Examples

• Bomber vs 1-hp enemy minion
• Avenging Wrath vs 4x 2-hp minions @ 4-hp
• Arcane Missiles vs Onyxia and Whelps at @ 3-hp
• Arcane Missiles vs 2-hp minion (@Kripp chat)
• Arcane Missiles vs 2x 2-hp minions (@Reckful chat)
• 19-damage Cthun vs /u/Jakabov (@Reddit →)

Configuration

Statistics

• Probability of killing anything: 0.000%
• Probability of killing Player 1: 0.000%
• Probability of killing Player 2: 0.000%
• Probability of completely missing Player 1: 12.500%
• Probability of completely missing Player 2: 12.500%

Chance of Individual Result

Board States

Algorithm

// turn an array of healths into a decodable-string
// note: we need strings since php arrays are shit
function encode($a) {
	return implode(':', $a);
}

// turn an encoded-string into an array of healths
function decode($s) {
	return array_map('intval', explode(':', $s));
}

// given a hash of states: encoded(healths) -> probability
// return the probability of each possible resulting state
// after applying one random attack to all remaining units
function bomb($states) {
	$u = array();
	foreach ($states as $enc => $prior) {
		$x = decode($enc);
		$a = array();
		for ($i = 0; $i < count($x); $i++) { // collect indices of living units
			if ($x[$i] > 0) {
				$a[] = $i;
			}
		}
		foreach ($a as $i) { // apply an attack to each unit
			$v = $x; // copy the healths
			$v[$i]--; // reduce hp by one
			$k = encode($v);				
			$c = array_key_exists($k, $u) ? $u[$k] : 0;
			$u[$k] = $c + $prior / count($a); // update probabilities
		}	
	}
	return $u;
}

Example

// initial board state
$healths = array(2, 2); 

// initial board distribution
// (100% chance we have 2x 2-hp units)
$s0 = array(encode(healths) => 1);
[2:2] => 1.00000
// apply one random attack
$s1 = bomb($s0); 
[1:2] => 0.50000
[2:1] => 0.50000
// apply another
$s2 = bomb($s1); 
[0:2] => 0.25000
[1:1] => 0.50000
[2:0] => 0.25000

Created by raffy