User:Spencer PK/Sandbox

“OK, so sometimes you attack a monster, and all of a sudden you see Lucky! appear... That shows that your attack power was stronger than usual!”

—Toadbert, Mario & Luigi: Bowser's Inside Story

LUCKY, originally known as lucky hit, also stylized as Lucky Hit, is a recurring game mechanic in the Mario & Luigi series. When a playable character deals damage, there is a chance that an attack will be LUCKY, causing it to deal more damage while being marked by a unique visual effect and sound. The bonus damage multiplier of a LUCKY hit, as well as what attacks can be LUCKY depends on the game. The chance of getting a LUCKY is based on the attacker's STACHE stat, or in the case of Bowser, his HORN stat.

The mechanics of LUCKY attacks is similar to other role-playing games having random critical hits. Despite other games calling them critical hits, and the Mario & Luigi series calling them LUCKY, the Mario & Luigi series has its own critical hit mechanics that are not to be confused with the LUCKY system.

History

Mario & Luigi: Superstar Saga

Lucky hits are introduced in Mario & Luigi: Superstar Saga, and are used by Mario and Luigi. Lucky hits can only happen when performing a solo Jump, Hammer, or Hand attack. Lucky hits cannot occur in Bros. Attacks, counterattacks, or first strikes. The bonus damage multiplier for a lucky hit is different if it is a Mario Jump, Luigi Jump, Mario Hammer, or Luigi Hammer attack. Hand attacks use the same multiplier.

Damage calculation

The formula for the damage of a solo attack and lucky hit is calculated as follows:

$0.4\times (AttackerPOW-1/2\times DefenderDEF)\times (AttackConstant)$

where:

• AttackConstant is the final value in the calculation that depends on if Mario or Luigi attacked, what type of solo attack they did, and if the attack was Lucky. All attack constants used for solo attacks can be found in the table below. The solo Hammer attacks have multiple attack constants which causes some damage variance. The Super Hammer and Ultra Hammer each have their own set of attack constants that causes greater damage variance. If the attack is a lucky hit, then the attack constants in the Lucky column are used instead.

Attack constant values
Attack	Normal (Mario)	Lucky (Mario)	Normal (Luigi)	Lucky (Luigi)
Jump	1.20	2.30	1.00	2.00
Normal Hammer	0.90/1.00/1.10	2.10	1.00/1.15/1.30	2.50
Super Hammer	0.80/1.00/1.20		0.90/1.13/1.36
Ultra Hammer	0.80/1.05/1.30		0.80/1.10/1.40
Hand	1.15	2.20	1.15	2.20

Using the knowledge of the attack constants and the attack constants for lucky hits, the approximate bonus damage multiplier for lucky hits can be obtained:

Approximate bonus damage multipliers

Attack	Mario	Luigi
Jump	≈1.916×	2×
Normal Hammer	2.1×*	≈2.174×*
Super Hammer	2.1×*	≈2.21239×*
Ultra Hammer	2×*	≈2.27×*
Hand	≈1.913×

^* - Approximate value obtained using middle attack constant value.

Lucky hit chance calculation

The formula for determining the chance of a hit being a lucky hit is calculated as follows:

$LuckyChance=clamp(LuckyBase+LuckyMult\times PlayerSTACHE/EnemySTACHE,MinChance,MaxChance)$

where:

• LuckyChance is the percent chance of a lucky hit, clamped to MinChance and MaxChance explained below. Three badges can modify this chance; the Lucky Attack special effect from Lucky Bros., Lucky Ribbon, or Wonder Badge will increase LuckyChance by 15%. This allows a max LuckyChance of 25% in the international versions, and 40% in the Japanese version.
• PlayerSTACHE is the STACHE stat of the attacking brother. Three pieces of gear can modify this value.
  • The Cobalt Necktie accessory doubles the wearer's STACHE stat.
  • The Mushluck Pants and Shroom Slacks clothing have the Lucky Mushroom special effect, which increases the wearer's STACHE in-battle depending on the number of Mushrooms Mario and Luigi have.

