Veblen

Join Date 03/2006

Exploring effects of simultaneous combat

Question: How will the simultaneous-firing system for combat (announced for 1.2) affect the ideal balance between weapons and armor?

This post attempts to answer this quantitatively using my combat simulator. I've started by writing a new version of the simulateCombat function that implements the simultaneous firing.

To show you the difference, I've uploaded two graphs. Here's how to read them: Combat is simulated a number of times (10000 here), and the "result" of each combat is saved. The result is defined as (Attacker hitpoints remaining - Defender hitpoints remaining), so a positive value means the attacker won, a negative value means the defender won, and (in the new system) a result of zero means both fleets were destroyed. The graphs show the number of times (frequency) that each result appears.
Attacking fleet: 3 ships, each 10 hitpoint, 6 beam attack, 4 beam defense
Defending fleet: same as attacking fleet
(Each ship has a small hull, Warp Drive II, 2 Phasors, 2 Shields II, miniaturization 25%, cost 252, size 32/32)
Current system:

Simultaneous firing:

The attacking fleet won 63.86% of the 10000 iterations in the current system, but only 47.74% of the 10000 iterations with simultaneous firing. Note also that the simultaneous system is quite symmetric around zero, which matches with our intuition: now that attackers and defenders are treated the same, we expect that when two identical fleets fight that it will be an even coin toss. More specifically, one expects that the true distribution is perfectly symmetric around zero. Also, note that while in the previous system there were no zero values, now they are common. In fact, there are (have always been) sharp spikes in frequency at the values that represent "whole" numbers of ships remaining, and zero is now one of these spikes.

So we set up the experiment as follows:
1. Pick two fleets, A and B, where A and B represent realistic options for a player at a certain tech level, and where A has only weapons and B has weapons and shields.
2. Using the sequential-firing simulateCombat function, estimate the probability that: (i) A wins attacking A, (ii) A wins attacking B, (iii) B wins attacking A, (iv) B wins attacking B.
3. Repeat (2) using the simultaneous-firing simulateCombat function
4. Interpret the data

1. Pick two fleets
We want to pick fleets that will give us meaningful results. In the interests of brevity, I'll skip to what I came up with.
Fleet A: Three ships, each with:
Small hull, Warp Drive II, 3 Phasors, miniaturization 25 =
10 hitpoints, 9 beam attack, 30/32 used space, 192 cost
Fleet B: Three ships, each with:
Small hull, Warp Drive II, 2 Phasors, 2 Shields II, miniaturization 25 =
10 hitpoints, 6 beam attack, 4 beam defense, 32/32 used space, 252 cost

The cost on the second ship is higher and it requires an additional technology (Shields II), but we're just going to ignore that. We're not looking for the best split between offense and defense, we're just looking to see how the effectiveness of each design type will change in the simultaneous firing system. Also, since the cost of researching Shields II isn't considered, note that while this may be useful in helping you decide which model to build if you have Shields II, it won't tell you if Shields II is worth researching in the first place. Despite these limitations, Fleet A and Fleet B are pretty representative, I think, and should be good enough for us to get something interesting.

2. Use sequential-firing model to estimate victory probabilities
Running sequential-firing simulateCombat with 5000 iterations,

(Probability attacker wins, median result, mean +/- standard deviation)
A attacks A: 86.88%, 15, 12.93 +/- 9.82
A attacks B: 62.06%, 9, 4.41 +/- 13.85
B attacks A: 86.70%, 16, 13.24 +/- 10.69
B attacks B: 64.04%, 9, 5.02 +/- 13.56

3. Use simultaneous-firing model to estimate victory probabilities
Running simultaneous-firing simulateCombat with 5000 iterations,

(Probability attacker wins, probability of tie, median result, mean +/- standard deviation)
A attacks A: 41.78%, 17.40%, 0, 0.04 +/- 8.25
A attacks B: 32.06%, 7.90%, -5, -3.99 +/- 10.37
B attacks A: 61.32%, 7.66%, 5, 4.17 +/- 10.37
B attacks B: 47.66%, 3.60%, 0, -0.07 +/- 12.28

4. Interpret the data
It looks like the ships chosen may have been... not so great. The results would have been clearer if, for example, B had been inferior in the first system but superior in the second. However, we see here that B is the superior ship is both: not surprising considering that it requires more research and has a higher production cost. Perhaps, in choosing ship design, Fleet A should have been given better weapons (thus more attack power and higher cost) in order to balance them. However, we can see some things worth noting in the data.

