Friday, November 30, 2007

Triple Cross Defense

After managing to kill everything at the Desktop Tower Defense, I was trying to be scientific to get higher scores. I used the Flying Boss at the easy and normal modes for measuring the effectiveness of the towers, when only one defense tower is present. You need a strong boss to survive after the assault so you can measure the residue health points.

The main deduction is the firing rate which isn't disclosed in the game. It confirms that the Swarm towers are much more effective than the Squirt towers. And that it's always much more cost efficient to upgrade than to duplicate one. And since Swarm towers are for air defense only, we have to have a mixed defense with Sw towers. Though I manage to kill all flying creeps with Sq towers only except for the Flying Bosses.

Looking at the range data explains a lot of things. Why the DNA2 defense is so effective with a Bash tower inside, but doesn't work that well when putting other things inside, or to join the basic unit into larger chains. It confirms what I have been doing is right, wrapping the creep's path around Sq towers, which seemed to be in conflict with the square defense.

Trying to force the creeps around your tower for as long as possible, the basic pattern is a cross build from squares, with your tower in the middle. You try to block the creeps to run around your cross. For maximum range of an Sq (90), the size of a cross is 5 squares in width. For short range weapons such as Bash towers (50), the cross degenerates into a single square, which explains the effectiveness of the square defense. For long ranges, variations of the cross maze are possible, as long as the creeps are forced to run around the circle within range.

Frost towers are the big surprise. They slows down the creeps from a factor of 0.85 to 0.6. So for $200, you can increase the damage of a tower by 1/0.6, or 66%. This is in a way much cheaper than a Boost tower, which cost $500 for 50%. Though they work differently. The frost towers slow down the creeps that pass through, while the Bo's increases the damage of the towers touching them.

Before building the most effective maze, we need to know what weapons are needed and how many of them. Oh yes, it's hen and egg, as the maze determines the total damage that a tower inflicts on the creeps.

Anyway the Flying bosses are one of the most difficult to kill. It turns out that you need 4 Sw6 (Swarm tower level 6, or Storm tower) and 4 Sq6 with Fr6. You can have more Sw and less Sq but the Sq are shared with ground defense. With Boost towers, it's never worthwhile to build more than two towers. So all you need is two Sw6 and two Sq6, all touching two Bo5 (50% boost). Fr6 has the same range as Sw6, so you probably need two Fr6 to cover the two Sw6's, ensuring a consistent 0.6 air speed reduction.

Spawn creeps are the most difficult to kill land creeps. When you kill one, two little spawn creeps are born with half the strength each. So the Spawns are effectively twice as strong as any others in the same level. It also means that you can not kill them with a short range weapon no matter how strong.

So the defense is based on three crosses, one for Ba (which degenerates into a square), and two for the two Sq, which are sufficient for land defense as well as air. You can do without Ba's but since they splashes (killing everyone within range), I think it's the key to high score by sending in creeps earlier. I doubt if you can do without Sq's because given enough time with a proper cross, it provides the most damage per unit cost.

So the basic strategy is for the Ba to at least kill the first generation Spawns, and then the other Sq's take over. Each Ba can deliver three blows when creeps (speed factor 1) are forced to run along it on all 4 sides. The upgrade sequence is something like this, the first is the level number which are spawns.

6 sq3
13 ba1 sq4 sw2
20 ba3 sq5 sw3
27 ba4 sq6 sw4
34 ba5 sq6 sq5 sw5
41 ba6 sq6x2 sw6
48 all +80% fr6
55 ba6 sq6x2 sw6x2 +100% fr6x2

Initially you have to merge a square, as in the DNA 2 defense earlier, with a small cross 3 square wide. Any larger you are wasting resources and wouldn't survive the attacks. When you reach sq6 you have to knock down the borders and enlarge the cross to 5 square wide if possible. When you have two sq you merge the two crosses together side by side overlapping. The total range are halved due to overlapping, but the fire power is doubled there. This also allows mounting space for touching Bo's and Sw's. The first Sw must be in the dead center of the desktop where the Flying bosses pass through.

The other way to force creeps running around your guns is to sell a Pellet tower to open up some 2nd passage and block the 1st passage. It's no fun as it's increasing slow to sell towers. You might save time by having three or more openings so one is open, one is closed and the other is being sold. But I don't think it's the road to high score, which needs a high kill rate. My strategy kill everything without selling and juggling except for the 2nd last Morph Bosses. You may go to the scoreboard to see my humble scores - theplayer, and there is a group score with me in it - players.

Now perhaps when there's nothing to discover, I might go back to my real desktop, top score or not.

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