How simulate a random distribution?

Question

I'm working on a battle algorithm for a text-based game and I stumble when it comes to randomly distributing attacks on a set of units.

E.G, 100 archers shoot 100 targets at the same time. I thought of doing like this :

1. The 100 targets are considered as a single block
2. The arrows are distributed inside
3. The units hit the same number of times are grouped together.
4. I manage the life of each new group
5. Repeat on each new group if necessary

I can distribute the arrows (step 2) and get the result (step 3) through a loop, but with many armies composed of millions archers, computing time & memory consumption becomes a problem.

// Step 2
const targets = new Array( 1000000000 ); 
targets.fill( 0, 0, 1000000000 );
const arrows = 1000000000;
for( let i = 0; i < arrows; i++ ){  
    const index = Math.floor( ( Math.random() * arrows ) );  
    targets[ index ] += 1  
}
//Step 3
const result = []
targets.forEach( value => {
    if( value ){
        if( result[ value ] ) result[ value ] += 1
        else result[ value ] = 1
    }
} )

Is there another way to solve this problem ? I believe that with large numbers, directly calculating the most likely scenario may be a good option. Unfortunately, I do not know anything about probabilities.

Answer 1

You need to set each archer with a random target. You could set it to any of the enemies but it would probably work better if they can only see a number of them. For the sake of simplicity, I'm going to use 10, not 100.

Archers:
0123456789

0123456789
Enemies:

Now, let's say each archer can only reach the enemy in front of him and two either side for his range so archer 0 can hit enemy 0, 1 and 2. Archer 1, can hit 0, 1, 2, 3. Archer 2 can hit 0, 1, 2, 3, 4 and so on until archer 9 who can only hit enemies 7, 8, 9.

Looping each archer, choose a random enemy then move onto the next archer to do the same.

Personally speaking, I'd also loop all archers before they fire which will add a bit of realism to the game by making some archers aim for enemies who are already dead by the time their arrow gets to their individual target.