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Scouse Git[1]

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- SilverDragon, scourge of the western skies

quote: Originally posted by DaveV on 01-25-2001 08:29 AM The guide is wrong. As Sieve Too said, this has been tested lots of times. It's easy enough to check for yourself: just crank up a couple units in cheat mode. Take my example above: the vet pike would only be 2+1+1+1+1+1 = 7 if you add numbers. Try attacking him with three vet crusaders (5+2.5=7.5) on the same turn - I'll bet you a doughnut they all lose.

If I remember right the pikeman has a defend advantage against attackers on horse, so this example isn't very good..

BTW, I think the statement in the subject is valid. Two numbers would suit the purpose.

A,D,H,F are attack, defense, hit points and firepower.
In fact, you need to know A*F*H and D*F*H. You may imagine that
A*F*H replaces A and
D*F*H replaces D and
H, F are set to 1.

H/F lowers accidental behaviour of units only (H lowers it and F raises it).

quote: Originally posted by ruoxiaohai on 01-27-2001 01:33 AM Well, if you guys want to be anal, the pikemen ONLY get defensive advantages for unit numbers 16 to 21, I think.

Not too sure of this. If you leave both the Pikeman and, say, Knight in their respective slots, but increase their HP, the Pikeman loses the 50% defense multiplier.

quote: Also, many scenario designers have found that special unit "places" have advantages.

There are a number of these: Only a unit with the settling role in the Engineer slot works at double speed. Only a unit with the diplomacy role in the Spy slot, has the Spy's extra abilities. Same thing for Freight. Only the Partisan slot gives the extra attack strength vs 0 attack defenders. Only the Fanatics slot is a unit that can only be built under Fundamentalism. There's more.

quote: Originally posted by DaveV on 01-29-2001 10:06 AM SlowThinker - I'm not sure I understand what you're saying. FP does make a difference for defenders, and HP for attackers.

I will present an example:
Artillery fights with Mech. Inf.

1. Civ2 offers four constants (a,d,h,f) for every unit:
Artillery (10a,1d, 2h,2f)
Mech. Inf. (6a,6d, 3h,1f)

2. You may translate theses four constants into two constants only (you may suppose h=1 and f=1 then):
Artillery (40a,4d)
40=10a*2h*2f; 4=1d*2h*2f
Mech. Inf. (18a,18d)

With the default numbers: the odds of mech. infantry winning each round are 11/12 (6 + 5 bonus vs. 1). Mech infantry needs to win 20 rounds, so will probably take 2 hits = 4 hitpoints.

Mech. Inf. has 0,1,2...6 on his die (7 sides).
Artillery has 0,1 on his die (2 sides).

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Scouse Git[1]

I hope I have understood it:

On defender's die	Nr. of attacker's wins	Nr. of defender's wins
0	47	1
1	46	2
2	45	3
...	...
6	41	7
7	40	8
Total:	(40+47)*8/2	(1+8)*8/2

Generally:
Suppose m=max(a,d), n=min(a,d). Then wins are distributed among both units following way:  

	Attacker's wins (AW)	Defender's wins (DW)	Total number of attacks
a>=d	m-n/2-1/16	n/2+1/16	m
a<=d	n/2-1/16	m-n/2+1/16	m

 

In our example:  Artillery wins 1/2+1/16, Mech. Inf. wins 5 1/2-1/16.

(Edited: DaveV multiply these numbers by two: it looks more functional:
Artillery wins 1+1/8, Mech. Inf. wins 11-1/8;
11=6+5, 5 is the "bonus" for the stronger unit)

quote: Originally posted by DaveV on 01-29-2001 12:33 PM With the default numbers: the odds of mech. infantry winning each round are 11/12 (6 + 5 bonus vs. 1).

Using other words, we always use all the product f*h.  Single f and h factors are not interesting (they affect accidental behaviour of units only).
 

In our example:  Artillery wins (1/2+1/16)*4=2.25, Mech. Inf. wins (5 1/2-1/16.)*3=16.31 average outcome: Mech. Inf. holds 86% of hit points (0.86=1-2.25/16.31), Artillery is dying

quote: Originally posted by SlowThinker on 01-29-2001 07:03 PM DaveV disregards sixteenths: Mech. Inf. wins 1 (or 1/2), Artillery wins 11 (or 5 1/2).

Yes, sorry, this was an approximation that overstates the attacker's strength. It provides a rough estimate of relative strengths without having to compute fractions. I use this formula in games so I don't continually have to resort to my calculator.

quote: Originally posted by SlowThinker on 01-29-2001 07:03 PM Am I right?

mech infantry damage/artillery damage = 16.31/2.25

Note:
If we disregard sixteenths, then weaker unit makes 1/(2*m/n-1) of damage.
For large ratio m/n, weaker unit looses a half of his power ("-1" in the expression looses his significance).

