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Twilight Suzuka 12-19-2006 20:39

Tower Defense
 
http://en.t45ol.com/play/2541/tower-defence.html
^- addicting game

Statistics for towers:
Code:

Fire                       
                       
                Damage        Range        Cost        Upgrade Multi
Deployment        4        100        18        5.78
Level Two        12        100        20        3.6
Level Three        36        100        30        2.67
Level Four        108        100        50        2.4
Level Five        300        100        80        2.36
Level Six        2056        110        600        1.06
Level Max        7021        120        1500        1.8
                                                       
Averages:                               
Avg Range        104.29                       
Avg Dmg        1362.43                       
Avg Cost        328.29                       
                               
Avg Upgrade +        2.32                       
Avg Effect val        1466.71                       
Avg dmg per $        4.15                       
                               
Totals:                               
Total Range        730                       
Total Dmg        9537                       
Total Cost        2298                       
Amortized Num        4.47                       
                               
Best Upgrade        5.78                       
Max Power        561.68

Code:

Nature                                       
                Damage        Range        Cost        Upgrade Multi
Deployment        5        100        15        7
Level Two        10        100        20        2.25
Level Three        45        110        40        2.8
Level Four        136        150        80        2.19
Level Five        405        160        160        2.02
Level Six        1215        190        320        2.09
Level Seven        3645        200        640        2.03
Level Max        9000        215        1100        2.06       
                               
Averages:                               
Avg Range        153.13                       
Avg Dmg        1807.63                       
Avg Cost        296.88                       
                               
Avg Upgrade +        2.21                       
Avg Effect val        1960.75                       
Avg dmg per $        6.09                       
                               
Totals:                               
Total Range        1225                       
Total Dmg        14461                       
Total Cost        2375                       
Amortized Num        6.6                       
                               
Best Upgrade        7                       
Max Power        1759.09

Code:

Water                                       
                Damage        Range        Cost        Upgrade Multi
Deployment        5        100        10        10.5
Level Two        15        150        20        2.25
Level Three        45        150        40        2
Level Four        135        180        80        2.1
Level Five        405        200        160        2.06
Level Six        1215        200        320        2
Level Seven        3342        200        730        1.64
Level Eight        6684        215        1000        2.24
Level Max        7335        300        1000        2.49
                               
Averages:                               
Avg Range        174.38                       
Avg Dmg        1480.75                       
Avg Cost        295                       
                               
Avg Upgrade +        2.1                       
Avg Effect val        1655.13                       
Avg dmg per $        5.02                       
                               
Totals:                               
Total Range        1395                       
Total Dmg        11846                       
Total Cost        2360                       
Amortized Num        5.61                       
                               
Best Upgrade        10.5                       
Max Power        2200.5

Conclusions:
Until the last two upgrades, fire is the most economical, but quickly becomes costly and uneconomical in the end game.

Overall, water is the most powerful, due to its extended range, which overcomes natures better damage.

Nature costs more, overall, than water, and its power doesn't beat waters range.

Since it takes $23,000 to buy the most powerful flower, the most economical choice is water.

SweatyBanana 12-19-2006 20:40

Re: Tower Defense
 
Great game.

Liquidz 12-19-2006 21:24

Re: Tower Defense
 
i got level 59 thats bad eh LOL

Zenith77 12-19-2006 21:38

Re: Tower Defense
 
Got me addicted :wink:.

Twilight Suzuka 12-19-2006 21:58

Re: Tower Defense
 
Buahhaha.

stupok 12-19-2006 23:33

Re: Tower Defense
 
It's handy to have that little guide you typed out.

XxAvalanchexX 12-19-2006 23:47

Re: Tower Defense
 
It's nothing like playing it on Starcraft.

sawce 12-19-2006 23:49

Re: Tower Defense
 
Quote:

Originally Posted by Twilight Suzuka (Post 417456)
Nature costs more, overall, than water, and its power doesn't beat waters range.

I think youve messed up some math somewhere.

A fully upgraded nature tower costs $985 less than a fully upgraded water tower.

