Can I Use Lucky on Someone Elses Roll

Many games that involve an element of luck use dice rolls (or an equivalent, such as random number generators for video games, drawing cards in card games, and so on) as a means of determining the outcome of a certain attempted action. In many cases the total "success" of the attempt is determined by adding static modifiers to the number rolled, but the dice roll itself cannot be changed beyond that: A poor roll represents bad luck, whereas a high roll represents good luck.

Some games, however, incorporate mechanics that allow a player to alter their luck by re-attempting the die roll if they do not like the original result, usually in an effort to achieve something more satisfactory. By re-rolling the original die, the player can in this fashion pull victory from the jaws of defeat.

The exact nature of this mechanic, and the limitations on its use, vary from game to game. While some games may only allow the player a single re-roll of the die and force them to accept the new result, other games may include a means of rolling multiple dice at once and allowing the choice of the result that is most preferable for the player. This type of mechanic can sometimes be used offensively, by allowing the player using it to force another player to re-roll their (formerly good) die result.

In games that use a deck of cards as the randomizing mechanic, the LMM often takes form of a special (often one-shot) ability to pick the top N cards from the deck, take a look at them and rearrange them in a manner most beneficial to the player. In-universe, this is usually described as some kind of precognitive ability.

The Luck Manipulation Mechanic may be used as a means of representing the in-universe nature of a character that is Born Lucky, or one who has the power to invoke Winds of Destiny, Change!. When the mechanic is inverted (by forcing a player to choose the least preferable result), it can represent Born Unlucky instead.

Compare Luck Stat, which is a stat that passively provides bonuses or penalties to random game elements. Contrast Honest Rolls Character, where the player or Game Master limit themselves to only accepting their initial stat rolls at character creation, with no re-rolling or "dice fudging" allowed. Bad Luck Mitigation Mechanic is a specific version of this that's used as an Anti-Frustration Feature for players.

Please note that in order to qualify for this trope, the Luck Manipulation Mechanic must be deliberately designed into the game. Cheating methods that allow for similar results (such as Save Scumming, including the Tool Assisted Speed Run type and/or placating the Random Number God) don't count.

Examples:

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Board Games

Descent: Journeys in the Dark has "Aim" and "Dodge" abilities that allow players to re-roll dice used in an attack (Aim) or force the player attacking them to re-roll (Dodge). Hero players can set either one as an order, the Overlord has cards that allow him to use these abilities.
- Luck manipulation mechanics are a staple of Fantasy Flight Games products, many involving abilities that allow reroll of selected dice or removal of an enemy die that would be devastating to a particular unit.
Talisman:
- Fate tokens, introduced in the revised fourth edition, allow the player possessing them to re-roll any single die at-will, expending the token in the process. Players are given a certain amount of fate tokens at the beginning of the game based on the character they are playing, and have means of gaining (or losing) more tokens throughout the game.
- The Warrior character has this mechanic directly incorporated. During battle, the player controlling the Warrior rolls two dice instead of the standard one, and chooses the result they wish to keep.
- The Misfortune spell allows a player to negatively affect another player's luck, by changing the result of any single die roll to a "1".
- The Prophetess character allows the player controlling it to manipulate the "luck of the draw" by re-drawing cards from the adventure deck if they do not wish to keep their original draw. The Orb of Knowledge object offers a similar mechanic to characters who possess it.
Arkham Horror has "Clue Tokens" that represent various bits of Mythos-lore the characters have learned through their combing the city. Spending a clue token after a die roll lets you roll an additional die, and you can continue to roll as long as you have tokens to spend, some Skills even add 2 dice instead of 1 per token to certain kinds of rolls.
- If an investigator is "blessed," die results 4-6 are successes instead of 5-6, which, in contrast to the typical Luck Manipulation, adds a significant improvement to the statistics. "Cursed" status works the other way - only 6s are treated as successes. In addition, one investigator has a "Research" special ability, which allows any investigator to re-roll any dice that were not successes.
  - During normal play, when the Ancient still sleeps, "Research" basically only grants a chance to turn a single test per round from failure into success. Even this is powerful enough when used in a right way. But if the game comes to the final battle, Research truly shines - in this phase, every single successful die counts as one hit. With good timing (and bad luck on the roll being rerolled by Research), this can result in 10+ extra dice (equalling 10+ possible extra hits) every round of the final battle.
Yahtzee incorporates this as a core game mechanic. Players roll five dice each round, and if they don't like how they come up, they can re-roll some or all of them up to twice in one turn in attempts to get specific dice combinations.
Blood Bowl has "re-rolls", which each team gets a limited number of at the start of the game. They can be used at any time to re-roll one of the player's own dice rolls that the player doesn't like. Different teams get different numbers of re-rolls, representing differing levels of luck. In addition to the team re-rolls, various players on the team can learn skills that grant them re-rolls in certain situations, such as when catching or throwing a pass, or trying to dodge out of an opponent's tackle zone.
The "Advantage" token is used this way in Breakout: Normandy - after using it, however, one must pass the Advantage to the enemy, plus it's worth something in the endgame point count, meaning both players have an incentive to hold onto it until desperate times. However, an exceptionally bad result can cause either player to forfeit the Advantage involuntarily (the "bad result" ceiling is lower for the Allies to represent the extra political sway of heavy losses on the populace back home), giving both players an incentive to use it before they lose it as well.
In Kill Dr. Lucky, Failure Cards represent the Doctor's namesake luck saving him from the murderous player characters.

