Pokémon Red and Blue's capture formula (pret/pokered)

A wild Pokémon's catch rate is its species' catch-rate byte, copied into wEnemyMonActualCatchRate when the battle loads it (45 for Bulbasaur). In the Safari Zone, bait halves that copy and a rock doubles it, capped at 255. pokered-capture/catch-rate

ItemUseBall first draws a random byte $R_1$: any value for a Poké Ball, redrawn until it is at most 200 for a Great Ball and at most 150 for an Ultra or Safari Ball. A Master Ball catches before the range test. pokered-capture/ball-roll

{
 "kind": "roll-range",
 "poke": [
  0,
  255
 ],
 "great": [
  0,
  200
 ],
 "ultra": [
  0,
  150
 ],
 "safari": [
  0,
  150
 ],
 "master": "caught"
}

Cited by: Capture

A status subtracts from $R_1$: 25 for sleep or freeze, 12 for any other (burn, paralysis, poison), 0 for none. If $R_1$ is below that value the Pokémon is caught at once; otherwise the ball fails when $R_1$ less the value is greater than the catch rate, and passes on to the HP check when it is not. pokered-capture/status-and-rate

{
 "kind": "status-subtract",
 "sleepOrFreeze": 25,
 "burnParalysisPoison": 12,
 "none": 0
}

Cited by: Capture

For the HP check, ItemUseBall computes $W=\lfloor \lfloor 255M/F\rfloor /\max (\lfloor H/4\rfloor ,1)\rfloor$ from max HP $M$ and current HP $H$, where the ball factor $F$ is 8 for a Great Ball and 12 for every other ball. A $W$ over 255 catches; otherwise a second random byte $R_2$ catches when it is at most $W$. The check runs only after the status and catch-rate test has passed. pokered-capture/hp-check

{
 "kind": "hp-check",
 "numerator": 255,
 "ballFactor": {
  "great": 8,
  "other": 12
 },
 "hpDivisor": 4,
 "minDivisor": 1,
 "cap": 255
}

Cited by: Capture

Computed, counting every value of each roll as equally likely: with no status, Red and Blue catch with chance $\frac{\min (C+1,N)}{N}\cdot \frac{\min (W+1,256)}{256}$, where $N$ is 256, 201, or 151 values of $R_1$ for a Poké, Great, or Ultra Ball. For a Bulbasaur (catch rate 45) with max HP 100 in a Poké Ball, that is about 6.0% at full HP and 46 in 256 (18.0%) at 1 HP. pokered-capture/chance

{
 "kind": "example",
 "catchRate": 45,
 "maxHP": 100,
 "ball": "poke",
 "status": "none",
 "fullHP": 0.0604,
 "oneHP": 0.1797
}

Computed: because the Great Ball's ball factor is 8 and the Ultra Ball's is 12, a Great Ball can beat an Ultra Ball. With a catch rate of 200 or more, both first rolls always pass, so the Great Ball never catches less often. For a Bulbasaur (catch rate 45) with max HP 100 at full HP and no status, the Great Ball catches about 11.4% of the time and the Ultra Ball about 10.2%. pokered-capture/great-over-ultra

{
 "kind": "example",
 "catchRate": 45,
 "maxHP": 100,
 "hp": 100,
 "great": 0.1144,
 "ultra": 0.1023
}

Cited by: Capture

When the ball fails, Red and Blue choose its shakes without a roll: $Y=\lfloor 100C/B\rfloor$, with $B$ 255 for a Poké Ball, 200 for a Great Ball, and 150 otherwise; then $Z=\lfloor \min (W,255)\cdot Y/255\rfloor$, plus 10 for sleep or freeze or 5 for another status. A $Z$ under 10 is a miss ("You missed the Pokémon!"), under 30 one shake, under 70 two, and 70 or more three ("Shoot! It was so close too!"). pokered-capture/shakes

{
 "kind": "shake-display",
 "ballDivisor": {
  "poke": 255,
  "great": 200,
  "other": 150
 },
 "statusAdd": {
  "sleepOrFreeze": 10,
  "other": 5
 },
 "thresholds": [
  10,
  30,
  70
 ]
}

Cited by: Capture

Before any roll, ItemUseBall makes the ball dodge an unidentified ghost and the Restless Soul Marowak on Pokémon Tower 6F, and catches the old man's demonstration Pokémon outright. pokered-capture/uncatchable

Yellow runs the same capture code as Red and Blue from the first roll to the shake count: the ranges, the status values, the ball factors, and the shake thresholds match line for line. Before the rolls it adds a Pikachu battle (BATTLE_TYPE_PIKACHU), which takes the old man's branch and catches outright. pokered-capture/yellow-same

About: Pokémon Yellow Capture

Cited by: Capture