In the current system, Fleet A and Fleet B perform about the same as attackers. Fleet B, however, is much better at taking a punch. Fleet A's chance of surviving is about 13.2%, while Fleet B's chance of surviving is about 36.9%, about 2.8 times higher.

In the simultaneous-firing data, we see two things right away: The advantage to the attacker is gone now, and it was big. Also, Fleet B is superior to Fleet A in every way now: It will win about 2/3 of the time, regardless of if it attacks or defends.

In the current system,
When Attacking: Fleet A and B approximately the same
When Defending: Fleet B 2.8 times more likely to survive (36.9% vs 13.2%)

In the simultaneous-firing system,
When Attacking or Defending: Fleet B wins about 61%, ties 8%, and loses 32% of the time.

And it looks like that may be it for conclusions. We know a bit more about what's going on that we did when we started, but I don't feel that we can answer the original question based on the somewhat murky results of one experiment.

I feel that the fleets should have been chosen better at the start... it's hard to say exactly how the change in system shifts the ideal balance between weapons, but it would appear that it shifts it towards defense. This might just be my bias, though, since I expected it to increase the value of defense. (Based on the reasoning the all-weapon ships are very bad at taking a punch and derive much of their current power from being able to take out half the enemy fleet before it fires).

If you can think of a good set of fleets to test against each other in the two systems, describe them in a comment and I'll run them through. Maybe with more/better data points we'll start to see a pattern.

As an aside, we expect certain things from a symmetric system, and we see them here. This serves as a convenient reality-check that the simulation is working as desired. First, when two identical fleets fight, the probability of victory should equal the probability of loss, and since Pr(victory) + Pr(tie) + Pr(loss) = 100%, then Pr(victory) + Pr(tie)/2 should = 50%. (41.78% + 17.40%/2 = 50.48%, and 47.66% + 3.60%/2 = 49.46%). Second, Pr(Attacker wins, X vs Y) should equal Pr(Attacker loses, Y vs X). So 32.06% should equal 100%-61.32%-7.66%=31.02%, and 61.32% should equal 100%-32.06%-7.90%=60.04. All in all, this checks out quite nicely. Also, the mean, median, and standard deviation values all behave as we would expect with the symmetry of simultaneous firing.

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That's one hell of an analysis. I won't pretend that I understood all of it.

At the risk of insulting you with an extremely simple response:

1. Approximately 20% of the tech tree deals with defense. By your analysis, this now means something to gameplay. ...............................Good.

2. In developing custom civs, I think people might look hard at spending a point on the LUCK trait now.

3. The combat system pre 1.2 is entirely unsatisfying after a few dozen repetitions. They key is logistic points: he who has the most (and fills them) wins. I have found that the AI won't fill a logistics cap efficiently. That's how I've been defeated 130+ ship navies, losing only 3-5 ships on average (typical turtling strategy)

4. Your simulations suggest that more randomization will occur during battles. Good. True conflict has that element and it will add to the tension of the game, knowing that...even though the odds may be with you...you still MIGHT lose.

1.2? Bring it on.

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Fleet C = 5 ships with
Medium hull, 1 Warp Drive V, 7 Disruptors, miniaturization bonus 70%
16 hp, 49 beam attack, hull size 63/64, cost 545

Fleet D = 5 ships with
Medium hull, 1 Warp Drive V, 5 Phasors VII, 4 Barriers III, miniaturization bonus 70%
16 hp, 25 beam attack, 12 beam defense, hull size 63/64, cost 580

Research point investment: rpi(Disruptors) = 22450, rpi(Phasors VII) = 18450, rpi(Barriers III) = 5775, so the ships in Fleet D cost a little more and take a little more research.

Probability of attacker winning in current, sequential-firing system, 10000 iterations:
C attacks C: 98.0%
C attacks D: 96.4%
D attacks C: 88.6%
D attacks D: 79.9%

Probability of attacker winning plus 1/2 of probability of tie in simultaneous system, 10000 iterations:
C attacks C: 50.1%
C attacks D: 64.9%
D attacks C: 34.9%
D attacks D: 49.8%

Before, C was better at attacking, D better at defending, but the overwhelming advantage was with whoever attacked. With simultaneous firing, C is a 65/35 favorite over D (counting ties as half a point each). In C and D, we have fleets that are in line with the hunch of many players (and myself) that later in the game, weapons-heavy ships dominate. It's interesting that while in the old system C was a much better attacker, D was a better defender: in the new system, C is flat out better. So we observe a big shift to favor the defender in the new system, but (another) ambivalent shift in the fitness of ships with respect to weapons/defense ratio.

