The Math of Dungeons and Dragons.

I have friends how played Dungeons and Dragons every single weekend. They'd disappear into a dorm room Friday night and reappear on Sunday sometime looking like death warmed over but it was their thing.  They got me to play it one time using their rules and I ended up with a +1 knitting needle. 

There have been a couple of movies on the topic along with some books but people still play the basic game and according to new information, it appears to help improve overall scores in children.  Don't think its just students who are above average. The game has hooked those who are struggling.

In general the game requires so much to do.  It encourages players to imagine a three dimensional world in their mind's eye while being lead by the Dungeon Master or DM.  Its a collaborative world building experience encouraging the use of geography via map reading, recursive mathematics every time they roll the dice, use addition and subtraction via modifiers, science for weather, ecology, climatology, chemistry, physics, and so many other skills.

In regard to mathematics, the game contains so much.  Players need it to modify their rolls by consulting charts and tables, calculate current rates for currency exchange, and figure out the number of experience points they could get. 

Their use of math begins when they are creating their character because the results of the dice rolls helps determine the type of ability the character has. If you are a fighter you want a high number to provide strength but if you need stealth, you'll go for numbers to give you that.

Math is also used to determine the order players carry out combat, sneak past an enemy, bluff, and just about any other action.  The higher the levels, the more complex the math.  Furthermore, it allows students to learn more about probability theory without knowing they are studying it. 

If a player is rolling one twenty sided dice twice, each roll is an independent event because the first roll does not influence the outcome of the second roll.  This uses the math formula p(A and B) = p(A) * p(B).  If the probability of rolling a 20 is 1/20, then the probability of rolling a 20 each time for two rolls is p(A and B) = 1/20 * 1/20 or 1/400 = 0.0025.

In addition, one can apply the binomial theorem to this game.  Basically, how well a player does in the game is determined by the roll of the dice.  Let's say the student is cornered, has only four rolls left but needs to get a 20 on three of those rolls.

So there are four trials left with 3 of those being successful.  So the formula for P(successess) = (n!/x!(n-p)!) *p^x *(1-p)^(n-x) So mathematically this looks like (4*3*2*1)/(3*2*1*1) * (1/20)^3 *(19/20)^1 = 0.000475 of being successful.

If anyone thinks D & D is for nerds only, its not since it provides skills in a cross curricular way that many students find enjoyable and engaging.  Let me know what you think, I'd love to hear.  Have a great day.