Oh, I see you were going by averages. Those are bad to go by for this; who uses low ranks?

Liquidz 12-20-2006 01:39

Re: Tower Defense
 
wow i keep getting level 59 -.- 4 times in a row lol

jRaven 12-20-2006 03:07

Re: Tower Defense
 
Simple... addicting... good game. Last was 67.

BAILOPAN 12-20-2006 04:28

Re: Tower Defense
 
My best was 72. sawce, why must you link to such addicting games in IRC.

Liquidz 12-20-2006 04:30

Re: Tower Defense
 
72 dam nice work. I cant get passed 59 :P

MaximusBrood 12-20-2006 09:04

Re: Tower Defense
 
Level 68.
I used to play these TD's on Warcraft 3: FT.

allenwr 12-20-2006 09:57

Re: Tower Defense
 
63, 1st try

69

Zenith77 12-20-2006 10:54

Re: Tower Defense
 
61, after I figured out how to play it right ^^.

geertjan88 12-20-2006 11:01

Re: Tower Defense
 
Nice game

http://img146.**************/img146/4849/castleyg0.jpg

allenwr 12-20-2006 11:32

Re: Tower Defense
 
70 :D

pulpy 12-20-2006 12:46

Re: Tower Defense
 
71's my highest so far :(

sawce 12-20-2006 15:40

Re: Tower Defense
 
http://xs110.xs.to/xs110/06513/greens.jpg.xs.jpg

Best that Ive screenshotted, I think I got an 83 the day before

Few things:

Maxed out greens placed properly are by far the best bang for your buck

Placing a tower at the END of a row has a very good effect

Red sucks

Blue sucks

Greens in the middle are very good because you can hit about 90% of the map but still get cheaper, more powerful damage than blue

Also, "flowers" cost 2k to place, but the display is bugged so it requires you to have 3k money. (Youll have 1k left over when youre done placing it). They suck until tier 3 which seems impossible to get to.

Zenith77 12-20-2006 16:32

Re: Tower Defense
 
I knew the green pickle things would come through!

edit
wow your plan sucks

stupok 12-20-2006 19:57

Re: Tower Defense
 
http://xs510.xs.to/xs510/06514/stupoktower.PNG.xs.jpg

The plan doesn't suck, that's my highest score so far.

Putting towers on the ends really does have an odd effect. I don't know what else to do to get the edge. The flower is probably worthless. The clouds are completely worthless.

sawce 12-20-2006 22:25

Re: Tower Defense
 
Quote:

Originally Posted by Zenith77 (Post 417752)
wow your plan sucks

??? Elaborate.

The only thing that sucks about going all green is its kind of hard to start with only a green and keep it in a spot that will be useful later on. I start here:
http://xs110.xs.to/xs110/06514/greenstart.jpg.xs.jpg

It works well later on, the only thing about starting there is you have to upgrade really fast (as in, right when the kill to earn the money is made) or some can slip through.

Emp` 12-20-2006 22:57

Re: Tower Defense
 
[img]http://img327.**************/img327/690/towerszo7.jpg[/img]
started with red circle. got 1 upgrade, then built the 1 all the way at the top. then worked both of the upgrades to the top, then started to build elsewhere.

the blue are where i double builded (apparently you can do that)

and the green is where one of mine disappeard :-/ (a seed was on the map instead)

sawce 12-20-2006 23:05

Re: Tower Defense
 
Id avoid the green circle and one all the way to the right, and i dont try double stacking because of the vanish issue (even when you dont double stack, if its close it can sometimes vanish... it happened to me on wave 75 before)

BAILOPAN 12-20-2006 23:06

Re: Tower Defense
 
sawce you should teach Tower Defense 101 at a university

stupok 12-20-2006 23:10

Re: Tower Defense
 
The red circle in Emp's snapshot is the best starting point if you're going with green. You can last with a single tower all the way to max upgrade without losing any civ's if you put it there.