Card Games

Some card games, such as the original Star Wars Customizable Card Game and the Warhammer 40,000 Trading Card Game use numbers printed on the cards in place of die rolls, so a 'random' number is generated by revealing the top card of your deck. Naturally, this opens up plenty of combo opportunities with abilities that let you know (or even choose) what that next card will be.
The Munchkin card game has several cards and extra collectibles that allow manipulating the dice.
Magic: The Gathering:
- Krark's Thumb and Goblin Bookie, both affect coin flips; The bookie allows you to re-flip a coin, while the thumb lets you flip two coins and ignore one, theoretically doubling your odds of achieving a desired result.
- The "Scry" ability on many cards in the 2011 Core Set, as well as cards in the Theros block, which allows you to look at the top few cards of your library (how many depends on the specific card), rearrange them, and send the ones you don't need to the bottom of your library.
- Fetch lands (lands which search your library for another land and put it in play, but are sacrificed in the process) weren't meant to be this but savvy players learned they could be used this way. After searching the library you have to shuffle it which means if you know there is something on top of your library that you don't want a fetch land can get rid of it.
  - A less useful application is to use them for "deck-thinning" since they effectively reduce the number of cards in the deck. This technique is most useful for decks that can benefit from a tiny change in probability and don't care about the damage the cards cause. As a result they show up in "suicide red" decks that need to ensure they don't draw extra lands even though those decks get no benefit from the intended use of being able to grab different colors of mana.
- Really any card that lets you search for another card is designed for this. If you have a combo deck then you rarely have the time or luck to just draw every part of it before a deck that doesn't rely on getting a specific combination of cards just kills you. But with search cards, if you don't draw a card you need, you may at least draw a card that can get it.
- The entire concept of "cantrips" is another form of deck thinning. These are cards that usually cost a small amount of mana (usually just 1 or 2), have a small effect, and ends with "Draw a Card". Unlike other "Draw" cards which usually only occur in Blue, Cantrips can come in any color (and in a few cases, on artifacts). The idea is you can fire so many of them off and use their first ability to hamper the opponent a bit while you try and speed through your own deck for that last piece of the combo.
Yu-Gi-Oh! has Second Coin Toss, and a similar card for die rolls. Which is called, oddly enough, Dice Re-Roll.
Pokémon Trading Card Game: Sabrina's ESP from "Gym Heroes" lets you re-flip coins for attacks. Victini from "Red Collection" has the same effect.
Draw poker incorporates this into its rules. Once per hand, you can Discard and Draw as many cards as you desire.
Thunderstone has the "rest" action, and recently added the "prepare" action. Resting lets you destroy (remove from the game) one card from your hand, thus thinning bad cards from your deck such as curses and the weak starting cards. Preparing lets you put any number of cards from your hand on top of your deck, letting you shape your future draws to have more favourable combinations of gold/attack power.
When playing Race For The Galaxy, the "Exploration" phase is the only method by which you can gain new cards. During exploration, depending on how you play it, you draw three cards and keep two, or draw seven cards and keep one. Some of the improvements you play allow you to draw more cards as well, but you'll never get to keep more than two. If you're looking for a specific card, then you'll want to draw more (it also denies cards to other players, at least temporarily).
- A later expansion added the Prestige/Search card, which allows you to go through the deck and look for a "good card", by various definitions (a valuable military world, a good military development, a cheap world, etc.). The definition of "good" is narrow enough that you'll probably get a card you like, but broad enough that it still might not be good for your particular situation. (i.e., you wanted "a valuable military world," but it's too well-defended for you to actually conquer.) You get to ignore one matching card when you search, but if the second one is still bad for you, you're stuck with it.
Sentinels of the Multiverse has several hero cards that let a player manipulate what card is drawn next on either their own, a fellow hero's, or the villain's decks. Some cards even let the player put specific cards at the bottom of a villain's deck, to ensure they don't come up for a while.