Lucky Mushroom bonus STACHE formula
(Mushrooms × 51 + Super × 51 + Ultra × 64 + Max × 76) / 256

• EnemySTACHE is calculated by taking the enemy's internal level statistic, then averaging the STACHE stat Mario and Luigi would have at that level assuming no bonus points from the bonus roulette during a Level up. Because the Japanese version changed Mario and Luigi's stat increases per level up as well as some enemy level statistics, EnemySTACHE is different in the Japanese version compared to the international versions.
  • See Mario & Luigi: Superstar Saga bestiary for a list of all enemy statistics.
  • See Mario & Luigi: Superstar Saga level up progressions for a list of Mario and Luigi's stat increases for each level up.
• LuckyBase, LuckyMult, MinChance, and MaxChance are constants that are different depending on how close the attacking brother's level is to the enemy's level. Three sets of constants exist for if the level difference is within 10%, 10% to 25% apart, or over 25% apart.

International version constants
Level Difference	LuckyBase	LuckyMult	MinChance	MaxChance
Within 10%	0%	10%	6%	15%
10% to 25% Apart	0%	12%	10%	20%
Over 25% Apart	0%	6%	4%	10%

Japanese version constants
Level Difference	LuckyBase	LuckyMult	MinChance	MaxChance
Within 10%	-0.83%	9.17%	6%	22%
10% to 25% Apart	-1.54%	8.46%	10%	30%
Over 25% Apart	-1.54%	8.46%	4%	15%

Mario & Luigi: Partners in Time

Lucky hits return in Mario & Luigi: Partners in Time, and are used by Mario, Luigi, Baby Mario, and Baby Luigi. Lucky hits can happen in solo Jump or Hammer attacks, as well as Bros. Item attacks. Lucky hits cannot occur in counterattacks or first strikes. The bonus damage multiplier for a lucky hit is 2× the original damage. It is possible for a lucky hit to apply to a critical hit; if this happens, the hit will say "Lucky!" instead of "Critical!" and will deal 3× the original damage.

Lucky hit chance calculation

The formula for determining the chance of a hit being a lucky hit is calculated as follows:

$LuckyChance=\lfloor ((AttackerSTACHE/4)-(EnemyLevel/8))\rfloor$

where:

• LuckyChance is the percent chance of a lucky hit, clamped to [1, 99]. This means that a lucky hit always has at least a 1% chance, and at most a 99% chance. Two gear items can modify this chance; equipping the Lucky Badge will double the chance, while the Lucky Badge A will quadruple the chance.
• AttackerSTACHE is the STACHE stat of the attacker in the hit.
• EnemyLevel is the enemy's internal level statistic.
  • See Mario & Luigi: Partners in Time bestiary for a list of all enemy statistics, including level.

Mario & Luigi: Bowser's Inside Story

Lucky hits return in Mario & Luigi: Bowser's Inside Story now stylized as both lucky hit and Lucky Hit, and are used by Mario, Luigi, and Bowser. Mario and Luigi can get lucky hits in their solo Jump or Hammer attacks, as well as Special Attacks. Bowser can get lucky hits in his Punch and Flame attacks, as well as his own Special Attacks. Lucky hits cannot occur in counterattacks or first strikes. The bonus damage multiplier for a lucky hit is 1.5× the original damage.

In the beginning of the game, after Bowser is sent to Dimble Wood after crashing the meeting at Peach's Castle, he encounters a cloaked figure. This figure claims that Bowser has won a Lucky Mushroom, and that it will give Bowser the luck to defeat Mario. The figure describes this by saying "Scoff this down and your luck will power up to super luck!", and "With every attack, lucky hits will shower in a happy waterfall!". This Lucky(?) Mushroom is then revealed to be a Vacuum Shroom, which causes Bowser to mindlessly inhale everything he sees.

Lucky hit chance calculation

The formula for determining the chance of a hit being a lucky hit is the same as Mario & Luigi: Partners in Time. See Mario & Luigi: Bowser's Inside Story bestiary for a list of all enemy statistics, including level. Some pieces of gear can modify the lucky chance. The Happy Charm accessory used by Mario and Luigi increases the chance of a lucky hit by 1.5×. The Lucky Charm accessory used by Mario and Luigi and the Lucky Band used by Bowser double the chance of a lucky hit.

Mario & Luigi: Dream Team

Lucky hits return in Mario & Luigi: Dream Team now stylized as Lucky Hit, and are used by Mario, Luigi, and Dreamy Luigi. Unlike previous games where only certain types of attacks can be a Lucky Hit, all attacks can be a Lucky Hit. This includes solo attacks, Bros. Attacks, Luiginary Attacks, counterattacks, and first strikes. The bonus damage multiplier for a Lucky Hit is 1.5× the original damage; choosing the Rank-Up Bonus Big Lucky will increase this to 2.0×.

