The Battle for... somewhere - Provisional Signups

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Re: The Battle for... somewhere - Provisional Signups

Postby BLANDCorporatio » Mon Oct 04, 2010 3:40 pm

(written Before Sihoiba's post above)

All right, let's try another tack.

"Cost to guarantee croaking": how many pop points do I need to spend to guarantee that I can kill a Diwigible? I'll be using the 41Cost Orc Archer (9Hits, 18Attack, 0Defense, 1Move).

I need 200Attack to guarantee a Diwigible croak (as the minimum roll is 50%). For 200 Attack I need 11 Orc Archers (and a little bit more), but already I need to invest 451 pop points. This is significant.

So a proposed way to a solution may be to make it so that the cost to guarantee a unit's croaking* must not exceed the cost of the unit itself.

*: fudge factors: croakable by what? Does it have to be guarantee, or can it be some other odds like 95% chance?

Sihoiba wrote:You're not making a comparison that tests my statement.

What you should be comparing is the 7*Orc Archer + 126HP Carrier stack, versus the best flying ranged stack you can build if limited to units with 30HP.


Why? Why limited to 30HP?

And I kinda thought the comparison is fair- ground units, vs. ground units that use the Diwigible hack to move faster. Plus, if "ground units will always be more efficient" then what's the problem? In any case, it's always worthwhile to compare air and ground stacks, to see what the extent of the imbaness is.

Will look over your numbers now.
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Re: The Battle for... somewhere - Provisional Signups

Postby HerbieRai » Mon Oct 04, 2010 3:48 pm

I would also like to add the price of failure to Blands mathmatics.

If the LOL cats get a 50%, and don't croak the diwi, then the next turn the diwi's as full hp.*

The LOL cats, on the other hand, are going to lose at least three of their number in the first turn (if ship gets 50%). So the diwi has almost no chance of wiping the enemy in the first turn, but a lot higher chance of winning the fight in the long run.

*if the percents go from 50 to 100, and they need a little over 75 to kill it, thats roughly a 50/50 shot as far as I can tell.

edit: you guys are posting fast today
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Re: The Battle for... somewhere - Provisional Signups

Postby zilfallon » Mon Oct 04, 2010 3:53 pm

HerbieRai, you wrote exactly what i was about to. A full stack of lolcatiushas (or whatevers) might be a bit stronger than a diwigible, but they are vulnerable to small hit-and-run raids, and their strength can be decreased by doing so. A diwigible however, is ONE big unit, and thus more resistant to such raids. And don't tell that such small raids are impossible, they are more than possible with the current retaliation system we are using(it's flaws were mentioned in the previous page)
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Re: The Battle for... somewhere - Provisional Signups

Postby BLANDCorporatio » Mon Oct 04, 2010 3:58 pm

HerbieRai wrote:I would also like to add the price of failure to Blands mathmatics.

If the LOL cats get a 50%, and don't croak the diwi, then the next turn the diwi's as full hp.*


Read what I wrote. If the LOLCats roll 50%, the worst possible roll, they STILL croak the Diwigible.

zilfallon wrote:A full stack of lolcatiushas (or whatevers) might be a bit stronger than a diwigible, but they are vulnerable to small hit-and-run raids, and their strength can be decreased by doing so. A diwigible however, is ONE big unit, and thus more resistant to such raids.


This is the thing I'm trying to wrap around now, with the whole "cost to guarantee croaking" thing. I'd like to have some numerical reason for a HP cap. Why 30? Why not 64?

The problem so far is that (almost) all my metrics involve a static comparison. Apart from the "surprise units" thing, none of them involve troop movement.

So this suggests one more approach. We would like the game rules to at least allow (ie not discourage) spreading units- while expecting those units to survive, I don't mean swave walls or such.

