Random Targeting
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:
D=4*x+2*(x-1)
The smallest size of a robot, in radians:
S=36/distance
The total escape area, in radians:
A=2*asin(8/(20-3*x))
Probability of a hit, assuming uniform spread of bullets over A:
P=min(1,S/A)
The expected damage from a shot:
E=D*P
The heat created by a shot:
H=1+x/5
The firing frequency:
F=1/ceil(H/0.1)
Expected damage per tick of combat:
DPS=E*F
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.
