Calculating Odds for D&D (long)

[Drawmack]

I am planning on doing up an adventure that takes place at a carnival. There will be bets taken on a number of the contests and in order to calculate the odds of winning accuratly I need to calculate the odds of the die rolls. So this thread is for discussion on this topic. The odds of a calculating a single roll in D&D are a matter of simple algebra. Here are some examples.

1) Hitting: (20 + Attack Bonus - AC) * 5
2) Completing a task: (20 + Modifiers - DC) * 5
3) Opposed Rolls: ((X*X)/2) * (100/(S*S)) (underdog winning)
X = 20 - (Higher Bonus - Smaller Bonus)
S = # sides on the die.

For example:

A 1st level fighter str 12 rolls a d20+2 against an ORC (AC 14). The odds that this is going to hit is (20 + 2 - 14) * 5 = 8 * 40 = 40% chance to hit the orc.

A 1st level rogue with wis 12 and four ranks in disable device attempts to disarm a trap with a DC 15. The of this working are (20 + 5 - 15) * 5 = 10 * 5 = 50% chance of disarming the trap.

A commoner with str 18 (+4) arm wrestles a commoner str 3 (-4). The odds of this working are (((20 - (4 - -4)) *(20 - (4 - -4)))/2 * (100/(20*20) = ((12 * 12)/2) * (100/400) = (144/2) * .25 = 72 * .25 = 18%. There is an 18% chance that the underdog will win and a 72% chance that the favorite will win.

Now we reach the point where my mathematical skills begin to break down. I have two types of odds left to calculate and I don't know how to do it. The two types that I wish to calculate yet are. More then two characters doing a single opposed die roll and two characters doing multiple opposed die rolls.

 

[diaglo]

pick up a stat book from your local library.

do some computations and permutations.

 

[RangerWickett]

I suggest Tournaments, Fairs, & Taverns, from Natural 20 Press, available for pdf purchase at www.rpgnow.com. It has a lot of games and ideas for festival and tournament settings. The print version, which should be coming out in early 2003, will have even more games and adventure ideas.

 

[CRGreathouse]

Now we reach the point where my mathematical skills begin to break down. I have two types of odds left to calculate and I don't know how to do it. The two types that I wish to calculate yet are. More then two characters doing a single opposed die roll and two characters doing multiple opposed die rolls.

Two characters doing multiple opposed rolls? What do you mean/do you have an example?

 

[CRGreathouse]

1) Hitting: (20 + Attack Bonus - AC) * 5
2) Completing a task: (20 + Modifiers - DC) * 5

These should both have 21 instead of 20. Attack bonus +0, AC 11 = 50/50 chance.