Fallout 3 skills

Skills in Fallout 3 are a primary attribute of the player character that determines their effectiveness in a variety of situations.

History
As in the previous games, the player chooses three Tag Skills out of thirteen to be the character's specialties. Unlike previous games tagging a skill only grants the player a 15 point bonus to that skill. Five skills have been cut from the game. (Fallout and Fallout 2 had 18 skills.)

Formula
The initial value of each skill is based on a character's value in the relevant attribute plus a bonus determined by their Luck attribute.
 * Formula: 2 + (Stat * 2) + Luck/2 (rounded up).
 * Example: A starting Endurance of 5 and a starting Luck of 1 will give you an initial Unarmed skill of 13. 2+(5*2)+1/2=12,5≈13
 * Initial values also function as base value, meaning any later change to the SPECIAL stat would also have similar change to the respective skill.

At level up, the character will gain 10 points plus a number equal to their Intelligence.

Improving and Maximizing Skills
Skills can be improved:
 * Temporarily
 * By wearing certain armor and clothing that offer skill modifiers.
 * By using chems that alter their base stats, thus increasing the related skills.
 * Permanently
 * Reading a skill book increases the relevant skill by one point, or two if the character has the Comprehension perk.
 * Finding a Bobblehead will increase the corresponding skill by ten points.
 * Receiving the Yew's Bear Charm will give you a permanent ten point increase to your Speech skill.
 * Certain perks offer a skill increase.

In order to reach the maximum number of points available in all skills, you only need to train all skills to 42 (at most) or sometimes not at all (see Glitches/Bugs below.) This is because most skills have 25 (some have only 24, hence the 42) skill books, which will give 50 points in all with the Comprehension perk, and then ten more points can be acquired through a bobblehead.

It isn't possible to raise a skill above one hundred points, but the game keeps track of increases past 100 just in case a skill is lowered (by something such as radiation or power armor,) so you may want to raise some skills to (theoretically) 102 or 104.

Glitches/Exploitable Bugs
It is possible to never have to put points into certain skills to max them out. In particular, certain skill books are on respawning NPCs - merely waiting 73 hours after killing will result in a new copy being created.
 * Big Guns - U.S. Army: 30 Handy Flamethrower Recipes: It is possible to obtain infinite copies of this book in Bethesda Offices East. A Raider with a Flamer normally on the top floor has this book in his inventory. When killed he'll respawn in 73 hours with another copy of the book in his inventory.
 * Science - Big Book of Science: It is possible to obtain infinite copies of this book in Shalebridge Tunnels. An Ant Researcher at this location has the book in his inventory.  When killed he'll respawn in 73 hours with another copy of the book in his inventory.