Fan Works

In the series Iron Hearts by SFaccountant the worlds of Warhammer 40,000 and My Little Pony: Friendship Is Magic combine and in every battle things fly around that could kill a pony with a glancing blow. Why have they survived? Because as the author states they have what would be a reroll ability if the story were a tabletop game.

Tabletop Games

Dungeons & Dragons has numerous examples of this:
- In the 2^nd Edition Forgotten Realms setting, certain clerics of Tymora, the goddess of luck, have the granted power to re-roll a die once per day. Similarly some clerics of Beshaba, goddess of misfortune, have the ability to force enemies to re-roll their dice.
- From 3^rd edition onward, the standard ability score rolling methods manipulate luck by giving you an extra die to roll for each ability while requiring you to drop the lowest, skewing results towards higher than average numbers.
- 3^rd and 3.5 edition:
  - One series of character Feats allows a player to reroll a saving throw that they just failed. Given that the prerequisite for those feats is a bonus to the saving throw in question, it makes it much more likely to succeed on the saves. Another line of luck Feats increases the number of times per day and the circumstances under which a reroll is allowed.
  - The Fate Spinner Prestige Class can shift around good and bad luck, forcing characters to reroll dice and adjusting the target values of dice rolls at whim.
  - The Fortune's Friend Prestige Class is based on being supernaturally lucky, rerolling or granting themselves bonuses to dice rolls as necessary.
- 4^th Edition:
  - Elves have an innate power that allows the player to re-roll a single attack roll during an encounter, though they must accept the second result.
  - The Human power Heroic Effort allows them to add an additional four to any failed D20 roll in an encounter.
  - The Wizard ability Shield reactively boosts the player's AC to block an attack that would otherwise hit.
  - Most leader-type Character Classes have powers in this vein, such as the Bard's Unluck, which allows him to swap an enemy good roll for a bad one and a friendly bad roll for a good one. The Virtue of Prescience build for Bards is based around this luck and fate manipulation.
  - Halflings have the power to force an enemy to re-roll an attack roll that would hit them.
  - In Eberron, the Dragonmark of Detection allows one to roll twice on perception checks and pick the best result.
- 5^th Edition:
  - This edition replaces previous editions' situational numerical modifiers to dice rolls with an "advantage/disadvantage" mechanic. A player with advantage (attacking a surprised opponent, making a skill check with another player assisting them, etc.) rolls an additional die and chooses the highest result, whereas the opposite occurs for players with disadvantage.
  - If a player does something that a DM is particularly impressed by during the game, the DM is allowed to award the player Inspiration, giving them the ability to grant themselves or another player advantage on one D20 roll of their choice.
  - Halflings have an inherent ability that allows them to reroll any d20 once any time they get a natural 1 (unless that 1 comes up in said reroll, in which case you have to use it). They can also have two unique feats that allow them to pass this onto nearby allies or force enemies to reroll an attack.
  - Wizards who specialize in Divination can roll a d20, store the result as a fragment of good or bad luck, and replace a nearby character's dice roll with their result later in the day.
  - 20th level Rogues can turn a missed attack into a hit or a failed skill check into a roll of 20, doing either of these once per rest.
  - The "Lucky" feat lets you reroll up to three rolls of your choice per long rest.
  - Clockwork Soul sorcerers from Tasha's Cauldron of Everything have a few abilities that fit the bill. At first level, they can negate advantage and disadvantage on rolls a number of times equal to their proficiency number, and later on they get a minute of automatic 10s or higher on rolls, guaranteeing success on anything they're proficient or have expertise with.
Pathfinder:
- Halflings can take the race-exclusive ability Lucky Halfling which allows them to grant any creature a free d20 reroll once a day; this same ability is found in numerous other abilities and items, with a popular one being the ability to roll a d20 twice and take the better option.
- A sufficiently powerful cavalier can become immune to luck itself. While all characters, from peasants to kings to dragons to gods, are vulnerable to random chance forcing a critical fumble or a stroke of improbable luck, a high-level cavalier ability allows them to treat a natural 1 as if they had rolled one lower than a natural 2.
- The Persistent spell feat can modify a spell so that the target has to save against it twice. Especially effective with multiple targets.
- It also has the witch's fortune and misfortune hexes, which allow you to roll twice and take the best result, or force you to roll twice and take the worst result.
- The Pathfinder Society organized play campaign has a rule that a player can reroll one d20 per session if they are wearing an official Paizo Publishing T-shirt.
