My Theorytard

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Platinum_Dragon
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My Theorytard

Post by Platinum_Dragon » Wed Nov 11, 2009 12:58 pm

This theory follows through that all units must balance with the most basic unit
The most basic unit is the infantry
The next basic units are mech and bike
These 3 units become the benchmark for unit cost
Units are then benchmark from weakest to strongest
Non-attacking units cannot be benchmark, so we can only "theorize their value" (double theory?)
CO units may push the efficiency of units a lot greater than this theory.
This theory defines the minimum value a unit must be to stay balance.

The greatest tard of this theory is when I calculate the indirect units later on.
I try this tard theory before and it says the M Tank is worth 4 Mech.

Infantry v Mech

Round 1 Player 1
Infantry attacks Mech
Mech takes 45 damage 55 remaining
Infantry takes 39 damage 61 remaining

Round 1 Player 2
Mech attacks infantry
Infantry takes 39 damage 22 remaining
Mech takes 13 damage 42 remaining

Round 2 Player 1
Infantry attacks Mech
Mech takes 13 damage 29 remaining
Infantry takes 32 damage
Infantry dies in counter attack

Infantry kills 71 health with first turn

Mech v Infantry

Round 1 Player 1
Mech attacks Infantry
Infantry takes 65 damage 35 remaining
Mech takes 18 damage 82 remaining

Round 1 Player 2
Infantry attacks Mech
Mech takes 18 damage 64 remainig
Infantry takes 45 damage
Infantry dies in counter attack

Infantry kills 36 health with second turn

On average, Infantry commits 53.5% damage to Mech before dying.
Luck will skew the favor towards Mech more
This yields Mech ~= 1.87 x Infanty
If Infantry = 1500, then Mech ~= 2800

List (Price rounded to nearest hundred)
Infantry = 1500
Bike = Mech = 2800

Infantry v Recon
Mech v Recon
Bike v Recon

Infantry v Recon

Round 1 Player 1
Infantry attacks Recon
Recon takes 12 damage 88 remaining
Infantry takes 67 damage 33 remaining

Round 1 Player2
Recon attacks Infantry
Infantry takes 67 damage
Infantry dies in attack

Infantry kills 12 health with first turn

Recon v Infantry

Round 1 Player 1
Recon attacks Infantry
Infantry takes 75 damage 25 remainig
Recon takes 3 damage 97 remaining

Round 1 Player 2
Infantry attacks recon
Recon takes 3 damage 94 remaining
Infantry takes 75 damage
Infantry dies in counter attack

Infantry kills 6 health with second turn

On average Infantry commits 9% damage to Recon
This yield Recon ~= 11.11 x Infantry
Recon is not establish because we still have bike and mech

Mech v Recon

Round 1 Player 1
Mech attacks Recon
Recon takes 85 damage 15 remaining
Mech takes 13 damage 87 remaining

Round 1 Player 2
Recon attacks Mech
Mech takes 13 damage 64 remaining
Recon takes 59 damage
Recon dies in counter attack

Recon kills 26 health with second turn

Recon v Mech

Round 1 Player 1
Recon attacks Mech
Mech takes 65 damage 35 remaining
Recon takes 34 damage 66 remaining

Round 1 Player 2
Mech attacks Recon
Recon takes 34 damage 32 remaining
Mech takes 26 damage 8 remaining

Round 2 Player 1
Recon attacks Mech
Mech 26 damage
Mech dies in attack

Mech kills 68 health with second turn

On average, Mech wins the game, but FTA is important
Movement may change the factor, but terrain will affect movement

without the Mech Bazooka, Recon will worth 16700

Bike v Recon

Round 1 Player 1
Bike attacks Recon
Recon takes 18 damage 82 remaining
Bike takes 58 damage 42 remaining

Round 1 Player 2
Recon attacks Bike
Bike takes 58 damage
Bke dies in attack

Bike kills 18 health with first turn

Recon v Bike

Round 1 Player 1
Recon attacks Bike
Bike takes 65 damage 35 remaining
Recon takes 7 damage 93 remaining

Round 1 Player 2
Bike attacks Recon
Recon takes 7 damage 84 remaining
Bike takes 58 damage
Bike dies in counter attack

Bike kills 14 health with second turn

Recon = 6.25 x Bike

The Mech v Recon cannot give an effective value

I'll weight it to 3400 (fisrt unlogical judgement)

List (Price rounded to nearest hundred)
Infantry = 1500
Bike = Mech = 2800
Recon = 3400
.
.
.
still not finish.