With Diwigibles however, there's too much punch that can be focused in one spot with impunity. If you want that thing downed, you need to keep troops fairly concentrated. So one source of HP cap may be a number that still does not discourage maneuvering of smaller units.
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Re: The Battle for... somewhere - Provisional Signups

Postby HerbieRai » Mon Oct 04, 2010 4:05 pm

Mathmatically you are correct sir, but your earlier post has 75.2

BLANDCorporatio wrote:What about the Diwigible on its own? It costs 422, from which I can get 7 LOLCatiushas with 2 points left spare. So I have a Diwigible with 100Hits and (effective) 54Attack vs. 7LOLCatiushas which together have 70HP and 133 Attack. The Diwigible cannot croak all LOLCatiushas but the LOLCatiushas can croak the Diwigible if they roll 75.2% or better. Alone, the Diwigible is way worse in the offense department.


I would say 30 is a good cap since we have 4 people sharing 200 pop points. If we want to pop our good units, we are still having to wait a few turns to get one. It is an arbitrary number in my reasoning though, that is tied to what the GM wants to give for pts/turn.
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Re: The Battle for... somewhere - Provisional Signups

Postby BLANDCorporatio » Mon Oct 04, 2010 4:08 pm

Ah dang, yes, the Diwigible alone vs. its weight in LOLCatiushas. Sorry.

Yes, see the "cost to guarantee croaking" above. I'm planning to make it so that it will not exceed the cost of the unit itself.

Now there's also the maneuvrability thing to consider, as I sketched in my previous post. Will think about this.

(EDIT: as far as I'm concerned, the rules- by which I mean stat caps, cost formulas, stacking rules/bonuses, hit-and-run and other misc rules etc- must obey this principle

1. There should exist a Rock-Paper-Scissors type equilibrium between at least 3 unit archetypes

and now I've added a couple more

2. AIR (allow informed reactions): at least in theory, a side should know what may be heading its way in one turn, with a reasonable (and small) margin of surprise.

3. The rules should be such that spread-out parties of small units are viable for non-suicidal missions.

3 is a bit fuzzy, will clarify)
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Re: The Battle for... somewhere - Provisional Signups

Postby Sihoiba » Mon Oct 04, 2010 5:41 pm

I think if you're going with a rock, paper, scissor (lizard, spock) style set up the cost of croaking a scissor should be balanced something along the lines of 0.66*scissors cost if it's a rock, 1.5*scissors cost if it's a paper.

30Hp because that's the number we currently have experience with so the numbers give us some context.

Edit: I'm planning to run a team v team game, with my acting as the overall GM. Want to try and take away one sides perfect information from the testing.

I'd also like to try different rules to the one in Nihila's game. The things I'm tempted to try are as follows:

Bland's cost to cwoak principle for max unit hits.
My move suggestion (though don't assume the amount of points will be similar)
Terrain capable unit specials (similar to Nihilas)
Dancefighting special
A Healomancy special
A Dirtamancy special
A Shockomancy special
A Foolomancy special
A siege special

It won't have:
Artefacts
Casters

I'll post my suggested rules in a new thread, give people a day to suggest any tweaks, and then start unit creation, not trying to take away from this thread at all, I just think it might be good to have a couple of different play tests going on at the same time, so we can try more things more rapidly.
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Re: The Battle for... somewhere - Provisional Signups

Postby BLANDCorporatio » Mon Oct 04, 2010 6:36 pm

I dunno about y'all, but I relish a challenge in world-building!

While I'm not having a specific ruleset in mind now, I'm in the process of crafting one based on

Sihoiba wrote:cost to cwoak principle for max unit hits.


Meaning, let's have a function called cost to guarantee croaking (I'll call it CGC for short).

Then, I have to design rules that obey:

1. Rock-Paper-Scissors: there exist unit types ("Rock" etc.) such that

CGC(a Rock unit at hex A; any collection of Paper units at hex B; either starter) < Cost(Rock unit);
CGC(a Paper unit at hex A; any collection of Scissors units at hex B; either starter) < Cost(Paper unit);
CGC(a Scissors unit at hex A; any collection of Rock units at hex B; either starter) < Cost(Scissors unit);

(hexes A and B are such that the starting player's units can get to the opponent's hex.)