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Scouse Git[1]

If you had a unit of A3,H1,F1 and attacked a unit of D3,H1,F1, its different from attacking a unit that is D1,H3,F1. Its also different from attacking a D1,H1,F3 unit.

In the first case, you might win or lose but the surviving unit will be half dead.

In the second case, if the defender survives, it will be almost dead

In the third case, if the defender survives, it will be only slightly damaged.

A second thing to take note is that HPs and FPs become important with modification that takes when air, helicopter and naval units fight land units or when city improvements like city walls are involved. Some modifications reduce the hit points while others multiply the attack factor without modifying the hit points. This give more depth in the design of interaction between units.

To understand the use of hit points and firepower, you need to take them to their extremes. In a game where all units have FP=10 and HP=1

You can have single blow deaths
The probability that a weak unit kills a strong unit becomes significant
Ships performing shore bombardment or defending cities are not disadvantaged - their firepower is reduced from one to one!

In a game where all units have FP=1 and HP=10

The weaker unit is sure to die
The stronger unit is sure to get damaged
Ships performing shore bombardment or defending in cities have fire power reduced to one (i.e. 10 times)

In the case of air units attacking ships in port, the planes have firepower doubled so the effect is not so pronounced as the ship example but there is still an effect.

But I'll throw in a comment on vet status. I seem to have noticed that a unit gets to be made up more often when the outcome of a particular combat was a close run thing. And (just maybe - memory loss makes me doubtful) it may be that this is more of a factor for the successful defender than for the attacker. If there's anything in this, I'm not altogether sure whether the state of health of the unit at the outset matters - but I think it does.

Or, put another way, a unit that emerges badly damaged but alive is likely to get made up.

kobayashi,
I don't agree. If I have understood the combat system well, then (accordingly to my post "posted January 29, 2001 19:03")

a)A3,H1,F1 attacks D3,H1,F1,
attacker wins (3-1/8)*1*1 times
defender wins (3+1/8)*1*1 times
(Note: I have doubled numbers in my table: Total number of attacks = 2m)
If we disregard eights then wins are divided in a ratio 3 to 3, i. e. 1 to 1

b)A3,H1,F1 attacks D1,H3,F1,
attacker wins (3+2-1/8)*1*1 times
defender wins (1+1/8)*3*1 times
wins are divided in a ratio 5 to 3

c)A3,H1,F1 attacks D3,H1,F3,
attacker wins (3+2-1/8)*1*1 times
defender wins (1+1/8)*1*3 times
wins are divided in a ratio 5 to 3

quote: Some modifications reduce the hit points while others multiply the attack factor without modifying the hit points.

quote: To understand the use of hit points and firepower, you need to take them to their extremes. In a game where all units have FP=10 and HP=1... ...In a game where all units have FP=1 and HP=10...

{combat system}{combat formula}
{pikemen}{vet status}
{}{SlowThinker}{end2}

Your calculations are not wrong as far as the statistical average is concerned. In a two system world, either A is killed or B is killed, they odds
are as you state them.

But they simply do not take into account

1. the distribution of events, i.e. the shape of the distribution curve

2. the amount of damage the survivor sustains after the opponet is killed.

If every unit had 1000 hit points, the outcome and damage would be exactly predictable, the stronger unit would always win everytime and be damaged by the same amount.

if ONE (2A 1H 5F 1H) attacks TWO(1A 1D 5F 1H)
(remember that 1H = 10 hit points)

Every round ONE has a 2/3 chance of landing a blow and TWO has a 1/3 chance of landing a blow.

Lets say ONE wins the first two rounds. In each round TWO loses 5 hit points and after losing 2 rounds, TWO is dead and ONE is undamaged.

TWO only has a 10.9% (33%x33%) of winning the first two rounds but if it does, ONE will be killed.

BUT if ONE (2A 1H 1F 5H) attacks TWO(1A 1D 1F 5H)
(Now they each have 50 hit points)

After ONE wins two rounds, TWO is down to 48 hit points from 50, far from dead. Now you need to win fifty rounds to kill an opponent (as opposed to two above). There is no statistically significant way that TWO can win fifty rounds before ONE so TWO is as good as dead - but ONE is sure to get damaged in the process.

1. combat damage is accumulated and units must "heal"
2. The FP/HP tends to make thestronger units more consistent at killing the weaker units. (i.e. removes much of the chance element that a battleship will lose to a phalanx becuase mulitple rounds of combat are simulated.

For a simple comparison, attack a warrior and a settler with a horseman.

warrior: 1d 1h/1f
settler: 1d 2h/1f