Doubleshot

Doubleshot grants a character a chance to do additional damage with their ranged or thrown weapon any time they make an attack. Doubleshot applies only to ranged and thrown attacks. (The similar mechanic for melee is Doublestrike.)

If your Doubleshot is greater than 100%, then a second shot is guaranteed, and the remainder is the chance at additional shots. For example:
 * If your Doubleshot chance is 100%, there's a 100% chance of doing double damage.
 * If your Doubleshot chance is 120%, you have a 20% chance of doing triple damage instead of double damage.

For shurikens specifically, Doubleshot does not apply to the additional shuriken thrown by the feats Shuriken Expertise or Ninja Spy Core Ability 2, Advanced Ninja Training. [confirm]

Doubleshot was introduced as part of the Update 19 combat changes. Many attack speed bonuses were converted to Doubleshot effects at that time.

Update 28 Patch 1 changes:
 * Manyshot and Ten Thousand Stars no longer reduce your doubleshot chance.
 * Repeating crossbows now have 1/3rd the chance for Doubleshot.
 * Doubleshot can now "wrap" and cause a third or fourth shot if it goes above 100%.

Update 45 changes:
 * Dual Crossbow combat style (from Inquisitive enhancements) uses 50% of your Doubleshot

Update 49 changes:
 * Prior to this change, Doublestrike gave you a chance to make multiple attacks. Now it gives you the chance to do extra damage with a single attack. (This change was made to reduce server lag.)
 * The exceptions to this rule are Repeating Crossbows and the Inquisitive Dual Crossbows style. They still fire 3 or 2 full projectiles (so you'll still see 3 numbers or 2 numbers, respectively). However, they still have Doubleshot penalties of 66% and 50%, respectively.

Feats

 * Doubleshot (ML28 Epic Destiny Feat): Passive +10% Doubleshot
 * Double Shot (Primal Past Life Stance): Passive +3% Doubleshot per stack
 * Manyshot (Feat): Active: Fires three arrows, each has Doubleshot equal to 1.5x your Base Attack Bonus, longbow and shortbow only
 * Multitude of Missiles (Feat): Active +100% Doubleshot, simple thrown weapons
 * Ten Thousand Stars (Feat): Active bonus to Doubleshot equal to monk level * 5 if you are centered (only affects shuriken)
 * Scion of the Astral Plane (Legendary Feat): Passive +4% and an additional +4% if you are centered
 * Simple Thrown Weapon Expertise (Feat): Passive bonus to Doubleshot equal to your Dexterity

Enhancement bonus

 * Category:Doubleshot items
 * Random items with Rapid Shots suffix
 * Random armors with Flurry prefix
 * Flawless Shadowscale Armor with Shadow Striker

Artifact bonus

 * Silent Avenger set: 5 / 15 (heroic / legendary)
 * Wallwatch set: 10 / 15 (heroic / legendary)
 * Eminence of Spring/Summer set: 15 (6 pieces)

Sentient Weapon/Filigrees (untyped bonuses)

 * Celerity - 2 piece set bonus: +2%
 * Enlightened Step - 5 piece set bonus: +5%
 * Zephyr - Doubleshot filigree: +1%
 * Crackshot Negotiator - 4 piece set bonus: +5%
 * Shattered Device - 3 piece set bonus: +3%
 * Splendid Cacophony - 2 piece set bonus: +2%
 * Voltaic Experiment - Doubleshot filigree: +1%

Class enhancements
Any class via Inquisitive enhancements
 * Tier 4 ability - Martial Inquisition: +5% with Light and Heavy (non-repeating) Crossbows
 * Tier 5 ability - No Holds Barred: +10%

Any class via Vistani
 * Third core: Knife Specialist - 5%
 * Fifth core: Vistani Fortune - 25% chance of 10%
 * Tier 1 ability: Rapid Throw - 20% morale bonus with Throwing Daggers
 * Tier 4 ability: Celerity - 5%
 * Tier 5 ability: Whirling Blades - Your throwing knife gains 100 doubleshot for 15 seconds. Cooldown one minute.

Artificer
 * Battle Engineer - Tier 4 Ability - Agility Engine +3%/6%/10% Doubleshot while wearing a rune arm

Bard
 * Swashbuckler cores: +1 per core
 * Swashbuckler - Tier 2 ability - Double Shot Boost: Activate to gain +10/20/30% Action Boost bonus to Doubleshot for 20 seconds. Usable 5 times per rest.
 * Swashbuckler - Tier 3 ability - Dashing Scoundrel: +10% while Swashbuckling
 * Warchanter - Tier 4 ability - Reckless Chant: Passive +2%/4%/6% Music bonus to Doubleshot.

Cleric / Favored Soul
 * Warpriest / War Soul - Tier 4 ability - Holy Sniper: 10%

Fighter
 * Kensei - Core ability 3 - Strike With No Thought: Passive +3% to 6% Doubleshot depending on how many Kensei core abilities you have.
 * Kensei - Core ability 6 - Alacrity: Passive +15% Doubleshot

Ranger
 * Arcane Archer - Core ability 5 - Shadow Arrows: Arcane Archer Secondary Imbue Toggle: +5% Doubleshot chance with bows.
 * Arcane Archer - Core ability 6 - Master of Imbuement: Passive +20% Doubleshot chance.
 * Deepwood Stalker - Tier 4 ability - Killer: +5% morale bonus to Doubleshot chance per stack. Earn stacks by killing. 15s duration. The Killer buff can stack up to 2/3/4 times.
 * Deepwood Stalker - Tier 5 ability - Strikes Like Lightning: +20% Doubleshot.

Rogue
 * Assassin - Tier 4 ability - Killer: same as DWS Killer
 * Mechanic - Tier 5 ability - Rapid Fire: Passive +3%/6%/10% Doubleshot

Race enhancements

 * Aasimar Scourge - Tier 4 ability - Divine Form: Active: +1% or more
 * Elf - Tier 4 ability - Skill: Passive +3% Doubleshot
 * Morninglord - Tier 4 ability - Skill: Passive +3% Doubleshot
 * Wood Elf - Tier 4 abilities:
 * Skill: Passive +3% Doubleshot
 * Through the Branches: +3% Doubleshot with Longbows and Shortbows.

Reaper enhancements

 * Memento: Reaper Strike: [10/20/30] reaper bonus to Doubleshot for 20 seconds

Guild bonus

 * Seasoned Archer - +2% Guild bonus to Doubleshot

Epic Destinies

 * Zeal of the Righteous - Divine Crusader Level 5 innate ability - Gain 50 stacks of Righteous Zeal (+1% doubleshot per stack). Decays by 1 stack every 3 seconds.