2. No unit is immortal:

there exists no unit/unit type X so that CGC(X at hex A; any collection of other units at hex B; either starter) >= Cost(X)

(hexes A and B are such that the starting player's units can get to the opponent's hex.)

Notice, this will put some interesting restrictions on garrison units.

And I'm currently trying to work out something about scouting too. Basically, I define a cost-to-scout an area around a hex (a very easy function to compute as opposed to CGC) and I'm now trying to think of how to balance "surprises" from outside this area to the scout cost*. It's worth mentioning also that if you know an area around your units, you can, sometimes, afford to spread some units out. Not all stacks must be able to kill a max-HP unit, after all.

(EDIT:

*: and I think I got it. Suppose you have a hex of combat units, and scouts, that you want to keep safe. The scouts can tell you what's in an area around the hex you want to guard; you have enough scouts to know what's in ALL hexes around yours in a range of whatever. But of course the enemy might, via relay, bring more units than are immediately visible in the scouted range.

Then, the cost for the enemy to bring in a number of HP equal to the number of scout units (that you need at the guarded hex to scout all around it in a given range) should equal the cost of the scouts themselves. This will have some consequences to mounting rules, move and scouting rules.

Hey, I invested in information, then an investment in surprise should be about as costly. What do you think?)

PS: for the mathematically minded, I define CGC(A, B; starter) as:

Spoiler: show
Let there be an infinite featureless plane of death.

Player A is given a unit/stack of units/collection of stacks of units (A), subject to some restrictions on unit types and/or placement relative to each other in the Infinite Plane of Death.

Player B is given another unit/stack of units/collection of stacks of units, subject to some restrictions on unit types and/or placement relative to each other in the Infinite Plane of Death.

Starter is which of the two gets first turn.

Usually player A is more restricted (a given unit or a given number of units will always be the case when I use CGC; all A's units may also be focused in one hex etc). Player B is less restricted (use any units of a given type).

Player A wants to survive, player B wants to croak player A's units regardless of survivability of B's units. Optimal play is assumed of both players with one restriction- if player A gets the first move, player A MUST attack one of player B's units.

Notice that several turns of combat may pass before one player remains unitless/player A exists the range of player B.

It is assumed that player A always gets the best rolls, while player B the worst ones.

CGC(A, B) then is the minimum cost that player B needs to spend in these conditions in order to win.


As you can see, it would be wicked to compute or analyze, but fortunately I just use it in this design with units that are located in 2 near hexes.
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Re: The Battle for... somewhere - Provisional Signups

Postby Nihila » Mon Oct 04, 2010 8:44 pm

Sihoiba, I'd be interested in that game. Were you going to leave siege relatively untouched or were you going to renovate it?

And BLAND, firstly, a possible trinity would be Cavalry beats Archers (have the Ranged Special directly inverse to Defense, have some kind of Mobility bonus); Archers beat Infantry; Infantry beat Cavalry.

I have no idea how to actually make that work, beyond what I suggested above. If Ranged is inversely proportional to both Defense and Move, you get what I call an Archer. If there is a mobility bonus to attack (possibly declining with the enemy stack's defense), then Cavalry can perform better against Archers but worse against Infantry. And then Archers just hit-and-run the Infantry to death.

Thus, Rock=Infantry; Paper=Archers; Scissors=Cavalry. My suggestion for the Ranged cost if anyone thinks that this isn't too insanely complex: SPECIAL={Attack+[(Defense+1)*(Move+1)]}. Unit examples:
4-6-0-2. Totally not plagiarized from my own game. If you want me to calculate cost with BLAND's formula, I will, but I'll use Twoy's for now.
Under old rules, Cost=15.
Under proposed rule, Cost=18. Not really a big change.

