balance considerations

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 # balance
 
-### turret effectiveness
-How strong is a turret compared to another? Are there trivial winning strategies? Are some turrets unuseful? 
+### lives density
+A turret is effective against a group of enemies.
+A turret that is dealing 1 damage per second (dps) and can shoot at 20 cells kills an enemy with 20 lives, if the enemy has a speed of 1 cell per second. 
+An enemy with 21 lives is not killed. However, infinite enemies with 1 life and 1 cell apart cannot get through the turret.
+Therefore the turret effectiveness can be gauged against a **density of lives**: how many lives per cell can the turret take away.
 
+A 1 dps turret can cope with a density of 1 life per cell. <br>
+A 2 dps turret can cope with 2 lives per cell.
+
+A turret that applies the slowness effect (50% speed) to an enemy for 10 seconds decreases the density, thus increasing the othe turrets dps.
+
+There can be two cases:
+- constant density for the whole path, the turrets damage only the enemies in their range so their effectiveness is lessened by range/path\_lenght.
+- the density is uneven, turret effectiveness is greater.
+
+### height
+An enemy with 100 lives and 100 enemies with 1 life (within the same cell) both have a density of 100 lives per cell.
+To capture this aspect, the height of a cell is defined as the maximum number of lives in that cell.
+- high cell: few enemies with a lot of life
+- low cell: a lot of enemies with low life
+
+---
+
+### turret balance
 Turret types:
 - apply damage
 - make the path longer
 - resource production
 
-I can compare how effective a turret is w.r.t. the others in its type.
+target type:
+- single target
+	- great with high cells
+- aoe
+	- great with low cells
 
-1. damage turret
-Effectiveness: damage per second
+What are the differences between turrets in the same group?
 
-2. path turret
-Effectiveness: elongation constant (adimensional)
+Special abilities (yikes, but it's an idea)
 
-3. resource turret
-Effectiveness: return on investment (adimensional)
+Tradeoffs:
+- short term gain / long term gain
+	- good stats / good upgrades or modules
+	- low cost, bad stats / high cost, good stats
+- specialized / generalist
+- reliability (misses)
+- synergies with other turrets
 
 ### random wave generation:
 A wave is generated based on a lives budget, which is a function of the wave number. Tuning that function changes the difficulty of the game.
 
 The current function is `hp_budget = pow((x + 10), 2.7) * 1.8 - 850`
 
-### total damage output (D)
-I need an estimate of how much damage a turret configuration is capable of dealing against enemies in a path of lenght L to derive the function of the wave number.
-
-```
-D = sum{d:damage turrets}( dps of d ) / enemy_speed 
-	* (1 + sum{p:path turrets}( 
-			elongation constant of p * (p.range*2 / L) ) 
-		* path_constant)
+The lives budget also control how many resources are given to the players.
 
-enemy_speed = 1
-```
+The density is crucial:
+- high density, more difficult
+- low density, easier
 
-The `path_constant` is how valuable it is to elongate the path in damage per meter.
+Height is also important:
+- Generating lots of enemies with low life is beneficial towards aoe
+- High enemies good for single target