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#1 dae Feb 28, 2008 22:02:26

NOTE: This article is meant for parents or friends of players. I sent a proposal to WotC about a week ago asking if they'd be willing to put an advertisement in our Mathazine-please get back to me on that when you have time. :D If I were to say ″Dungeons and Dragons″ (D&D), your first thoughts would probably be of dark rituals in musty, cluttered basements or of cloaked boys, between twelve and fourteen, consuming pure sugar sodas and cheese-flavored puffs. In any case, I doubt that your first thoughts would be of math. However, math is rampant in the D&D game – most notably, probability. The entire game is based on rolling polyhedral dice (poly, meaning many, and hedral, meaning ″of a specific number of surfaces″), adding a modifier, and setting the result of said equation up against a Difficulty Class (DC), a previously selected number. If the result is greater than the DC, the player succeeds. If it is lower, the player fails. This is very similar to graphing on a calculator, except that a DC is involved: basically, that instead of creating a graph, the equation produces a result which determines whether the character succeeds or fails at any task they set to complete. So what other elements of probability show themselves in D&D? The die rolling itself. Basically, there is a 5% chance of receiving any one number when rolling a twenty-sided die, because 100/5=20. So if the DC for a task is 10 (a good example of a DC 10 task is climbing a rough rock wall-a DC 0 task would be trying to hear a pitched battle from five feet away, and a DC 20 task would be to track a rogue across hard ground), and the roll is Strength based (That is, that the modifier to the roll is equal to the character's Strength modifier), then a fighter with a strength level of 14 (which gives a +2 modifier to Strength checks) will have a 60% chance of success. However, let′s make this more difficult and say that the wall is slippery from water (+2 to the DC) and that the climber is a wizard with a strength level of 7 (-2 modifier). In that case, the wizard would have a 30% chance of success. Another example of probability is the d% (which is basically two ten-sided dice with one die selected to be the ones place and the other selected to be the tens place). Now, this die roll would obviously have a 1% chance of displaying any single number. Since a d% is used for most Dungeon Master decisions (what race a NPC is, for example, or what monster attacks the Player Characters), there are often 100, 25, or any other number divisible by 100 options. This makes for a multitude of options, each with the same probability of occurrence. Formulas Experience points required for next level = (XP needed last level+1000) Damage dealt with melee weapon: 1dX (provided in weapon statistics) + strength modifier + weapon's magic bonus. Initiative: 1d20+dex (dexterity modifier)+ misc. Modifier to ability score: Score-10/2. Fact of the Day: The die roller function in the ProbSim section of the graphing calculators isn't limited to d6's. It works for the d8, d10, d12, and d20. The random number generator is good for generating 1 through 4 and 1 through 100. Vocabulary: dX: Literally, a die which can have any number of sides. DC: Difficulty Class D&D: Dungeons and Dragons Dex: Dexterity NPC: Non-player Character Str: Strength