Fallout: New Vegas skills

Background
Fallout: New Vegas shares a similar skill set to its predecessor, Fallout 3, but with several differences. Thirteen skills still remain, but the combat skills have been revised. Small Guns and Big Guns having been combined into the Guns skill, which now covers all conventional firearms with bullet projectiles. Weapons using explosive ordnance (missile and grenade launchers, for instance) are covered by Explosives. New throwing weapons, such as the throwing spear, have been added and are categorized as Melee Weapons. The Survival skill, which is similar to Outdoorsman, was re-added. It allows the player to craft a number various items, such as food, stimpaks, and poisons to augment the effectiveness of weapons.

As opposed to in Fallout 3, skills other than Speech have an effect on dialogue choices. The player must have a certain amount in the particular skill or else the dialogue option cannot be passed. In the case where a player's associated skill level is too low, a dialogue option (highlighted in red) is presented that will fail the skill check, and will not grant a speech success. Unlike Fallout 3, where the same dialogue option is presented regardless of your success or failure, a check that will fail uses a humorously unconvincing response, while a passable check uses a well-thought out argument, thus reflecting the nature of the check.

Unlike in Fallout 3, there are not enough skill points in the base game to max out every skill, even when accounting for every perk and skill book/magazine. Without add-ons installed, it is only possible to achieve a functional maximum in roughly ten skills by using skill magazines and the Comprehension perk for a temporary boost to 100 from a base level of 80.

To offset the necessity of a minimum value for a certain skill, Fallout: New Vegas introduces skill magazines, which provide a large but temporary boost to their associated skill (+10 or +20 with Comprehension). By using one prior to conversation, a check can be passed that might otherwise be failed. They can also be used to boost skill with weapons temporarily or gain access to crafting recipes beyond the player's current skill. Like skill books, magazines are consumed once used, and more need to be collected to maintain the effect.

Formula
The initial value of each skill is a base value of two, plus an amount depending on a character's value in the relevant attribute, plus a bonus determined by their Luck attribute, rounded up.
 * $$2 + (\mbox{Stat} \times 2) + \left\lceil\frac{\mbox{Luck}}{2}\right\rceil$$

Example: A starting Endurance of five and a starting Luck of five will give you an initial Unarmed skill of 15.
 * $$2 + (5 \times 2) + \left\lceil\frac{5}{2}\right\rceil = 15$$

Later changes to the SPECIAL stat have a similar influence on the respective skill.

During character creation, the player will tag three skills, instantly adding 15 points to each one. When leveling up, the character will distribute ten skill points plus a number equal to half their Intelligence, totaling 15 at maximum IN. The Educated perk grants two additional skill points per level if chosen. Assuming the player has an Intelligence of ten from level 1 and takes the Educated perk at level 4, a maximum of 487 skill points can be distributed without any DLC. Each DLC raises the level cap by 5, thus adding a possible maximum of 5 x 15 = 75 points (or 5 x 17 = 85 points with Educated) to the total available.

Skill Points available with a starting INT of 10 and with/without Educated:

Base game : 487 / 435

One add-on : 572 / 510

Two add-ons : 657 / 585

Three add-ons: 742 / 660

Four add-ons : 827 / 735

It can be seen from the above figures that the Educated perk confers an advantage relative to the number of add-ons/levels, so that a player with three DLCs and Educated actually has more skill points to distribute than a player with four DLCs but without Educated.

Temporary

 * Skill magazines will raise the particular skill by 10, or 20 if the Comprehension perk is chosen.
 * Certain armor or clothing can raise certain skills when worn.
 * Taking chems can augment S.P.E.C.I.A.L. stats, and thus raise the coinciding skill by a small amount.

Permanently

 * Reading any skill book will raise that particular skill by 3, or 4 if the Comprehension perk is chosen.
 * Certain perks can raise skills permanently.