My suggestion for the Mobility bonus: Cavalry units get a bonus of their own Move to their Attack, but they deduct the enemies' Defense score from this bonus, which doesn't become a penalty. If we don't mind obscene complication, we can even add a defense bonus of (.5*Move), rounding down, against Ranged units. This makes Cavalry vs. Archer: Archer fires at Cavalry, inflicts a hit or two of damage, Cavalry butchers Archer.

Now, Infantry will have 4 or 5 Defense, which nerfs or eliminates the uber-powerful mobility bonus. Then, it's just down to which there's more of, and Infantry will be cheaper, overall. Hopefully.

I don't have the time to thought-test this now, so feel free to nitpick these to death.

And, BLAND, you read Irregular Webcomic? :lol:
"The Infantrymen of Erfworld have nothing to lose but their chains. They have Erfworld to win. Infantry of all sides: Unite!"--Kawl Mawx, Master-class Moneymancer
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Re: The Battle for... somewhere - Provisional Signups

Postby WaterMonkey314 » Mon Oct 04, 2010 10:07 pm

I haven'tthe time to address everything brought up here, but I very much like nearly everything BLAND said. :P (Particularly the AIR thing - the orly relay attack is wayyy too overpowered)
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Re: The Battle for... somewhere - Provisional Signups

Postby BLANDCorporatio » Tue Oct 05, 2010 3:06 pm

Greetings again,

I have some news from the rules design front. No, alas, not something about Rock-Paper-Scissors yet, but soon.

Today's rant is again AIR-headed, and it concerns scouts, the cost of the scout special, and the range of scouting.

Here's the problem setup. You have a hex. You want to keep it. So you want to know what the enemy has, that can threaten this hex. Fortunately you have as many Scouts as you need in order to scout all hexes that are in a certain range around that hex.

Those scouts cost something. They also, if push comes to shove, provide some defense for the hex. So the idea is, how much would the enemy need to spend, to "surprise" the scouts: deliver a quantity of hitpoints to the hex that you want to keep, that is equal to the number of scouts. The cost of the scouts should be less or equal to the cost that the enemy needs to pay to surprise them.

Now, notice that scouting a big area around a hex is a HUGE investment. In practice, you'll rarely have enough scouts to fully scout anything within 10 hexes. Therefore, surprise is easier. But as a guideline, let's proceed.

We know that the maximum move is 5. I allow a scout to be able to look into a number of hexes that is twice its move, and these hexes need to be scouted as if the scout moved through them- you know, usual Gobwin Bump rules. You can't have a scout at hex A and use it to see what's in five hexes on the opposite corner of the map. Instead, a scout will first scout a neighbouring hex, then a hex neighbouring to that one etc.

So in principle I can scout 10 hexes with each modified hex, meaning I can see any hex that is at most 10 hexes away from the hex I want defended. This means I need 60 scouts (one for each outmost hex).

Now let's see how much the enemy needs to pay to bring a payload of 60HP to the hex I want guarded. I'll ignore any HP caps for now, and say that the enemy has access to the following units:

payload (60H, 1A, 0D, 5M) of cost 151,
relay (120H, 1A, 0D, 5M) of cost 301 and
stepper (360H, 1A, 0D, 1M) of cost 181.

It's cheaper, for a payload of HP, to be focused in one unit (minimal attack of 1 means several units need to spend more on attack). It's also cheaper to have larger HP units with lower move, which is why the stepper is slow. Anyway, together the units bring the cost level to 633 pop points to deliver a 60HP payload across a range of 10 hexes.

A basic scout (1H, 1A, 0D, 5M) would cost 4 + Scout special. So 60 Scouts would cost 240 + 60 times the Scout special. So in other words, the 60 times the Scout Special should be no more than 393.

Roughly, this means the Scout Special should cost no more than 6.5 (6, because the cost formula rounds up and 6.5 becomes 7).