- The dual-cursed oracle archetype gains access to their own misfortune and fortune abilities. In particular, the misfortune revelation would force a target to instantly reroll any d20 roll. Meant by description to force foes to roll the chance to miss, it didn't take long for players to start using it on allies when said allies rolled poorly in hopes for a better result.
- The prevalence of this is somewhat inhibited by the existence of the luck bonus type, which is this in-universe (representing something granting good fortune, whether from items, spells, class abilities, etc.) but not mechanically (it is simply a type of static modifier).
Early editions of Shadowrun had the Karma Pool, which allowed a character to re-roll dice for failed tests, buy additional dice for a test or even buy successes directly. 4th Edition calls it Edge, and even allows players to burn a point (sometimes at great expense) to ensure, for example, a Never Found the Body situation.
Star Wars d20:
- In Revised edition, Force Points can be spent to add a number of D6 to all D20 checks in the current round. Spending force points is permanent (barring GM discretion for "dramatically appropriate" circumstances), but each level increase gives one force point.
- In Revised edition, some Force powers or class features give D20 re-rolls, or the ability to "take 10" (assume the D20 yielded 10 instead of rolling it, for skill checks only) even in stressful situations (which otherwise forbid it).
- Most species in Saga edition have the ability to roll a single skill twice and pick the best result.
In West End Games' Star Wars d6 game, a character could spend Force Points to double his skill and attribute codes, which greatly increased his chance of success.
- The same is true with Brownie Points in West End's Ghostbusters and Character Points in other games that use the d6 system (like Septimus).
BattleTech: A Time of War gives characters an Edge stat, which may be burned either for a reroll, or to nudge the result.
CthulhuTech has Drama Points. Spending them adds to your dice pool or subtracts from your opponent's dice pool.
In the Buffy the Vampire Slayer RPG, Drama Points can be used to increase the chance of success for Heroic Feats.
Dreamblade, a short-lived WOTC miniatures game, had an ability called Fortunate which let you re-roll attack dice as well as one called Rewind that let you re-roll your initiative die.
Warhammer 40,000 is loaded with them:
- The Twin-Linked rule allows re rolls with missed shooting attacks. Master crafted allows one re-roll per weapon in close combat. Preferred Enemy allows rerolls in close combat. The psychic powers Doom (inverted example that harms enemy luck), Fortune, Guide, and Warp Time all allow re-rolls. However, no matter how many of these are stacked together (Such as a Fortune'd squad with Prefered Enemy and a pair of master crafted weapons) only one reroll is ever allowed.
- There is also a special reroll where you reroll the scatter dice. Unlike normal dice, Scatter Dice have an arrow all pointing in the same direction on 4 sides; this is to represent a direction the shot deviates to. The remaining 2 sides are "Hit" symbols, meaning the shot was dead on. Rerolling the Scatter Dice means you get another 1/3rd of a chance to directly hit the target, or deviate it into something else (especially useful if the the winds of chance weren't particularly favourable and blew your own weapon back to you]]).
- With several Dice Modifiers in place, it can actually be hilarious to watch as each one cancels out eachother. During combat, it's entirely possible that if you fail your morale check, your unit would be automatically wiped out. This is because any unit fleeing can be caught by the two sides rolling a dice, and adding it to their initiative value (representing how quick they are). If the pursuers get a total score equal to or greater than the fleeing unit, the latter is destroyed. It's entirely possible that the difference is greater than 5, meaning no matter what you roll, your guys die. Similarly, a Space Marine Psychic Power allows you to reroll any failed Saves. The aforementioned Eldar Doom Power forces you to reroll any successful saves. This means that, no matter what the roll, you have to reroll the dice on any unit with both effects applied, effectively cancelling both out.
  - On that latter case, a FAQ entry explicitly specifies that both rerolls cancel each other out (so the die is just rolled once and for all), "to avoid headaches".
Warhammer Fantasy Roleplay:
- Creatures with the Hatred special rule are allowed rerolls in close combat with the object of their hate. The Always Strikes First special rule when combined with base initiative being faster than an enemy works in a similar fashion.
- Player Characters have a small daily pool of Fortune Points, which can be spent to reroll a skill test.
- The Lore of the Heavens has several spells that bestow Fortune Points or grant the target a reroll while the spell is active. They're described in-universe as either manipulating the target's luck or granting foresight.
In The Dresden Files RPG, you have the option to spend a Fate Point in order to reroll all the dice in a given exchange if you really blow the roll, or your opponent rolls exceedingly well. This is meant to represent the character's mortal free will asserting itself.