Some pieces of gear interact with the Lucky Hit system. The Mini Boots and Mini Hammer give the user guaranteed Lucky Hits only if they have the Mini status effect. The Lucky Gloves and Lucky Gloves DX increase the chance of a Lucky Hit. The Birthday Ring increases the user's Lucky Hit chance only if it is the player's birthday as set in the Nintendo 3DS system settings.

Some badge effects interact with the Lucky Hit system. The Virus Badge + Gold Badge combo when used activates the Lucky Chance effect, which temporarily adds 0.5 to the bonus damage multiplier for Lucky Hits. This causes a Lucky Hit to deal 2.0× the normal damage, and a Lucky Hit with the Big Lucky Rank-Up Bonus to deal 2.5× the normal damage. The Miracle Badge + Bronze Badge combo when used activates the Lucky Time effect, which temporarily increases the chances for Lucky Hits.

Mario & Luigi: Paper Jam

Lucky Hits return in Mario & Luigi: Paper Jam, and are used by Mario, Luigi, and Paper Mario. Like Mario & Luigi: Dream Team, all attacks can be a Lucky Hit. This includes solo attacks, Bros. Attacks, Trio Attacks, counterattacks, and first strikes. The bonus damage multiplier for a Lucky Hit is 1.5x the original damage; choosing the Rank-Up Bonus Big Lucky will increase this to 2.0×.

Some pieces of gear, namely some accessories interact with the Lucky Hit system. Mario and Luigi can use the Star Brooch and Star Brooch DX to receive Star Points upon getting a Lucky Hit. Paper Mario can equip paper versions of the Star Brooch and Star Brooch DX to get the same effect.

Some Battle Cards, namely amiibo Character Cards interact with the Lucky Hit system. The amiibo for Mario, Luigi, Peach, and Yoshi have LV 1 Cards that doubles the chances of Lucky Hits. The amiibo for Yoshi has a LV 2 Card that quadruples the chances of Lucky Hits. The amiibo for Mario, Luigi, Peach, Yoshi, and Toad have LV 2 Duo Cards that triggers a Lucky Attack, which guarantees a Lucky Hit.

Mario & Luigi: Superstar Saga + Bowser's Minions

Lucky Hits return in Mario & Luigi: Superstar Saga + Bowser's Minions now stylized as lucky hit, and are used by Mario and Luigi. Unlike the original Game Boy Advance version, and like Mario & Luigi: Dream Team and Mario & Luigi: Paper Jam, all attacks can be a lucky hit. This includes solo attacks, Bros. Attacks, counterattacks, and first strikes. The bonus damage multiplier for a lucky hit is 1.3× the original damage.

Some pieces of gear interact with the lucky hit system. The Mushluck Pants has the Lucky Mushroom special effect, which increases the chance of a lucky hit based on the number of Mushrooms Mario and Luigi have. The Casual Coral and Piranha Suit have the Lucky Critical special effect, which increases the power of lucky and critical hits by 50% of the user's base POW stat. This allows lucky and critical hits to get a bonus damage multiplier of up to 1.95× if the user has no POW bonuses; having a POW bonus from something else like a badge would lower the 1.95× multiplier, but a big enough bonus would not lower it past the normal 1.3× bonus damage multiplier. The General Badge has the Lucky Speedster special effect, which increases the rate of lucky hits based on the user's SPEED stat. The Lucky Bros. and Lucky Ribbon badges have the Lucky Attack special effect, which increases the chance of a lucky hit. The Ohoracle Badge, Bowser Fist, and Popple Badge AA all have the First Striker special effect, which gives +100% base POW and a 100% lucky hit rate to the user only if they have the first turn in a battle and only in their first attack.

Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey

Lucky hits return in Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey now stylized as both lucky hit and Lucky Hit, and are used by Mario, Luigi, and Bowser. Unlike the original Nintendo DS version, and like Mario & Luigi: Dream Team and Mario & Luigi: Paper Jam, all attacks can be a Lucky Hit. This includes solo attacks, Bowser's Punch and Flame attacks, Bros. Attacks, Brawl Attacks, counterattacks, and first strikes. The bonus damage multiplier for a Lucky Hit is 1.3× the original damage. The Rank-Up Bonuses Lucky and Good and King's Blessing for the Mario Bros. and Bowser respectively will increase the damage of their Lucky Hits to 1.5× the original damage.