Remember, this is for rules that allow 10-hex scouts. EDIT: it also assumes all scouts are in one hex, not the most efficient arrangement if you just want to cover a large area. To cover the 10-hex range around a hex, you'd need a minimum of 33 scouts, all spread out. But OTOH, spread-out scouts are easy pickings, so you know. I went with the assumption that leaves scouts defended. Anyway, to deliver a 33HP payload, an enemy needs to pay 350, which in the end brings the cost of the scout special to no more than 6.6 (6, because the cost formula would round up). So no change.

Nihila wrote:And, BLAND, you read Irregular Webcomic? :lol:


One of the fanarts is me-made actually! :)

EDIT, EDIT:

Another assumption in the above analysis is that you don't care about enemy units that your scouts have located in the 10-hex range. This includes units that could be themselves used as relays for something located outside the 10-hex range.

This is intentional, and here's the reason behind it: your scouts tell you of those units' existence. You therefore have an idea of what the enemy can bring from the 10-hex range into the hex you want to keep, as well as what extra capacity the enemy has for a relay. This information you can use for planning. If you see a big fast unit 10 hexes away, you can plan for the situation when that unit will be used to ferry other units to the 5-hex range.

The surprise thing was meant to cover something that you just couldn't see at all through scouting- an unforeseeable payload brought in by relays you had no idea were available.
Last edited by BLANDCorporatio on Tue Oct 05, 2010 3:44 pm, edited 2 times in total.
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Re: The Battle for... somewhere - Provisional Signups

Postby zilfallon » Tue Oct 05, 2010 3:18 pm

Hmm, the point where you said scouting shouldn't cost more than 6 seems good. And we aren't even using "move x 2 hexes scouting" thing, so it should be even cheaper. But that cheap means everyone will probably add scouting to every single unit.
To prevent this, we might need a hp and attack cap to units with scouting special. You know, imagine the Diwigible with scout special, it is like a map hack :D
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Re: The Battle for... somewhere - Provisional Signups

Postby Sihoiba » Tue Oct 05, 2010 3:21 pm

One of the things I was considering suggesting for the scenario was to tie scouts special cost to HP/defence in some way, enough to make basic scouts cheaper seeing if both sides are limited by a fog of war they'll need plenty of scouts, but to discourage one side making an unkillable scout in order to allow killing scouts to be a viable tactic.

On an unrelated note, I'm off to look at the fanarts.
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Re: The Battle for... somewhere - Provisional Signups

Postby Nihila » Tue Oct 05, 2010 3:45 pm

Scout Special cost suggestion: Cost=5+(Hits+Attack*Defense)

For BLAND's Basic Scout, that gives a cost of 6. If we make a Diwigi-scout, the cost is more like 105, which is slightly inefficient.
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Re: The Battle for... somewhere - Provisional Signups

Postby BLANDCorporatio » Tue Oct 05, 2010 4:00 pm

I don't know, I thought that any non-zero cost to the scout special would make people less inclined to use all units as scouts. If you want many scouts (and you do), those will, usually, be small cheap units ...

But OTOH, when you have a unit that costs 100 without specials, a jump to 106 is meh whatever. So why not, make the scout special also dependent on Hits etc to make that jump more of a jolt.

EDIT: and now onward to the Rock-Paper-Scissor thing. Also with "no unit is immortal" and I've just thought of "no shotguns" principles.

Nihila, the trinity of Gobwin Bump was supposed to be Fast Ranged (Flier), Slow Ranged (Archer) and Slow normal (Infantry). So any tweaks I make will first try and take advantage of the GB rules as they are now.