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A very informative post and with some interesting conclusions to boot. I was a little surprised to see that defence actually gets better with simultaneous firing (after all, if you're guaranteed a shot, survival is less important). It would also mean I was dead wrong on my assumption then.

Oh well, it's not the first time that happened to me (and I still believe a normal distribution would improve combat because of better small sample properties

).

Perhaps you could run one more experiment for me, just to nail the point home? I'd like to see what would happen if you put two late-game fleets together. Now, I'm a novice so I don't know the values or research costs of the equipment but the only prerequisite would be to have the ratio of HP/(Attack+Defence) drastically lowered. So a small hull with 50 Attack and another balanced ship to match would represent what I was aiming for.

The idea is to replicate small sample battles. In these one-shot games, variance becomes more important (that's my guess anyway). After all, I'd like to know whether *this* fleet has good odds of surviving a battle and a mean is only useful when many rounds are played then.

Could you perhaps compute the variance or standard error of the win-probability?

Thanks and again, great post.

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At the risk of insulting you with an extremely simple response:

Never!

1. Approximately 20% of the tech tree deals with defense. By your analysis, this now means something to gameplay.

It looks like weapons-heavy ships will dominate less, but that may just be because they will actually suffer losses now. The major shift is going to be in favor of whoever is defending, which will make the AI rather tougher (since against strong players they are the ones defending most of the time). I can't say definitively one way or the other if defenses are going to get stronger relative to weapons, though. Not yet at least.

3. The combat system pre 1.2 is entirely unsatisfying after a few dozen repetitions. They key is logistic points: he who has the most (and fills them) wins. I have found that the AI won't fill a logistics cap efficiently. That's how I've been defeated 130+ ship navies, losing only 3-5 ships on average (typical turtling strategy)

Logistics has a huge effect. Going from 8 to 9 ships can mean a jump in victory probability from 50% to 75%. You're right, the AI doesn't "fill out" it's fleets as effective as a player can. That's a really tough thing to do in a small amount of time, though, in all fairness. It's one of those things that's just limited by how much time you can afford to let the computer think about it.

4. Your simulations suggest that more randomization will occur during battles. Good. True conflict has that element and it will add to the tension of the game, knowing that...even though the odds may be with you...you still MIGHT lose.

Yeah. It'll be a whole lot harder to get 130 kills with 3 losses, since the attacker won't get a big advantage anymore. That will be nice.

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Sorry-sorry-sorry!

You posted the results I was asking for before I even pressed the submit-button. Damn, you're fast!

I'm not able to edit my post so I have to double-post sadly.

But it seems to show that offensive systems have a certain edge over balanced ships which was what I feared although I would've drawn it to more of an extreme, your setup already depicts this.

I hope your experiments get the attention they deserve.

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Yeah, that was the post that got me thinking about this. I went in with the position that defenses would get stronger, but I haven't seen confirmation of this like I had expected. The more I look at it, the less certain I become. You may still be right

(see my reply #2, for example).

Perhaps you could run one more experiment for me, just to nail the point home? I'd like to see what would happen if you put two late-game fleets together. Now, I'm a novice so I don't know the values or research costs of the equipment but the only prerequisite would be to have the ratio of HP/(Attack+Defence) drastically lowered.

Does reply #2 fit?

In a few minutes I'm going to start setting up another simulation, I'll see what I can do about looking ships with higher Attack / HP.

Could you perhaps compute the variance or standard error of the win-probability?

I'm not quite sure what you mean. I could run multiple 1000 iteration runs, get a win probability for each, and compute the variance of that set, but I can't just compute the variance of the win probability for one 10000 iteration run. The win probability is a single value, and not a set, so it doesn't have a variance (or zero variance I guess). I can compute the mean, variance, standard deviation, et cetera of the "results" (Attacker hitpoints - defender hitpoints) for a 10000 iteration simulation, because the results are stored in a 10000 element vector, where each element is the result of one iteration. Can you clarify what you'd like to see?

