Charisma/Fallout 4

Charisma is one of the seven primary statistics in the SPECIAL system.

Gameplay
Charisma influences several game mechanics. It directly controls your ability to charm and convince others, replacing the Speech skill in governing one's chance of successfully persuading in dialogues. It also replaces the Barter skills from previous games by governing the prices you get from trading with merchants.

Base Game
A base charisma of 12 can be achieved. Combined with all base game items a maximum Charisma of 32 can be reached, while with all add-ons included 48 is the maximum.
 * Increase base Charisma to 10 by spending SPECIAL points on it.
 * Take Daddy-O, drink Vim Captain's Blend or suffer addiction withdrawal to temporarily decrease Charisma below 10.
 * Use the You're SPECIAL! book while Charisma is still below 10 and when the effect wears off you will have 11 Charisma.
 * Pick up the Charisma Bobblehead to reach 12 Charisma.

Items
Several items grant bonuses while equipped for a maximum of +18 increase to Charisma:
 * Charisma increasing hat +1
 * Black-rim glasses or Fashionable glasses +1
 * Green shirt and combat boots clothing for +1
 * Five Sharp armor pieces 5x +1, or five Unyielding armor pieces 5x +3 to all stats (except Endurance) when the player character is at 25% or less health.

The summer shorts +2 fills outfit and chest armor slot that can be used instead of Green shirt and combat boots and the Sharp chest piece to preserve weight.

Consumables
Several consumables increase charisma temporarily up to +12.
 * Beer or any other alcohol except bourbon, rum, vodka, whiskey or wine for +2 with Party Boy/Girl tier 2 perk, +1 without it.
 * Grape Mentats for +5
 * Day Tripper for +3
 * X-Cell for +2

Far Harbor

 * The Dapper Gent hat for +2
 * Equip five pieces of Unyielding armor for a total of 15 in all stats.

Vault-Tec Workshop

 * The barber chair provides a semi-permanent boost of +1 Charisma that is lost when choosing to use one of the other statistic boosting workshop items.

Nuka-World

 * Fancy plaid suit & tie clothing for +2
 * The Smooth Operator chem +3

Perks

 * Cap Collector; Get better prices from merchants and invest in their stores
 * Lady Killer / Black Widow; Be more effective against the opposite sex in combat, persuasion, and use of the Intimidation perk.
 * Lone Wanderer; Grants various bonuses to the Sole Survivor when traveling alone or with Dogmeat.
 * Attack Dog; Grant various bonuses to Dogmeat.
 * Animal Friend; Pacify, Incite or Command Wasteland animals below the player character's level.
 * Local Leader; Build workshops and traders at settlements and establish supply lines to link them.
 * Party Girl Party Boy; Increase the effects of alcohol and remove any chance of addiction.
 * Inspirational; Grant various bonuses to companions.
 * Wasteland Whisperer; Pacify, Incite or Command Wasteland creatures below the player character's level.
 * Intimidation; Pacify, Incite or Command human enemies below the player character's level.

Settlements
Charisma affects the maximum amount of settlers allowed at a settlement:
 * $$\text{Max Population} = 10 + \text{Charisma}$$

Speech
Charisma affects the chance of passing a Speech check:
 * $$\text{Chance to Succeed} = \text{Charisma} * 15\% - \text{Speech Check Difficulty Modifier}$$

Additionally, each rank of Lady Killer or Black Widow adds 10% if the target is of the opposite gender. The final result of the Chance to Succeed formula is limited to a minimum of 5% and a maximum of 100%, so there is always a slight chance of success.

One has a 100% chance of success to pass a Red check with a Charisma value of 11 or higher; this includes all clothing, armor, and drug effects.

Barter
Charisma affects item buy/sell values; the value of an item for buying or selling is its innate value multiplied by either the buying price modifier or the selling price modifier:
 * $$\text{Buying Price Modifier} = 3.50 - \text{Charisma}\times 0.15$$
 * $$\text{Selling Price Modifier} = 1 / \text{Buying Price Modifier}$$

Multiply the modifier from Charisma and all applicable modifiers above to get the (near) final modifier.

If one gets a final buying modifier that is less than 1.2, the game will use 1.2. If one gets a final selling modifier that is greater than 0.8, the game will use 0.8.

Note: The minimum purchase price is 120% of the item's value, and the maximum selling price is 80% of the item's value. It appears that this applies even after one gets a discount from a vendor.

To get the best prices:
 * Without any of the other factors above, one needs 16 CHA for buying, 15 CHA for selling.
 * With the Cap Collector 1 perk, one needs 15 CHA for both buying and selling.
 * With the Cap Collector 2 perk, one needs 13 CHA for both buying and selling.
 * With the Cap Collector 2 perk and the Barter Bobblehead, one needs 12 CHA for both buying and selling.
 * With the Cap Collector 2 perk, the Barter Bobblehead, and all 8 ranks of Junktown Vendor, one needs 8 CHA for buying and 12 CHA for selling.
 * With the Cap Collector 2 perk, the Barter Bobblehead, and all 8 ranks of Junktown Vendor, and having done the relevant quest to make the vendor like the player character enough for a discount:
 * One needs 7 CHA for buying and 11 CHA for selling with Alexis Combes.
 * One needs 3 CHA for buying and 9 CHA for selling with Connie Abernathy.

These factors are multiplicative and not additive; for instance, rank 2 cap collector gives a 1.32 selling modifier. Friend Discount is when the player character gets better prices from a vendor for completing a quest. For example, returning the locket to Connie Abernathy's husband unlocks a Friend Discount with Connie. Other vendors may have the same or other discounts.

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