- Applies to the FATE system (that Dresden Files uses) in general; invoking one of your character's freeform Aspects to either get +2 to your one of your rolls after you've already made it or else pick up all the dice and try again is one of the more basic uses for Fate points. (You can get a +1 bonus this way even without an applicable Aspect, but don't get the reroll option then.)
The Horrors of Earthdawn had this ability: their "cursed luck" power could change a certain number of dice from whatever they rolled into "1"s. The Dragons had a lesser version of this power that only forced the player to re-roll his dice.
This is the purpose of the Probability Control power in Hero Clix.
GURPS has multiple levels of the Luck advantage, which grant a character the ability to reroll, with the frequency dependent on what level it was purchased. The base version allowed for once per session, and the highest level allowed a player to do so once every ten minutes of gametime. And these could be purchased along with Super Luck, which would, once per session, allow the player to instantly declare a success on an action.
- An interesting application of the Luck mechanic (first seen in aTranshuman Space character in Pyramid magazine) is to give a methodical character with high ranks in a certain skill Luck restricted to that skill. In this case, it doesn't represent destiny being on the character's side, but that the character is very careful about what they do.
Mutants & Masterminds has had Hero Points in all three editions, which can be used for rerolls that are guaranteed to be better than average. Also, since 2nd edition, characters can buy the Second Chance feat which allows them to roll twice and pick the higher number for a given narrow task.
Feng Shui has the Fortune stat, which you can spend points from to add a positive die to any roll. The Everyman Hero has the most of any character archetype, and he or she can make Fortune rolls as if he or she had the full amount of points, no matter how many points he or she spends.
Weapons Of The Gods and its Spiritual Successor Legends of the Wulin both have "Joss", which can be used to add dice to your rolls, or to take dice away from an opponent's.
- An even better example is the River, which allows for dice from earlier rolls to be stored there and added to later rolls. Good use of the River is very helpful in early play and absolutely vital in late play, where you can constantly fall back on the River dice to succeed at the heroic deeds expected of the characters.
Exalted has several versions of this. Most Exalted have access to a Third (something) Excellency, which lets them re-roll on a failure. The Sidereal Exalted have several varieties of this, as befits their office as Fate Ninjas. For example, they can cause long-term bless/curse effects on other people by manipulating Astrology, and they can change what numbers on their dice count for success.
Mage: The Awakening has the Fate Arcanum, which is involved with luck and messing with destinies.
The Lord of the Rings Strategy Battle Game has Might, Will and Fate points, which nearly all the named characters and generic leaders get. The first two can be spent in order to modify certain dice rolls, whereas Fate points are spent to give a character a one-in-two chance of avoiding taking damage they would otherwise have suffered.
Adventure! has Inspiration, which, in the grand pulp tradition, can be used for "creative editing." "Oh, we crashed fifty miles out from Tripoli in the middle of the desert? I know a guy in the French Foreign Legion who set up shop in a small village fifty miles out from Tripoli! It might be a day's hike east..." However, it doesn't allow players to adjust the dice, but to adjust the setting.
Dark Heresy, Rogue Trader, and Death Watch all have Fate Points, which allow you to do this in a Warhammer 40,000 setting. The system will eat those fate points up even if you don't have a Killer Game Master; someone with a 60 in a skill is one of the best in the sector at that thing but will still fail well 40% or more of the tests they have to make. Combat is a rare exception as it's easy to get plenty of bonuses from choosing tactics well, but your enemies can do the same. Lethality ensues.
Deadlands had a Luck Manipulation Mechanic that could be invoked by spending "Fate Chips"—actual, real-world poker chips the players and GM draw blindly—to amend the results of particularly unfortunate dice rolls. Many Arcane Backgrounds have extensive Fate Chip Manipulating Mechanics, to add further robustness. The particulars would require a long-winded explanation, but the generalities live on in a more general ruleset made by the same company, Savage Worlds.
In Paranoia XP and 25th Anniversary, Perversity points are a combination of this and Experience Points. On skill rolls, they can be used to push someone's chances to succeed in an activity up — or down. There is also a luck manipulation mutation, but it has limited use on the grounds that really lucky people aren't in Alpha Complex to start with.
