Game Balance for White Box is a bit different than what "balancing" has come to mean in later editions of the game. The authors of White Box, especially Gary Gygax, wrote frequently about the need for balance in the game and claimed giving away too much treasure and too many magic items quickly unbalanced the game and deprived everyone of fun. I infer from the rules and commentary (as I now recall it) as well as play aids such as the Monster & Treasure Assortment(s), that White Box balance means a slow steady rate of character progression, encounters that will not kill the characters too quickly and that gave the players a chance to use their game skill and common sense in order to limit the risk to their character. Balance among characters means making humans attractive as a player character race so they are likely to outnumber non-humans in the campaign. It does not assure players that all character classes are of equal power nor does it give undue confidence to players that their characters will survive every encounter. This last sentence sums up one of the major differences between so called "old school play" and the modern game as I understand it.
White Box uses a character class and an experience system to level-up characters thereby increasing PC power over time, giving them additional abilities and making it possible for them to successfully combat more powerful monsters and challenges. The experience points required to advance in level varies according to the various character classes and this is one way the game seeks balance. Magic Users advance more slowly and wearing no armor start out relatively weak compared to Fighting Men and Clerics. Clerics get no spell ability until 2nd level, but have access to armor and the ability to turn undead. The demi-human player character races have additional abilities such as the ability to see in the dark or spot certain dungeon features better than humans, but are also limited in terms of class choice and have level caps as a means of balancing their apparent advantages.
The referee is advised to challenge the players with level appropriate monsters and give players a degree of advance warning when they are entering more deadly territory. Dungeon level is a concept corresponding to how far below ground the player characters have traveled and the deeper levels can be expected to hold greater monsters, challenges/dangers, and treasures. One Hit Die monsters (the weakest) are common on the first level of the dungeon, two Hit Die monsters on the second level of the dungeon, etc. Monsters with more Hit Dice generally guard bigger treasures (reward) as a balance. The White Box includes tables which organize monsters by level. The Monster & Treasure Assortment play aid(s) list monsters and treasures by level as a guide and an aid to the referee in populating the underground with challenges and rewards in a balanced fashion. The single volume shown above includes the contents of three earlier volumes. The booklet is organized so that referees may make random rolls or pick and choose from the tables.
It was a concern of the designers of White Box that a referee who is too generous with treasure and magic items might spoil the fun of their campaign. Players naturally seek to improve their characters and doing so is one of the rewards of playing the game. Pacing that advancement is part of the challenge of refereeing a campaign. It has sometimes been suggested that an appropriate pace be for the players to attain a new level every 6-10 sessions. With weekly sessions, that will mean players can take a character from first to ninth or tenth level in a couple years of play (if the PC survives!).
The amount and power level of the magic items characters acquire can also greatly affect the campaign and it is generally advised that referees not unbalance play by being over generous with magic items. Again, a guide such as the Monster & Treasure Assortment can assist the referee in determining which magic items are balanced for a particular level of play. Ultimately, there is no attempt at a formula for balance as can be found in some versions of the game. The balancing act in White Box is more an art than a science, but there are tools to assist the referee.
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