Some pieces of gear interact with the Lucky Hit system. Mario and Luigi can use the Brawny Wear, Master Wear, and Muscle Wear, while Bowser can use the Ironclad Shell to increase the power of their Lucky and Critical Hits. Mario and Luigi can use the Mushroom Stone accessory, which increases the user's chance of a Lucky Hit based on the number of Mushrooms they have. Bowser can use the Lucky Ring and Lucky Ring DX, which increases the power of Lucky and Critical Hits by "a small amount" and "a good amount", respectively.

Mario & Luigi: Brothership

Lucky Hits return in Mario & Luigi: Brothership now stylized as LUCKY, and are used by Mario and Luigi. Almost every type of attack can be LUCKY. This includes solo attacks, combo attacks, Bros. Attacks, counterattacks, most first strikes, and most Luigi Logic damage. While Jump, Hammer, and Bro Bomb first strikes can be LUCKY, crashing into the enemy with Ball Blitz will never be LUCKY. Despite that a Bro Bomb first strike can be LUCKY, the Bro Bombs used while chasing down Reclusa in part of the final battle cannot be LUCKY. Luigi Logic damage against Sharpcask and Glohm Bowser can be LUCKY, but the damage caused to Pipegunk by switching the arena to the opposite temperature area cannot be LUCKY. The bonus damage multiplier for a LUCKY is 1.3× the original damage; choosing the Rank-Up Bonus Big Lucky will increase this to 1.5×.

Some pieces of gear, namely some accessories interact with the LUCKY system. The Lucky HP Bangle heals the user by 10% of their max HP if their attack has a LUCKY hit. The Luck Charm and Luck Charm DX increase the chance of getting a LUCKY by 1.5× and 2×, respectively.

Sandbox notes

Name sources

The formatting/stylizing of LUCKY has changed a few times across the series. This section will include examples from each game that I am aware of. At the beginning of looking into this it seemed that there was some difference with every sequential game, but that was actually from encountering misinformation caused purely from the wrong capitalization being used in the descriptions(!!!) of gear on this wiki.

• Superstar Saga
  • "Increases frequency of lucky hits." - Lucky Bros., Lucky Ribbon, and Wonder Badge descriptions.
  • "The higher your Stache points are, the easier it is to get lucky hits in battle." - Book in Beanbean Castle.
• Partners in Time
  • "Make lucky hits easier to land." - Lucky Badge description.
  • "Make lucky hits much easier to land!" - Lucky Badge A description.
• Bowser's Inside Story
  • "About lucky hits" - Something you can ask Toadbert in Toad Square.
  • "1.5x Luck Booster [line break] Increases rate of lucky hits." - Happy Charm description.
  • "The bigger this number is, the easier it is to land lucky hits and get winning scratch tickets." STACHE/HORN description in pause menu.
  • "The higher the number, the more likely you are to get a Lucky Hit or a Scratch Card." - STACHE/HORN description in level up screen. WHY IS IT DIFFERENT HERE. This line makes this game use two stylizations.
• Dream Team
  • "Boosts the power of Lucky Hits so you deliver 200% of normal damage." – Big Lucky description.
  • "Temporarily increases the power of Lucky Hits." - Virus Badge + Gold Badge combo description.
• Paper Jam
  • "Increases the damage of Lucky Hits to 200%." – Big Lucky description.
  • "Grants Star Points whenever you land a Lucky Hit" - Star Brooch (DX) description.
• Superstar Saga DX
  • "Strengthens critical hits and lucky hits." - Stealth Suit description.
• Bowser's Inside Story DX
  • "With every attack, lucky hits will shower in a happy waterfall!" - Fawful before Bowser gets the Vacuum Shroom. This line being unchanged from the original makes this game use two stylizations. WAHOO!
  • "Increases the power of your Lucky Hits." - Lucky and Good and King's Blessing descriptions.
• Brothership ("LUCKY hit" is never said)
  • "If you up your STACHE stat, you'll get more LUCKY results in battle." - Snoutlet School loading screen tip.
  • "Get 250 LUCKY ratings." - Lucky Star challenge description.
  • "Restores 10% of your max HP when you get a LUCKY." - Lucky HP Bangle description.

Miscellaneous

• Unrelated to the lucky hit stuff, a Paper Jam critical hit deals 1.3x damage. In my testing, a single Luigi fireball vs. a Spiny and a Paper Spiny dealt 35 and 46 damage respectively. 35 × 1.3 = 45.5, rounds up to 46. Spinies and Paper Spinies are statistically identical.