Difference between revisions of "Random Targeting"

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Bullet damage, assuming firepower > 1:
 
Bullet damage, assuming firepower > 1:
<pre>D=4*x+2*(x-1)</pre>
+
 
 +
<math>D=4x+2(x-1)</math>
 +
 
  
 
The smallest size of a robot, in radians:
 
The smallest size of a robot, in radians:
<pre>S=36/distance</pre>
+
 
 +
<math>s=\frac{36}{d}</math>, where <math>d</math> is the distance to the other bot.
 +
 
  
 
The total escape area, in radians:
 
The total escape area, in radians:
<pre>A=2*asin(8/(20-3*x))</pre>
+
 
 +
<math>\alpha=2 \cdot asin(\frac{8}{20-3x})</math>
 +
 
  
 
Probability of a hit, assuming uniform spread of bullets over A:
 
Probability of a hit, assuming uniform spread of bullets over A:
<pre>P=min(1,S/A)</pre>
+
 
 +
<math>P=min(1,\frac{s}{\alpha})</math>
 +
 
  
 
The expected damage from a shot:
 
The expected damage from a shot:
<pre>E=D*P</pre>
+
 
 +
<math>E=DP</math>
 +
 
  
 
The heat created by a shot:
 
The heat created by a shot:
<pre>H=1+x/5</pre>
+
 
 +
<math>H=1+\frac{x}{5}</math>
 +
 
  
 
The firing frequency:
 
The firing frequency:
<pre>F=1/ceil(H/0.1)</pre>
 
  
Expected damage (DPS) per tick of combat:
+
<math>F=\frac{1}{ceil(10H)}</math>
<pre>DPS=E*F</pre>
+
 
 +
 
 +
Expected damage <math>D_t</math> per tick of combat:
 +
 
 +
<math>D_t=EF</math>
 +
 
  
 
Back substitution to get the expected damage per tick in terms of distance and x and optimization of DPS are left as an exercise for the coder.
 
Back substitution to get the expected damage per tick in terms of distance and x and optimization of DPS are left as an exercise for the coder.

Revision as of 23:11, 5 February 2013

A method of targeting that simply chooses a random angle among the angles that could possibly hit the opponent. Some successful NanoBots use this firing method. Its implementation is very small and for unpredictable movements, it will give a consistent hit percentage.

Example

// Add import robocode.util.* for Utils
// This code goes in your onScannedRobot() event handler.

public void onScannedRobot(ScannedRobotEvent e) {
    double randomGuessFactor = (Math.random() - .5) * 2;
    double bulletPower = 3;
    double maxEscapeAngle = Math.asin(8.0/(20 - (3 * bulletPower)));
    double firingAngle = randomGuessFactor * maxEscapeAngle;
    double absBearingToEnemy = e.getBearingRadians() + getHeadingRadians();
	
    setTurnGunRightRadians(Utils.normalRelativeAngle(
            absBearingToEnemy + firingAngle - getGunHeadingRadians()));
    fire(bulletPower);
}

A simpler solution

A simpler method is to assume that the enemy is traveling in a circle around you (see Musashi Trick), which is often true among NanoBots and 1-vs-1 bots. If the enemy is traveling in a circle around you, the maximum distance it can cover before a bullet reaches it is enemy velocity / bullet velocity (in radians). For example, a power 3.0 bullet fired at an enemy going at full speed should be fired at a bearing offset between -8/11 and +8/11.

Selecting firepower

The advantage of a random gun is that it should have a roughly equal hit rate on any type of movement. This makes ideal firepower selection pretty easy to pre-calculate. In the following equations x is the choice of firepower. It is assumed that damage output per tick is the quantity you're interested in maximizing, it may not be.

Bullet damage, assuming firepower > 1:

<math>D=4x+2(x-1)</math>


The smallest size of a robot, in radians:

<math>s=\frac{36}{d}</math>, where <math>d</math> is the distance to the other bot.


The total escape area, in radians:

<math>\alpha=2 \cdot asin(\frac{8}{20-3x})</math>


Probability of a hit, assuming uniform spread of bullets over A:

<math>P=min(1,\frac{s}{\alpha})</math>


The expected damage from a shot:

<math>E=DP</math>


The heat created by a shot:

<math>H=1+\frac{x}{5}</math>


The firing frequency:

<math>F=\frac{1}{ceil(10H)}</math>


Expected damage <math>D_t</math> per tick of combat:

<math>D_t=EF</math>


Back substitution to get the expected damage per tick in terms of distance and x and optimization of DPS are left as an exercise for the coder.

See also