New High Score:
http://xs110.xs.to/xs110/06514/stupoktower2.PNG.xs.jpg

With flowers, I only got to 75, but they weren't positioned quite right. Awful expensive upgrades, but they are cheaper than a fully upgraded nature tower.

Liquidz 12-21-2006 00:10

Re: Tower Defense
 
I went a different way and got me to level 70.

http://i35.photobucket.com/albums/d1...Adam/score.jpg

Meh highest i ever got.:)

Twilight Suzuka 12-21-2006 02:22

Re: Tower Defense
 
My highest was 85 or so.

The level one flower actually has more damage/range ratio per dollar than the green at max, but placement is difficult.

In order to get a third tier flower, one has to use as little as one unit for as long as possible (I can go up to level 50), and then place a flower, and hope to god you can get it before being overrun.

Twilight Suzuka 12-21-2006 02:37

Re: Tower Defense
 
In the interest of fairness, let me explain what these stats mean before hand.

Success in Tower Defense is limited to a certain upper bound (which I have not quite established), because two competing factors inevitably intersect:

Enemy health: Exponential (1.25^n)
Allied Money: Linear (60 + (x * n) )

Exponential growth inevitably overwhelms linear growth, so unless I am wrong about money growing linearly (it could grow based on the amount of damage dealt to the enemies, which is also exponential). However, signs and observations dictate that, at some point, money begins to run out and things get increasingly harder to build. This shows there is some upper limit.

Now, this means that to maximize how far we can go in Tower Defense, we have to maximize how much damage we do per dollar, as we start to quickly run out of dollars in later levels, and in earlier levels we don't get much to begin with anyway!

However, if we gauge purely by how much damage we do per dollar, we ignore the range factor, and get false readings. For the purposes of the statistics, I have assumed that range is a linear scale, which observation confirms. To elaborate, range is a multiplier that arises through this: (range / 100).

Of course, merely calculating the damage|range per dollar is not sufficient to explain HOW to maximize Tower Defense returns, but it does show what the resulting placements should look like.

On to the stats!

Code:

Lightning        Damage        Range        $  Lvl $  Dmg per $        BVR
Deployment        40        100        40    40      1          1

Code:

Fire                Dmg        Range        $        Lvl $        Dmg/$        BVR
Deployment        4        100        18        18        0.22        0.22
Level Two        12        100        20        38        0.32        0.32
Level Three        36        110        30        68        0.53        0.58
Level Four        108        150        50        118        0.92        1.37
Level Five        300        160        80        198        1.52        2.42
Level Six        2056        190        600        798        2.58        4.9
Level Max        7021        200        1500        2298        3.06        6.11

Code:

Water                Dmg        Range        $        Lvl $        Dmg/$        BVR
Deployment        5        100        10        10        0.5        0.5
Level Two        15        150        20        30        0.5        0.75
Level Three        45        150        40        70        0.64        0.96
Level Four        135        180        80        150        0.9        1.62
Level Five        405        200        160        310        1.31        2.61
Level Six        1215        200        320        630        1.93        3.86
Level Seven        3342        200        730        1360        2.46        4.91
Level Eight        6684        215        1000        2360        2.83        6.09
Level Max        7335        300        1000        3360        2.18        6.55

Code:

Nature                Dmg        Range        $        Lvl $        Dmg/$        BVR
Deployment        5        100        15        15        0.33        0.33
Level Two        10        100        20        35        0.29        0.29
Level Three        45        110        40        75        0.6        0.66
Level Four        136        150        80        155        0.88        1.32
Level Five        405        160        160        315        1.29        2.06
Level Six        1215        190        320        635        1.91        3.64
Level Seven        3645        200        640        1275        2.86        5.72
Level Max        9000        215        1100        2375        3.79        8.15

Code:

Flower                Dmg        Range        $        Lvl $        Dmg/$        BVR
Deployment        9090        150        2000        2000        4.55        6.82
Level Two        15050        100        5000        7000        2.15        2.15
Level Three        909090        90        15000        22000        41.32        37.19

Damage, range, $ (cost) are simple to understand. The next column is total level damage, which is the accumulations of costs till that level. Next over is damage per dollar, raw, which is the raw damage per dollar ratio. The last column is with range factored in.

