the stats showed. I expected them to loose about 5% of the time in the test they only lost once in 200 tries or 0.5% which is too much of a swing to be explained away.

I am not 100% sure that this is it but I am pretty sure the simpler formula is not correct

	06-03-2001 11:00									#34
	Support Apolyton buy from Amazon

I think the Unified Field Theory is simpler!

	06-03-2001 17:48									#35
	Enter the AD-FREE zone

Eight side die? Does this mean there is a Dungeons & Dragons influence on CIV II?

	06-03-2001 18:00									#36
	Put an end to popups!

It's not really an 8-sided die; it's an n-sided die, where n is AF*8 for the attacker, DF*8 for the defender. AF is attack times any bonuses; DF is defense times any bonuses. The attacker and defender each rolls his die; if there's a tie, the defender wins (thus the -.125 for the attacker and +.125 for the defender).

Kull - I think Mark's program requires the user to calculate all of the bonuses before running the program. I agree that something like a spreadsheet would be a good way to show all the special cases.

	07-03-2001 01:32									#41
	Get a bigger avatar today!

Duh! I read "turns in the air" as "moves in the air".

Still, the multiple attacks by Bomber is interesting. That may explain some of Xin Yu's success as Japan in the first 2194 Days PBEM game!

	07-03-2001 01:33									#42
	Put an end to popups!

DP (This is what happens when you work with 2 PCs at the same time....keeping track of which keyboard is which gets problematic!)
[This message has been edited by Kull (edited March 06, 2001).]

	07-03-2001 10:18									#44
	Support Apolyton, buy Galactic Civilizations

As to the spreadsheet calculating the odds and damage here is what I did:

4 columns for the attacker (aa,ad,af,ah)
4 columns for the defender (da,dd,df,dh)

(Although ad for the attacker and da for the defender are not used, it makes it easier to copy a unit from the attacker to defender column to see how it fares in the opposite role)

Next two columns calculate the "corrected" a and d factors, Ca and Cd based on the difference between aa and dd

Ca=Max(2*aa-dd,aa)
Cd=Max(2*dd-aa,dd)

Next column, the odds of the attacker winning a round:

odds=Ca/(Ca+Cd+0.125) (Display in percent)

Next the number of rounds won required for Attacker to kill defender:

aw=dh*10/af

Next the number of rounds won required for Defender to kill Attacker:

dw=ah*10/df

Next the "BIG" formula the Attacker's odds to win the entire battle:

ODDS=BINOMDIST(dw-1,aw+dw-1,1-odds,True)

Translates as "odds that Defender wins dw-1 or less rounds out of aw+dw-1 rounds considering that the odds of the defender to win each round are 1-odds" (Changing True to False would change "wins dw-1 or less" to "wins exactly dw-1")

Now the average damage sustained by the attacker by the time the defender is dead: aw*(1-odds)/odds * df (odds=odds to win one round)

And the average damage sustained by the defender by the time the attacker is dead: dw*odds/(1-odds) * af

Of course for the loser of the ODDS equation this number will exceed the unit's hitpoints.

This should allow anyone with basic knowledge of EXCEL to reproduce the spreadsheet. I copied the formulas down each column so I can display multiple combats situations simultaneously. I also added a column before the attacker and defender with the respective unit names so I can keep track of what is what.

Did I put everyone to sleep?

	08-03-2001 00:22									#45
	Increase the size of your Attachments

Zzzzz ... *** WAKES UP *** ... Great stuff, Nemo!


No really, it is great, a huge help. Thanks.

	27-03-2001 02:21									#46
	Increase the size of your Attachments

I think the terrian your attacking from is also taken into account.