Swashbucklers of the 7 Skies has "style dice," which are earned for acting in genre or otherwise entertainingly and constructively. They net a player extra dice for rerolls, or flat +1 bonuses to any roll (useful when you need just a little more but a reroll is more likely to harm than help). There's a limited pool of style dice available which replenishes as they're used, meaning players are encouraged to not only act outrageously to acquire extra dice but spend them like water (usually on said outrageous actions) to keep the dice flowing.
The Serenity RPG has the character traits "Things Go Smooth" and "Things Don't Go Smooth". The first one allows you to re-roll once per session except on a natural 1, or twice, including natural 1's, if taken as a Major Asset. The second allows the GM to force you to re-roll once or twice per session and take the lower of the two rolls, and only exists in the character creation rules as a Minor Complication. Worth mentioning: Malcolm Reynolds' character sheet has "Things Don't Go Smooth" as a Major Complication.
Karma points in the old Marvel Super Heroes (a.k.a. FASERIP) system were a combination of this and Experience Points with an added dash of, well, Karma Meter: your character earned them for acting like a proper superhero, could lose them for unheroic behavior, and they could be spent either in game to adjust die roll results or use your character's powers in new and unusual ways or between games for mechanical character advancement. The game also had a separate "Probability Control" superpower that let the character's player dictate in which order his or her (percentile) dice would be read after any given roll.
In the Wild Talents miracle cafeteria, this is represented by the Aces power. Notable in that it requires willpower to use.
Psionics: The Next Stage in Human Evolution: The synchronicity talents are all about this.
- Lucky Break allow you to reroll failed checks.
- Improved Lucky Break allows you to let your allies reroll failed checks.
- Twist Fate forces enemies to reroll successful checks.
- The Good Luck ability allows you to just have things go your way in general.
Anarchy Mages in Ponies & Parasprites use a resource exclusive to them called Spin. They can spend Spin to modify die rolls, which is useful in all circumstances but almost critical when they Channel their powers.
Half-elves in 13th Age have the ability to subtract one from their to-hit D20 occasionally. This sounds extremely awkward, except that 13A has a system called "flexible attacks" where fighters and bards use the die to determine which of their effects they can apply rather than choosing it like other classes. As a result, a half-elf fighter who gets a hit on a 17 can decide that one of their manoeuvres, which triggers on an odd roll, isn't well-suited to the tactical situation and instead reduce it to a 16 to use a different manoeuvre. The power is also useful for sorcerers, whose chain attack spells can go after extra targets on an even roll.
In Numenera, you can use unspent Experience Points on short-term benefits, one of which is a one-time re-roll.
In Eclipse Phase 1st edition Moxie points can be spent to "flip-flop" the numbers on a d100 roll, ignore penalties on a test, upgrade a success to a critical success or a crit fail to a regular failure, or go first in an action pass. In 2nd edition Moxie is one of four "pools" used to represent transhuman capabilities, Moxie applies only to social checks while Vigor is used on physical and Insight on mental, with "Flux" as a wild card.
Planet Mercenary allows players to spend an RiPP (Role Playing Point) to reroll one or more dice on a skill check. Having a Specialty in a skill allows rerolling one dice. Lastly, some weapon Qualities either skew the probability curve or allow for rerolls.
The Helm in Betrayal Legacy lets each player put a crest sticker on it once per chapter to redo a dice roll. After the chapter where the Helm will almost certainly have been completely filled up with stickers, family photographs are used as the "free reroll" items instead.
A special version of Monopoly based on The Avengers - a round board based on the Avengers shield, not the conventional square board - gives special powers to each player, based on which character (from the 2012 film) the player chooses. Thor's power gives the player the ability to either reroll the die or force another player to do so. This power can only be used once on each journey around the board, but is reactivated every time the player passes Go. Iron Man's power means that he can use that power too if Thor has yet to use it.
Big Eyes, Small Mouth has an Attribute called Divine Relationship (or Mulligan in 4^th Edition), which grants the player a number of rerolls per game session.
- BESM 4^th Edition also adds Edges and Obstacles, a system similar to Dungeons and Dragons 5^th Edition's Advantage and Disadvantage. A normal skill check uses 2d6, but if a character has an Edge they instead roll 3d6 (for a minor Edge) or 4d6 (for a major Edge) and keep the two highest results; Obstacles work the same way, but force the player to keep the lowest two dice instead.
Critical Role: Tal'Dorei Campaign Setting: The Fate-Touched Background comes with a unique benefit, Fortune's Grace, which allows a player character to re-roll one of their rolls on a d20 once per day. This is meant to express the character's ability to manipulate destiny and adds to the pool of re-rolls a character gets from the "Lucky" feature available in fifth-edition Dungeons & Dragons.