This theorytard only takes numbers as is.
Yeah, I'm just brute forcing the calculations without counting luck or terrain.

Edit: Maybe I should change it so luck = current HP/2 for "average" as I'm measuring average ability of units.

Edit: If I remove the attributely unlogical prediction for recon value, then its value is 16700!
From that high value, I can tell the other units prices will be exponentially larger.
In this game, the higher tier units are truly more cost efficient if you can maintain tempo with your CO unit.

Edit: Well, under theory, two mech diagonally next to each other is a better defense against a tank than two mech adjacent to each other.
In the case a tank attacks, then the full HP mech can strike first and the damage mech (3 or 4)can strike again or merge with the first mech (7 or 8).
In the second case, a tank can attack so that the damage mech (3 or 4) must move before the full HP mech gets first strike.
The only case the diagonal formation is weaker is during snow or when there are a lot more units around.
In tight areas, use two mech, and in broad areas use tank because the tank has a greater mobility.
Last edited by Platinum_Dragon on Thu Nov 12, 2009 9:52 am, edited 2 times in total.
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DTaeKim
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Re: My Theorytard

Post by DTaeKim » Wed Nov 11, 2009 3:25 pm

Doesn't this go out the window once defense is factored in?
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GipFace
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Re: My Theorytard

Post by GipFace » Wed Nov 11, 2009 6:19 pm

Your comparison doesn't work for various reasons:

1. Nobody uses 100/100 mechs
2. The COs who use mechs extensively have boosted mechs, which completely dominate infantry:

Lin mech vs. Penny infantry, no terrain DEF:
65 x 1.3 / 1.1 = 76% (round down to 7)
45 x .3 x 1.1 / 1.3 = 11% (round down to 1)

Penny infantry vs. Lin mech, no terrain DEF:
45 x 1.1 / 1.3 = 38% (round up to 4)
65 x .6 x 1.3 / 1.1 = 46% (round down to 4)

Lin wins 9-3 if her mechs get the first strike, and comes out even 6-6 if the infantry attacks first and the mech loses the luck roll. Either way, Lin adds to her CO meter and will work towards either building md tanks to completely smash Penny, or massing additional mechs and b-copters to outnumber her. (Infantry cannot 2HKO mechs, so the mechs are able to retreat to a city and heal, thus keeping up the unit count) Either way, she completely dominates Penny and the rest of the underpowered tier due to this virtual 4 com tower advantage.

3. Recons are rarely used to attack units 1:1 unless they are disrupting captures, in which case they deny the opponent $1K for each day that property remains uncaptured. They provide the first strike against a soldier so that one of your soldiers finishes it off, or are used in tandem with another vehicle to 2HKO artillery.
4. Expensive units have a "tempo" factor which offsets costs to some degree. For example, in one game against Sneetch, I had 3 Lin antiair to deal with his Will mech cluster. I used my CO md tank to destroy the first mech, then my three antiair destroyed three more mechs and covered the CO md tank. Now he was suddenly outnumbered and lost all his initiative: 4 lost mechs = $10000, while if he counterattacked my two exposed antiair with mechs, I would lose 11 x $700 = $7700 (Will mech vs. Lin antiair: 55 x 1.3 / 1.3 = 55%) and he would lose an additional $2500 (Lin antiair vs. Will mech: 105 x .4 x 1.35 [it killed so it is at least Lv1] / 1.1 = 51%). The next day, those weakened antiair are able to finish off the weakened mechs. Will would lose 6 units and $15000, and Lin would lose no units and $7700 at most. This swing in numbers is crippling.