As you can see, excluding third tier flower, the highest damage per dollar is the first tier flower. Factoring in range, the nature max outruns it by a healthy margin however.

Third tier flower rapes all other values; this is the thing to aim for in the end game.

Conclusions:
Lightning outbeats all others for a significant number of levels, 3 across the board. It can be used as a quick stopgap measure, but fire outruns it as a stop gap measure, for a pretty small price increase.

Fire is the best deal in the middle game. It has a very low cost, under 1000, for a rather high BVR of around 5, and can be built quickly. However, its end game is the lowest of the three mains, and thus shouldn't be used except as a stop gap measure.

Notes: Use as stop gap in endgame

Water is the lowest dmg/$ of all in the max level, however with range factored in, is beat only by the green max. However, the additional range MAY be a factor, in placement.

Notes: Placement can render a higher amount of damage in endgame.

Nature has the highest BVR, which factors in range, and thus in the end game is the most economical. However, its dmg/$ is low UNTIL the end game; its second to last level is comparable to fires second to last level, despite such a higher cost. Nature is the way to go for the end game, but not for stop gap measures.

Notes: Best value, without factoring in placement. Try to put at end of hallway.

Flower has the highest in the end game (which is almost unobtainable), and is the only one to go DOWN when leveling up. The first tier is comparable to the max of nature, though at a reduced cost (which doesn't really matter, as it is insignificant). Unfortunately, the range means it sucks in the end game.

Notes: Get the third tier flower. WINRAR.

Next up: Placement notes.

Twilight Suzuka 12-21-2006 03:54

Re: Tower Defense
 
New: Algorithm for coming up with health and income.

_root.health = _root.health * 1.1 + _root.wave * 8.6;

_root.income = _root.income * 0.02 + _root.wave * 1.1;

Ok, so I was slightly wrong. Health grows exponentially, but income grows logarithmically.

Why?
n^8.6 + 25^1.1n = health
n^1.1 + 60^0.01n = income

That kind of exponential can be written as a logarithm, but I won't go into it. The point is, income quickly becomes bounded, while health is unbounded.

Thanks to KoST for this info. More to come.

Sean D 12-21-2006 03:55

Re: Tower Defense
 
just to add on to twilight suzuka's informative and researched post, DON'T DO THIS EITHER

Twilight Suzuka 12-21-2006 04:01

Re: Tower Defense
 
partially decompiled swf:
http://ampaste.net/5390

Has following useful functions:
Price calculations
Health calculations
Placement functions
Income calculations

Anyone who can provide a more detailed decompile, please post it!

Also, SeanD, I can get farther than that on mostly lightnings!

KoST 12-21-2006 15:43

Re: Tower Defense
 
1 Attachment(s)
http://webuser.hs-furtwangen.de/%7Ek...erclocking.gif
tower-defence.swf - decompiled (.as)

OneEyed 12-21-2006 16:31

Re: Tower Defense
 
I just loaded it into Macromedia Flash 8 and it works. I compiled it and it works.. Time to make the flower cost $1

I have no clue how this flash works, and how this guy coded stuff so it'll take me awhile to learn it.

Spanky McNutnut 12-21-2006 16:51

Re: Tower Defense
 
I got to 72 ^.^

Da_sk8rboy 12-21-2006 17:16

Re: Tower Defense
 
I got 85..

stupok 12-21-2006 18:08

Re: Tower Defense
 
I love the detailed analysis, good job Twilight Suzuka :up:. It actually was quite helpful to be able to see the BVR.

Twilight Suzuka 12-21-2006 19:01

Re: Tower Defense
 
Yeah, I just wish BVR stood for something.

Battle variance radius?

OneEyed 12-21-2006 19:04

Re: Tower Defense
 
This is with cheating after editing the decompiled version of the game.

http://www.soccer-jam.com/flowerpower.jpg

Da_sk8rboy 12-21-2006 19:18

Re: Tower Defense
 
Could you give me that version?


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