Lamp

A Lamp was a reward from the random event gift and Genie random event and could not be traded or banked. Rubbing the lamp gave the option of adding experience to a skill of your choice. The amount given was your current level in the skill multiplied by ten (e.g. level 13 Attack increases by 130 experience). This was not considered a large reward by most players unless it was being used to level up skills that are time consuming or expensive to level up, such as Summoning, Prayer and Construction. However, people usually chose a lamp from the random event gift, as they felt the experience reward was more worthwhile than any other reward in the box. Since the removal of random events, there are few ways to obtain these particular lamps.

Using the lamp
Genie lamps were most commonly used by players to advance skills that are either low or considered hard to level. Combat skills were seen as a poor use of the lamp, unless one was a Combat pure, as lamps allowed pures to gain Combat experience without training Constitution. Skillers often used lamps to train Slayer without raising their combat. Sometimes, a player would hold on to the lamp until they gained a level, especially if they were close to one. This is because it would give slightly more experience (10 more per increase) at a higher level. However, as retaining the lamp takes up inventory space (as it cannot be banked) it was often viewed as counterproductive when training some skills.

Another common reason for a player keeping a lamp would be for the ease of reaching celebrated levels like a 99. This made the level-up significantly easier and allowed the player to have a much wider choice of level-up locations. An example might be a player achieving 99 slayer in their player-owned house by using the lamp to obtain the final experience required to level.

Lumbridge Lamps
You can get two Lamps from Sir Vant in Lumbridge. He is located in the building east from the general store. There is a ladder that will take you down to him. He talks about killing a dragon, so ask him if he wants you to slay the dragon. Vant will say something to the effect of it would disgrace him as a knight if you killed it for him, so he just gives you two 250 XP lamps that you can use on certain skills - Attack, Strength, Defence, Prayer, Constitution, Ranged, Magic, Mining, Smithing, Fishing, Firemaking or Woodcutting. (This is only if you had not done the quest Unstable Foundations).

Trivia

 * It would take exactly 15,057 genie lamps to level a skill from level 1 to 99.
 * Level 10 experience of 100 gives the highest percentage (49%) of the difference to the next level. The levels 5 to 18 give 40% or more, levels 4 to 23 give 30% or more, levels 2 to 30 give 20% or more and levels 1 to 40 give 10% or more.
 * When trying to bank a lamp it will say "A magical force prevents you from banking this item", and the lamp will stay in your inventory.
 * When a new skill is added, there is no option to receive experience from the Lamp until several weeks after release.

Lamp