EDIT: Oh, I found the game. Here's the before and after screenshot:

Before:
Image

After:
Image

He surrendered after I ended my turn. Anyway, play some games before you look at units in a vacuum.

ptd

Post by ptd » Thu Nov 12, 2009 1:04 am

Yeah, I forgot about Lanchester Square Law[b/] where you can dictate what hits what. In those case, indirect tend to value up faster than direct combat as long as the shield is maintain.

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x0_000
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Re: My Theorytard

Post by x0_000 » Fri Nov 13, 2009 10:25 am

so basically everything you just did has no valid assumptions to back it up
Only in math can you buy 600 cantaloupes and not look like a nutter.

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Re: My Theorytard

Post by Platinum_Dragon » Fri Nov 13, 2009 12:34 pm

Well, Lanchester has two Laws: the linear law and the square law. In Lanchester Linear Law, units can only kill exactly one other unit and be killed by one other unit, or in the case of indirect units, two units fire blindly in each other. It this law, it says that larger side will win with the difference remaining. In the square law, units can choose their target so the strength is the square ratio of units. In this game, the direct units have tendency the concentrate their power, but there is a limited the the square law, because you can only surround on four sides. With indirect, there is a larger the the limitation, but essentially, you can say that 2 artilleries is 4 x stronger than 1 artillery. But we know that unit price cannot reflect the dynamic change in the units ability, so we have to define an average and maintain the price base on the average for balance.

My method will increase the price of the units too fast, so the game will become impractical because the price range of the units are too high. A practical game should have the unit price in ranges so that any of the units have practical usage with any of the situation. In other words, we can balance the game by decreasing the firepower of all the higher tier units, but this will make the CO unit even more important than it ever was. This is actually a good situation for those whom are not in the meta game level because they still cannot effectively use their CO unit.

I forgot the mobility portion as well. The game has three portion. Attrition (damage ratios), Mobility (movement type and movement points), and logistic (unit price, property, and unit ammunition). Attrition and Mobility are the tactical portion of the game, but the logistics is 2/3 of the game. Thinking ahead of more than a single unit movement is call strategy. When you see ahead multiple turns, this is where we consider true strategy -- the one where I had a definition war at the beginning of this year.
Most topics are 6 months old. It is so tempting to revive them.

As I'm consider 80 percentile or better for my age group, My Brain Age and Wii Sport's Fitness Test says I'm 60 years old before I complete my first two decade of life.

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x0_000
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Re: My Theorytard

Post by x0_000 » Sat Nov 14, 2009 8:40 am

x0_000 wrote:so basically everything you just did has no valid assumptions to back it up
Only in math can you buy 600 cantaloupes and not look like a nutter.

Platinum_Dragon
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Re: My Theorytard

Post by Platinum_Dragon » Sat Nov 14, 2009 11:54 am

The assumption is valid at the soldier tier. As you can see, the mech and bike are more efficient than the infantry, 2500 v 2800. Of course, the 12% inefficiency of using the infantry has a slight advantage in saving up your funds for a larger unit in a later turn, but the difference is not large enough for you to use once the fund or income exceed a certain level. As the income increase, the higher tier units become more efficient than the lower tier units. Essentially, you will only need enough unit for support for the larger units, and if you can maintain an economy large enough for one of the large units, you can just pump out the larger unit. The balance of having enough support and teching up to the next unit tier is the key to the game.

So one of the tactics that can use is continue to pump out mech from one base and build the strongest tier unit in the expo base. Typical maps have 3 flanks of battle, so be certain that the expo base closest to the CO unit will continue to build a unit similar to the CO unit.
Most topics are 6 months old. It is so tempting to revive them.

As I'm consider 80 percentile or better for my age group, My Brain Age and Wii Sport's Fitness Test says I'm 60 years old before I complete my first two decade of life.

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