If I can ensure that RPS, no-immortal and no-shotgun hold, that would seem ok so far.
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Re: The Battle for... somewhere - Provisional Signups

Postby Nihila » Tue Oct 05, 2010 4:22 pm

BLANDCorporatio wrote:Nihila, the trinity of Gobwin Bump was supposed to be Fast Ranged (Flier), Slow Ranged (Archer) and Slow normal (Infantry). So any tweaks I make will first try and take advantage of the GB rules as they are now.
Yes, but the actual "trinity" was Ranged slaughters melee, gigantic monstrosities squish everything except gigantic monstrosities, normal infantry gets to be used as cannon fodder. Especially with our gigantic monstrosity Ranged units. Like WaterMonkey's Field Gun and Sihoiba's Hurricanes. Now, the giant monsters weren't quite immortal, just close.

But it doesn't even work as Rock-Paper-Scissors if we ignore those. For one, Infantry doesn't really beat Archery, because Archers can slice through half the Infantry stack before the Infantry even engage. The end result is that Infantry loses, whether they face Archers or Fliers. There are definitely fixes to this, I just can't think of any now.
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Re: The Battle for... somewhere - Provisional Signups

Postby BLANDCorporatio » Tue Oct 05, 2010 4:37 pm

Nihila wrote:But it doesn't even work as Rock-Paper-Scissors if we ignore those. For one, Infantry doesn't really beat Archery, because Archers can slice through half the Infantry stack before the Infantry even engage. The end result is that Infantry loses, whether they face Archers or Fliers. There are definitely fixes to this, I just can't think of any now.


But you just said where to look. That's what I'm going to do.

The fixes I'll play with first are:

the Ranged special to be more expensive (so as to make Infantry > Archers),
Attack to be slightly cheaper (to make hit-and-runs more efficient and thus Fliers > Infantry, as well as to obey the no-immortal unit principle),
and nothing else seems needed (to make Archers > Fliers); this might depend of course on just how more expensive the Ranged special gets.

Note that under both Twoy and my cost formula, high-HP units are not the best when it comes to attack; my formula in particular favours units of 9HP or less for this. Higher HP units are tougher to move around, get smaller maximum attack and are tougher to defend.

Then there's the no-immortal units principle, which will probably result in an HP cap.

Finally there should be no-shotgun, meaning one unit type superior to all else. Using CGC, there exists no "Shotgun" unit so that for any and all other units X that you can pick, CGC*(X, Shotgun, either starter) <= Cost(X).

EDIT:

*: CGC(A, B, whatever) is wickedly biased against B. To properly check that there are no shotguns, I'll need to no longer assume that A gets perfect rolls while B gets the worst ones.
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Re: The Battle for... somewhere - Provisional Signups

Postby Nihila » Tue Oct 05, 2010 4:48 pm

BLANDCorporatio wrote:Then there's the no-immortal units principle, which will probably result in an HP cap.
Hm. I, as usual, don't like HP caps, but under Twoy's formula, a unit with 30 Hits has a cost of 112.5 from the Hits alone, more if it has move. That unit would not be immortal, but it might be hard to kill, but not impossible. How many hits is "immortal"? With a defense of 5, 3 hits out of every 8 get through. The random factor can halve the damage, so 3 hits out of every 16 get through. But how high does Hits have to be to make a unit immortal?

To be honest, as a GM, with the kinds of costs that would accompany an immortal unit, I'd just cut the players' supply line (and mine, fairness is important) so that they couldn't ever pop a massive unit. And no matter how good your humongous unit is, my horde of Minitwoopers will out-attack it if they have the same total cost.
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Re: The Battle for... somewhere - Provisional Signups

Postby BLANDCorporatio » Tue Oct 05, 2010 5:13 pm

One more rant before signing off for tonight. The topic is effective hitpoints.

A unit of defense 4 has, for combat purposes, twice the number of Hits that it claims to have. This results in a question- is a unit with defense 4 (about) twice as expensive as a unit that is identical, except for having defense 0? (Ignore attack and specials. Compare a unit with X Hits, 0 Attack, 4 Defense, Y Move with one with X Hits, 0 Attack, 0 Defense, Y Move. Yes, 0 attack is not valid but attack's just a distraction in this comparison. Move is NOT, since some formulas weigh Hits by Move.)