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Wow Veblen that's one hell of a Monte Carlo you have there

It cerainly confirms my intuitions that 1) defences will be more important 2) combat will be more uncertain and 3) first-mover advantage will be diminshed.

I would just point out to anyone reading this post that although the tactical advantage of attacking is gone the strategic advantage is not. That is to say that once battle has begun it won't matter who is attacking the attacker gets more choices over the composition of each force, which is a definite advantage. This means that there is still a point to attacking, avoiding WWI-esque stalemates and/or mutual slaughter.

That isn't a criticsim of your method Veblen as incorporating strategic concerns into your simulator would be borderline impossible.

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Oh, just read your reply. The hazards of chatting on forums. Well, if you're here reading this, if you want to see something in my next run I'm going to start setting it up in the next 15 minutes, so speak up and I'll try to accomodate

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Can you run one based on fighting with Dread Lords? That's the one that has me worried, because of the massive weaponry they have. Cover the hull in as much ultimate invulnerability as you like and their 10 doom rays are still gonna reach in and tear the guts out of your battleship.

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Ok, I'll do a Dread Lords one, probably tomorrow. I realized it's somehow gotten rather late...

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1. Pick two fleets, A and B, where A and B represent realistic options for a player at a certain tech level, and where A has only weapons and B has weapons and shields.

In the current system, Fleet A and Fleet B perform about the same as attackers. Fleet B, however, is much better at taking a punch.

No ****, sherlock, you had to do a statistical analysis to figure this out?

So basically, what you are saying is, the new patch does exactly what it was meant to do: severely reduce the effect of the "first strike" advantage, to something much more reasonable.

It took playing 2 (unfinished) games for me to figure that out, testing various ships and varying the ratio of weapons/defenses. Before this patch, defenses were virtually (though not completely) useless if you maintained the first strike advantage, now they are critical. I have found that a fleet of 7 ships with high defenses keyed to the weaponry of your opponent and minimal weapons will do far greater than a fleet with loads of weapons that the opponent has no defense against, and moderate or lower defense.

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i'd like to see the following simulation:

take a fleet of 10 ships, 10 attack and 10 defense each (lets say beam, can be any one weapon/armor type)

then let em fight vs a fleet of 10 ships without defense and just 15 attack
then 16 attack
then 17 attack

and so on, until 50:50 win chance is reached

so we see how much more attack does compensate those 10 shields (for both combat systems)

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Veblen,

Extremely Insightful, wish the button worked so I could push it a few times for your post. Thanks!

W/R
Suralle

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Great post. I new defense would be better but I am glad it actually works. I am looking forward to the challenge of facing the game where I know that I will lose ships if I just match the number with attackers and not worry about the other ships. What do I mean: my current strategy is to look at how many ships the ai has and then just take my superior attackers and match the number 4 ships to 4 , 3 to 3 .... This way since my attack is soo high they die and don't touch me back. Now if I do that they die but so do I. I guess I go back to what I did before. Huge defensive ships with the right def tech. This way I am hard to damage and will have all my ships still stick around.

Great work.

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mikeswi wrote:

I dug a little and I don't have stats for a typical DL ship handy. I can run this if you can tell me more specifically what ships or fleets you want to test.

I'm running MegaVolt's suggestion (#12) now, should be ready in twenty minutes or so.

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Control Fleet: 10 ships, each
10 hitpoints, 10 beam attack, 10 beam defense

Test Fleet n: 10 ships, each
10 hitpoints, n beam attack
for n from 10 to 30

For each of the 21 Test fleets, three simulations are run:
Data set 1: 2000 iterations of the Test fleet attacking the Control fleet (sequential firing),
Data set 2: 2000 iterations of the Control fleet attacking the Test fleet (sequential),
Data set 3: 2000 iterations of the Test fleet attacking the Control fleet (simultaneous).

We compute three statistics:
Probabiliy of Test fleet winning (when attacking, sequential) = (number of results > 0) / iterations, data set 1
Probability of Test fleet winning (when defending, sequential) = (number of results < 0) / iterations, data set 2
Probability of Test fleet winning (when attacking or defending, sequential) = (number of results > 0) / iterations + 0.5 * (number of results == 0) / iterations, data set 3

Note that for simultaneous firing, we're counting ties as "half-points".

Graphing these three statistics versus n, we get

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Ok..... This seems to be typical Dread Lords....

