by Galloglaich » Tue Dec 04, 2012 2:51 pm
Ok so an explanation of this.
I wrote a program a few years ago to do a 'brute force' test of die rolls. This came out as a result of an argument / challenge I had on this forum in it's earliest days, about the probabilities of the pool die rolls (the guy raising the argument felt that there was no value in rolling multiple dice).
In this case, these are runs of about ten thousand (actually 9999) die rolls, with different numbers of dice in the pool. In each of these runs, the results from two 'players' are shown, one using multiple dice and one using one die. I did runs here for 4 dice vs. 1 die (Larry vs. Sue), 3 dice vs. 1 die (Larry vs. Moe), 2 dice vs. 1 die (Larry vs. Sue) and 2 dice again (Larry vs. Moe).
In spite of running the numbers 10 thousand times there is a certain margin of error on the results, about 0.1% to +/- 1.2% depending on the figure.
But it does give us an approximation of the actual effects of using the pool. The results are as follows:
4 Dice.
Roll a natural 20: 18%
Roll a natural 1: 0%
Roll a tie / bind: 5%
Average Die roll: 16
Chance to 'Win' vs. one d20: 78%
3 Dice
Roll a natural 20: 14%
Roll a natural 1: 0.09%
Roll a tie / bind: 5%
Average Die roll: 15
Chance to 'Win' vs. one d20: 72%
2 Dice
Roll a natural 20: 9%
Roll a natural 1: 0.72%
Roll a tie / bind: 5%
Average Die roll: 14
Chance to 'Win' vs. one d20: 64%
1 Die
Roll a natural 20: 5%
Roll a natural 1: 5%
Roll a tie / bind: 5%
Average Die roll: 10
Chance to 'Win' vs. one d20: 50%
So it seems like the effects of extra dice kind of taper off a little, you get a huge jump from 1 die to 2, but 3 dice may be the sweet spot in terms of your chances of rolling high, and rolling a 20, vs. the amount of dice used.
G