So to repeat, is a unit with defense 4 (about) twice as expensive as a unit that is identical, except for having defense 0? Probably not, and it doesn't have to be. Maybe you'll want to make defense into a slightly better way to increase (effective) hitpoints. This is fine.

However, you'll probably want this way of beefing up Hitpoints to be about as effective regardless of how fast a unit is, or how many hits it has. Neither my nor Twoy's formula satisfies this. Both formulas make the Defense stat more efficient at increasing effective Hitpoints for units with large amounts of Hits.

Finally, there's stacking to consider. A large, but def-0 unit, like the Diwigible, would benefit more from the presence of a high-def, but small, unit (assuming the rule that a stack's defense is the average of the component units' defense). This is ok- stacking bonuses, bonus accumulation etc all being very Erfworld-like. But it's something to control.

This discussion has an impact on the cost of Defense for units. What that impact actually will be I can't say yet. Just thinking about it.
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Re: The Battle for... somewhere - Provisional Signups

Postby BLANDCorporatio » Wed Oct 06, 2010 1:51 pm

Okay, new day, new rant. Today's topic is Defense, Combat Hitpoints, Cargo Capacity and the Hitpoint Cap. Quite a lot of material ...

Here's the problem setup. I am designing a unit, it has whatever stats and specials I like- except, Defense is 0. Now, I'd like to spend some more points on this unit and I'm contemplating a choice: either I spend more points to increase Defense, or more points to increase Hits. What exactly am I buying, if I choose either of these?

If I buy Hits, I am buying: primarily, combat hitpoints (I increase the Attack that an enemy needs to croak this unit); secondarily, I increase Cargo capacity and the ability of this unit to "gain" combat hitpoints through stacking.

If I buy Defense, I am buying: primarily, combat hitpoints; secondarily, I increase the unit's ability to "offer" combat hitpoints through stacking.

First, let's look into the offering-receiving of combat hitpoints through stacking. If I have two units, separately they will have a certain sum of combat hitpoints
Spoiler: show
Unit A with H1 hits and D1 defense, unit B with H2 hits and D2 defense, have, if kept separate,

H1*8/(8-D1) + H2*8/(8-D2) combat hitpoints. That's the damage the enemy needs to inflict to kill them both.


while stacked, something that may well be a different amount
Spoiler: show
(H1 + H2)*8/(8 - (D1 + D2)/2)


A similar analysis goes for stacking more units together, but the effect is less dramatic the more units you add. The significant changes happen when stacking two units, so that's what I'm looking at. Already, it's a very bizzare function, I assure you. One unit, the one with less defense, will "gain" combat hitpoints; the higher defense unit "loses" a few. Will the trade be fair?

Here's a case of weirdness. Suppose I have a unit with 100 Hits, 0 Defense. And then, I have one with 50 Hits, and X defense. Should I stack? Should I leave them separate? If X is 0, no difference. Stacking results in a gain of combat hitpoints if X is 1, 2 or 3. If X is 4, then it doesn't matter: either together or apart, a 100H 0D and 50H 4D unit have 200 combat hitpoints. If X is 5, I actually lose combat hitpoints. Paradox?

Spoiler: show
You'll usually want to stack the two units, regardless, since the 100H unit always benefits from the exchange and gets harder to kill. However, if the enemy has enough firepower to kill the two units if stacked, keeping them apart may offer you better chances of survival.


Anyway, I've done some numerical testing and, for valid Defense values between 0 and 5, here are some conclusions:

- if you use a unit with high defense to beef up a stack made of that unit and another unit with 0 defense, then the 0 defense unit needs to have at least 15% hitpoints than the high defense unit. (And this bonus would be merely theoretical; a 115H 0D unit and a 100H 1D unit stacked gain 0.05 combat hitpoints; stacking a 115H 0D unit with a 100H xD results in a combat hitpoint loss for any x from 1 to 5!)

