A novel concept in gaming, often attributed to Dave Arneson, is the advancement of a character along a path toward increasingly powerful class abilities based on in-game achievements called "experience". Success in the game of White Box (and many RPGs that followed) can be measured much like winning in Monopoly, specifically the accumulation of imaginary wealth and power leads to "winning". In other words the more success a player has with the game, the more treasure they accumulate.
In White Box play more treasure brought out of the dungeon means more experience is awarded for the character in play. Acquire some treasure, survive to enjoy it and you will be awarded some experience points that you can use to improve your character's abilities. Accumulate enough experience points and your character gains a "level" and some additional powers improving hit points, saving throws and ability to successfully strike an enemy. Casters receive additional spells and clerics improve their ability to turn undead creatures.
Failure in White box (and many other RPGs) is termed "character death". Bankruptcy is the result of failure in Monopoly, but it's just a game using play money. Character death in White Box just results in rolling up a new character, which you may find is even more fun to play than your last one. Rolling characters is quick and easy in White Box and in most old school campaigns players had several characters of various levels available for play at any given time.
As referee, you have some control of how experience is awarded. Various editions of The World's Most Popular Role-Playing Game have given various formulas for awarding experience. It is common in old school play to award experience for treasure taken from monster lairs and brought back home (and sometimes spent). This encourages recovering treasure, usually in the form of coins looted from the dungeon, over killing creatures or other endeavors. Players are therefore encouraged to develop creative ways to gain treasure without risking the lives of their player characters and to avoid wandering creatures, which seldom carry much treasure and therefore pose unrewarding risk. If, as referee, you wish to encourage some other aspect of play, such as achieving certain plot points or role-playing their alignment, awarding experience points is one method to do this.
Over the years since White Box first appeared many "houserules" have seen print in various publications and on the internet, many dealing specifically with experience; how it is earned; how it can be used to advance levels and what "leveling-up" means. Many referees require a period of training to occur prior to advancing a level earned through experience. Training can also be a good way to spend some of that acquired loot and help keep the PC hungry for more adventuring.
In the White Box advancing a level entitles the character to additional advantages according to the class chart. Some houserules have incorporated a list of possible advancements associated with each class level from which the player then chooses or rolls a random result. This has the added benefit of making each character a little more mechanically distinct from other characters of the same class and level. It can also add a little more excitement to leveling-up if the player enjoys rolling randomly for the resulting character benefit.
It sounds simple, but anyone who has played more than a session or two of the White Box (or any of its subsequent versions) knows the thrill of reaching that experience point threshold that allows for the "leveling-up" of their character. The leveling-up concept has been so popular that it has been recreated across game media platforms from tabletop pen and paper games to computer role-playing games, console games and massive multi-player online role-playing games.
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