There's two scenarios actually. Early in the game, I'll be using fighters with laser cannons. Once 1.2 comes out, I'll be adding some defense to them, although I don't do that now usually.

So that's 7 fighters with 4 beam attack, 2 missile defense, 11HP (with xinathium hull plating)
Against a DL frigate with 22HP 189 Missile attack

I'll usually stick with those fighters and avoid the DL whenever possible until I get my research cranked up. This is the sort of fleet I put together when I go hunting for them:

1 Dreadnought - 77HP 88Beam Attack 30 Missile Defense
4 Frigates - 24HP 48Beam Attack 20 Missile Defense
6 Fighters - 15HP 40Beam Attack 10 Missile Defense

Against this sort of Fleet:

3 Escorts- 14HP, 94 Missile Attack, 14 Shield Defense (or maybe 13 defense, whatever 9 + 50% is)

Actually, it's usually 2 frigates and a fighter, but I spent 10 in-game years on a test game with it on auto-turn and they never once produced a fighter with defenses, so I can't give you the attack/defense numbers on that. I finally got fed up waiting and quit.

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On the subject of your medium class ship simulation (fleets C and D). The conclusions I came up with are that the defense of fleet D (12) is woefully inadequate to deal with a 49 beam attack with only 16 hp's per ship. Therefor, the tradeoff to take defenses over more weapons in this circumstance wouldn't be worth it. The mean attack value of fleet C is ~25 - ~6 = 19 damage per shot. While for fleet D it's ~ 13 damage per shot. I expect that even using a mod that gave the fleets more hp's that fleet C would still win the majority of the time. This all leads to the conclusion that if you're going to put defenses on your ships, that you'd better be sure that they are adequate for the fleets they will be encountering, (and you'll probably need a somewhat decent tech lead to pull that off). Otherwise, you're still better off just going weapon heavy, interesting. I wonder if defenses overall would need a boost to their defense values to make them more useful, vs. the same amount of tech spent for all weapons research.

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Cool, thanks Mikeswi, I'll use that information to run a DL simulation tonight (it's barbeque weather in Seattle right now).

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This all leads to the conclusion that if you're going to put defenses on your ships, that you'd better be sure that they are adequate for the fleets they will be encountering, (and you'll probably need a somewhat decent tech lead to pull that off)

Yeah, I that that's right. In the C vs D test, each fleet takes about the same research, but the stats on C are much higher.

Think about it this way: C is full of Disruptors, each representing 22450 research; D is full of Phasors VII (18450) and Barriers III (5775), which means the average tech level of the components used on D is way lower than the average tech level of the components on C, even though it takes the same amount of research to produce C and D. I think that the tech lead you mention is key. In fact, from what I can tell, you need 4 things for shields to be clearly useful: larger ships, mid to late game weapon and armor techs, a tech lead, and correctly matched defenses.

Very early in the game, there might be a golden zone with 3 attack, 1 defense ships being useful (especially with starbases), but I find the first ships I build are 6 attack at least, and it's better just not to research defenses.

It's interesting... one of the nice things about the simulataneous-firing system is that it's going to be much easier to compare two fleets. Before, you'd get situations where Fleet A is a better attacker than Fleet B, but Fleet B is a better defender than Fleet A, so it wasn't clear how to compare them. With the simultaneous system, it'll be much easier to construct tests to determine things like the ideal balance between weapons and defenses.

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I have no idea how he's running these simulations so I can't say mathematically one way or the other. However, I can say from experience that defenses are better than no defenses.

I played a game yesterday on tough that was all out war the whole time. I had frigates and fighters with fairly heavy point defense standing up to battleships and frigates armed with Stinger and Harpoon missiles. I had beams, they had no defense at first, then light missile defense later on.

I even had one frigate with heavy point defense get jumped by two fleets, each with one battleship and two frigates. I lost the frigate, but they lost 4 frigates, 1 battleship and the remaning battleship was in very bad shape.

And think about; who is the toughest enemy in the game? Pirates. Why? Because, unless you have some serious firepower, their defenses are so tough that your fleet is half dead by the time you kill their escorts.