- as expected, the more hits the low-defense unit has, the better it stands to gain from stacking.

- I tried stacking a "large" unit with a 5H, x D unit, and see how much combat hits I gain. Consistently, the best gains happen for "large" H 2D stacked with 5H 5D. So if you want large hit gains, stack a large unit that has Defense 2 (or 3, or 0, in this order) with a 5H 5D unit.

- If I stack a 20H 2D and a 5H 5D unit, I gain 4.44 combat hits; for 30H 2D and 5H 5D, I gain 8.89; for 40H 2D and 5H 5D, I gain 13.33; for 100H 2D and 5H 5D, I gain ~40 combat hits, and for 1000H 2D and 5H 5D, I gain ~440 combat hits. What happens is that the 5H unit "loses" about 5 combat hits (alone, it has ~13.6; in the stack, it has a bit less than 9); the large unit gains Hits*(8/(6) - 8/(4.5)): so, proportional to the number of its own hits, and if this number of hits is large, it dominates the number of hits gained by the stack.

This suggests one idea of where to put a unit cap: make it so that the cheapest highest defense unit cannot offer a combat hitpoint gain more than -> and here you're free to tune.

It also suggests something else. See, when I buy Hits or Defense, I need to make another investment also in order to access the secondary effects. If I want to use a unit as a carrier, I need to buy the cargo; if I want to use a unit to gain combat hitpoints by stacking, I need to buy a larger unit to stack it with. However, cargo will be cheaper than a unit that, if stacked, will result in a beefier stack.

So when comparing the cost of increasing defense, and increasing hits, I think I can ignore the hitpoint gain by stacking effect, since it's costlier to actually manifest significantly.

So then, to return. I buy Defense for my unit, I'm increasing its combat hits. Here's by how much:

0D: no increase; 1D: 8/7, or about 14% increase; 2D: +33%; 3D: +60%; 4D: +100%; 5D: +166%.

Notice that the combat hitpoint increase is not linear in Defense. In fact, the best way to replicate this behaviour in the cost formulas we have now is to replace the Defense factor by 8/(8-Defense) (optionally, multiplied by some constant). So my formula for example should become:

Cost of the unit = Hits*Move*0.5 + (8/(8 - Defense))*some constant*0.5*Hits^(2/3) + Attack + Specials

Ok, now let's do one more thing and call it a rant for today.

Let's say I beef up a unit's defense by 1. This gains me more combat hitpoints, let's say 4. Then I change my mind; I undo the change, and instead want to buy 4 Hits. They should be more expensive (and this will put a limit on how big that constant in the formula just above can be). That's because that cost for those 4 Hits should cover the fact that I'm beefing my unit's combat hitpoints by 4, but also giving it the ability to carry 2Hits extra of cargo.

So, the difference between the cost I payed for the defense, and the cost I payed for the equivalent extra hits, is the cost for cargo capacity. This cost, I think, should be move-sensitive (fast cargo is more valuable tactically), so this means that in a cost formula, the Hits term must be multiplied by Move, and the Defense term must not contain Move at a power of 1 or more. (Check; our formulas obey this). Optionally, cargo can become more expensive the bulkier it gets; to ensure that this happens, the Defense term should not contain Hits at a power of 1 or more (check; both our formulas obey this).

The big conclusion of today is then:

In a unit cost formula, the Defense term should be of the form (8/(8 - Defense))*some constant*(Hits^less than 1)*(Move^less than 1). The "some constant" must be chosen such that it is cheaper to increase a unit's combat hitpoints by increasing its Defense, than it is by increasing its Hits. (Also, the Hits term should include Move at a power of at least 1.)

(In my formula, Move in the Defense term is at power 0. Move^0 = 1 :) )
The whole point of this is lost if you keep it a secret.
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BLANDCorporatio
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