Examples
Configuration
Statistics
- Probability of killing anything: 70.370%
- Probability of killing Player 1: 0.000%
- Probability of killing Player 2: 0.000%
- Probability of completely missing Player 1: 3.704%
- Probability of completely missing Player 2: 21.296%
- Probability of killing all 1 minion for Player 1: 70.370%
- Probability of killing any 1-health minion: 70.370%
- Probability of killing any 1-health minion for Player 1: 70.370%
- Probability of any minion at or less than 1-health: 100.000%
- Probability of any minion at or less than 1-health for Player 1: 100.000%
- Probability of all minions at or less than 1-health: 100.000%
- Probability of all minions at or less than 1-health for Player 1: 100.000%
Chance of Individual Result
Player 1 | #1 (1hp) | Player 2 |
---|
HP | Chance | Σ↑ |
---|
Full | 21.296% | 21.30% | 29/30 | 46.296% | 67.59% | 28/30 | 28.704% | 96.30% | 27/30 | 3.704% | 100.00% |
| HP | Chance | Σ↑ |
---|
Full | 29.630% | 29.63% | Dead | 70.370% | 100.00% |
| HP | Chance | Σ↑ |
---|
Full | 21.296% | 21.30% | 29/30 | 46.296% | 67.59% | 28/30 | 28.704% | 96.30% | 27/30 | 3.704% | 100.00% |
|
Board States
1 attack (3 outcomes)Chance | P1 | #1 (1hp) | P2 |
---|
33.333% | 30→29 | 1→1 | 30→30 | 33.333% | 30→30 | 1→0 | 30→30 | 33.333% | 30→30 | 1→1 | 30→29 |
| 2 attack (5 outcomes)Chance | P1 | #1 (1hp) | P2 |
---|
27.778% | 30→29 | 1→0 | 30→30 | 27.778% | 30→30 | 1→0 | 30→29 | 22.222% | 30→29 | 1→1 | 30→29 | 11.111% | 30→28 | 1→1 | 30→30 | 11.111% | 30→30 | 1→1 | 30→28 |
| 3 attack (7 outcomes)Chance | P1 | #1 (1hp) | P2 |
---|
35.185% | 30→29 | 1→0 | 30→29 | 17.593% | 30→28 | 1→0 | 30→30 | 17.593% | 30→30 | 1→0 | 30→28 | 11.111% | 30→28 | 1→1 | 30→29 | 11.111% | 30→29 | 1→1 | 30→28 | 3.704% | 30→27 | 1→1 | 30→30 | 3.704% | 30→30 | 1→1 | 30→27 |
|
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