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Ok, here's what I've been able to do regarding mikeswi's Dread Lord question:

So that's 7 fighters with 4 beam attack, 2 missile defense, 11HP (with xinathium hull plating)
Against a DL frigate with 22HP 189 Missile attack

One thing I can tell you right here is that missile defense is not going to be worth it here, in either system. The 189 attack on the dread lord is going to wipe out an 11 hp ship with one shot most of the time; the shields will make a difference only a very small percentage of the time. On the other hand, without the shields, it could probably be a 6 beam attack ship. WIth 50% more attack power, a 6 beam attack ships will do better in either situation... actually, don't take my word for it. We'll just test it.

Fleet A: 7 fighters, 6 beam attack, 11 HP
Fleet B: 7 fighters, 4 beam attack, 2 missile defense, 11 HP
Fleet DL: 1 frigate, 189 missile attack, 22 HP

We run these simulations:
1. Fleet A attacks DL, sequential.
2. Fleet A is attacked by DL, sequential.
3. Fleet A versus DL, simultaneous.

And repeat these for Fleet B.

Er... its 100% every time (10000 iterations for each of 6 runs, not 1 DL victory). 7 ships versus 1 (unshielded) ship isn't a contest.

Repeating the experiment with 5 ships in Fleet A and Fleet B instead of 7:
(Probability Fleet wins when attacking DL [seq], Pr Fleet wins when attacked by DL [seq], Pr Fleet wins versus DL and counting ties as half-points [sim])
Fleet A: (100%, 99.6%, 100%)
Fleet B: (100%, 87.5%, 99.9%)

With 4 ships in Fleet A and Fleet B:
Fleet A: (99.6%, 54.3%, 98.9%)
Fleet B: (86.7%, 11.6%, 77.9%)

With 3 ships in Fleet A and Fleet B:
Fleet A: (51.0%, 3.6%, 38.1%)
Fleet B: (6.7%, 0.4%, 4.5%)

So Fleet A (A/D=6/0) performs better in both systems than Fleet B (A/D=4/2). Also, the number of ships in the fleet plays a huge role: With 3 ships, you'll lose; 4 ships, win most of the time; 5 or more ships, win all of the time.

Looking at the other numbers provided

1 Dreadnought - 77HP 88Beam Attack 30 Missile Defense
4 Frigates - 24HP 48Beam Attack 20 Missile Defense
6 Fighters - 15HP 40Beam Attack 10 Missile Defense

Against this sort of Fleet:

3 Escorts- 14HP, 94 Missile Attack, 14 Shield Defense

I can say the 11 ships will take out the 3 every time. I'm not sure what you want me to do with this, since your fleet is going to win every time

This isn't very helpful to you, so sorry about that. Honestly, a big part of the problem is I'm still not sure what the goal here is. I can tell you that from the tests I've done, to take out vastly superior ships like the Dread Lords, your best bet is to use weapon-only ships and try to get the first strike. Another huge factor is logistics: If you have 7 ships in your fleet and the enemy has 1, then you are guaranteed 6+5+4+3+2+1=21 attacks against him if you defend, 28 if you attack.

Does that help? If you have another question and can chisel it down to something easy for me to do (see MegaVolt's), I'm happy to take another crack at it. Like I said in the OP, I'm looking for good questions to try to answer with the simulator, so keep 'em coming.

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'd like to see the following simulation:

take a fleet of 10 ships, 10 attack and 10 defense each (lets say beam, can be any one weapon/armor type)

then let em fight vs a fleet of 10 ships without defense and just 15 attack
then 16 attack
then 17 attack

and so on, until 50:50 win chance is reached

so we see how much more attack does compensate those 10 shields (for both combat systems)

I second this .

Any chance of doing this ? Velben?

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Sure thing Richrf--see comment #16

According to that run, in the simultaneous-firing system coming with 1.2, a fleet of 10 ships each A:(20-0-0) D:(0-0-0) will be evenly matched against a fleet of 10 ship each A:(10-0-0) D:(10-0-0). This doesn't look at cost, though; I expect the 20-attack ships would be cheaper.

I have some new routines in the pipeline to analyze the value lost (ships destroyed times cost... a little more complicated, but that's the gist) for each side, hopefully I'll get some results today if I have time.

Er, there's a typo in comment #16 now that I look at it; one of the "sequential"s should be "simultaneous", but hopefully people can figure this out by context since I can't edit the comment now...

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What I would be really intrested in knowing is, what is the average ( mean ) casualty rating for the victor in example two? I mean they still win, but casualtys would help me decide the fleets value more.
( If you win but lose 4/5 ships it's not much of a victory. )

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