Video Games

Arcanum: Of Steamworks & Magick Obscura has fate points, which may be used to force a critical success (or do something else if you prefer).
Billy vs. SNAKEMAN has this in a few areas.
- BillyCon's Cosplay minigame lets you reroll once per level of Combat Sewing you have.
- High level opponents in Mahjong and Flower Wars can redraw cards to make them more formidable. You can do the same, but doing so causes you to lose your "No Cheating" bonus, and puts you at risk of getting caught cheating.
- Once per Zombja map you can break Rule 17 and "Be a Hero", automatically giving you the best rollable result for one attack ^note not counting the flamethrower's special effect; that's still an honest roll.
- "This Fist Of Mine" does the same thing with Worldkai, but with a stamina cost instead of a frequency limit.
- "Escape Jutsu" lets you reroll what Mission you're assigned, and "Sight Beyond Sight" forces your next Mission to be the same as your last one.
Heroes of Might and Magic V has an ability that adds an extra roll for all luck-based abilities.
Call of Duty: Black Ops: The "care package" killstreak is a random drop of any of the other killstreaks, plus the nearly worthless box of ammo. The Hardline Pro perk allows players to "re-roll" those care packages to try their luck again.
Case 02: Paranormal Evil: The game has various events where the player must roll die to get a value, which is then used to determine the outcome of the event. Equipping better gear will add additional die to these events, making it easier to reach higher value thresholds. Lucy's items can also be used to spend LP to increase the die values, effectively increasing the range of good values.
The Binding of Isaac features an (arduous to get, but extremely powerful) item, the almighty D6 die, which allows you to transmute power-ups & activated-items into another random item of either kind. This allows to try to swap Powerup Letdowns or Mutually Exclusive Powerups for something potentially more useful for your current playthrough.
- The Wrath of the Lamb DLC adds the even harder to unlock D20 die, which instead transmutes more common items (trinkets, keys, bombs, pennies, hearts, and chests).
- Rebirth adds the Guide Dang It! to unlock D4 die, which rerolls your passive items you've collected, the unlocked-by-default D10 die, which rerolls enemies, and the insanely hard to unlock D100, which is the D4, D6, and D20 combined.
Unlimited Saga, as part of its attempt to create the feel of playing a Tabletop RPG, has something similar in concept to this: it's replaced the endless literal dice rolling of a Tabletop RPG with spinning reels that the player stops by pressing a button, giving the player some degree of control over the outcome. Which just makes it even more frustrating when you get a bad result.
Kingdom of Loathing has effects that increase item drop percentages, which for most items can guarantee an item drop if it's boosted high enough, and effects that make monsters "more/less attracted to you", which affects the odds of encountering combat or non-combat encounters when adventuring. There's also Transcendent Olfaction, which increases the odds of encountering the same monster, and banishing effects that prevent the monster from showing up for a while. Manipulating all these is the key to faster ascensions.
Ancient Domains of Mystery had luck-affecting status conditions: Doomed, Cursed, Lucky, and Fate Smiles. This changed the mechanics of the RNG, to be more or less favorable to the player.
NetHack has a hidden luck stat which affects the RNG. Luck can be decreased by a number of means, and increased by sacrificing corpses at an altar, or by tossing gems to a co-aligned unicorn. The luck stat will decay over time towards zero (making both good luck and bad luck temporary) unless you have a luckstone in your inventory.
The Pokemon TCG for Game Boy uses coin flips as per the card game, but here it's possible to always get heads if you know how to time your flips correctly and during which battles (some battles have heads if the coin was flipped tails up, or the other way around, or on its edge, or...)
In Yu-Gi-Oh! Duel Links, the mobile game version of the famous TCG, there are various Skills that can manipulate coin toss result, dice roll result, and even what card you draw next.
In Fallout: New Vegas, the Luck statistic is established as the ability to calculate and manipulate probability; a high luck means you can nudge chance into giving more favorable outcomes. In general, this means that every casino game gives you better odds, critical hits are more likely, and all of your skills gain a slight increase. This also means that low luck makes critical hits less likely, and can actually jinx your gambling odds.
- When gambling, a player with high Luck can easily take any casino for everything until they get banned (which usually happens after net winnings of 10,000 caps). On the contrary, a player with low Luck will have a much harder time. Playing perfect blackjack strategy means nothing when the dealer repeatedly gets blackjacks with the accompanying message that "You feel unlucky".
- In-story, Mr House has been calculating the probabilities for an extensive web of plans in order to rule New Vegas; in-game, he has a maxed-out Luck of ten.
World of Warcraft introduced special tokens in Mists of Pandaria that allow players a second chance at getting an item when killing a raid boss. The number of tokens a player can have is limited to a maximum of ten for the current raid tier and only three can be earned each week through ordinary means. Opinion in the player base is split due to the relatively low chance of receiving an item and the low gold pay-out compared to the cost of the token. The tokens have their own built-in manipulation mechanic to protect against bad luck streaks. Each failed bonus roll increases the chance of receiving an item on a subsequent bonus roll.
The World Ends with You allows you to raise or lower your level (and therefore Maximum HP) on the status screen whenever you pause, for a 1:1 drop rate increase per level below max, up to 100 (further increased by chaining battles, which multiplies enemy stats and your drop rate per encounter, for up to sixteen battles). Since the in-game Noise Report states the base drop rates for some pins are set at 0.03%... you are going to need it.
Azure Striker Gunvolt: After every mission you're given some tries of taking an item out of 15 "covered boxes". The mechanic comes in where getting a higher rank in the mission and/or collecting medals on the run will let you take more tries on the same 15 boxes.
Fallout 4 has the ability to force an Always Accurate Attack Critical Hit to occur in V.A.T.S., by filling up the critical bar via hits in V.A.T.S. It's a great way to hit an opponent if your attack was about to miss. Certain Luck perks make this easier, such as Critical Banker to store more critical hits, and Four Leaf Clover to instantly fill up a critical bar by hitting enemies in V.A.T.S.
Golden Sun: By killing enemies with the type of Djinn they're weakest to, you gain additional gold and experience, and the chance of dropping its item is greatly increased (though it still takes a lot of Level Grinding depending on the monster, some drops are only bumped up to 1/256 with this method). Other methods include manipulating the RNG with specific commands (which character attacks, in what order, using what skill, etc. but requires a lot of resetting).
In Pocket Quest, a game where you literally roll giant dice to move to board tiles, you can use Loaded Dice (purchasable from shops and dropped by some monsters) to specify the number of spaces you want to move. Additionally, a traveling merchant sells the expensive Red Ears which skews the Betting Minigame's odds in your favor.
Hand of Fate and Hand Of Fate 2: Some equipment gives you better odds on the minigames; Mask Of Holy Fortunes causes one of the Chance Cards fail cards to always be visible, Gambler's Ring adds 2 to any dice roll, Grifter's Friend allows you to outright shift the Spin-the-card-wheel one card in any direction, etc. Blessings ^note the game's perk system can also affect minigames.
For the King: Stat checks (including attacks) normally make one to five rolls against a specific character stat, tallying successes and failures. Characters can spend points of Focus for automatic successes on rolls. However, each character has a small Focus pool and limited means of restoring it, including consumables, leveling up, and rare events.

Web Comics

Darths & Droids has a mention of the "Fate Manipulation Re-roll" Jedi power. Jim's misunderstanding of how the rule works turns out to be important: he refrains from using it at first because he thinks it refers to re-rolling in-game dice. Later, confusion over how to interpret this power's "one use per day" restriction when interplanetary travel is involved contributes to Qui-Gon Jinn's death. Much later, Annie uses a re-roll to help Anakin survive Pete's factory sequence.
In Homestuck, God Tier Vriska literally has the ability to manipulate luck in her favor — such as rigging a coin flip to land in her favor or stealing her enemy's luck, causing it to fall through the floor. She suffers an extremely Ironic Death because of this: Terezi flips a coin to determine her fate. Vriska predictably manipulates the outcome and leaves - only to be backstabbed because they both knew the toss didn't actually matter: The actual game was a bet on whether Terezi would have the guts to stab her. Specifically, she can force a million to one shot to work in her favor, but can't get around a 100% chance to fail such as Heads I Win, Tails You Lose.
Luckamancy in Erfworld is described as this. It's possible to bless units with good luck, but only by being willing to take the luck from other allied units. In one of the side-stories, the protagonist gets hold of a double eagle with a luckamancy special. It can curse allies to gain points that it can later use to bless them. Proper use of this special is the only hope the protagonist has of surviving the upcoming encounter, and it properly demonstrates the power of being able to move luck around to where it's most needed.