Opposed Roll Probabilities

Post/Author/DateTimePost
#1

FrogReaver

Mar 12, 2015 0:17:58

How to calculate opposed roll probabilities.

 

1.  Determine the difference in standard bonuses that you have.

For example if I have an athletics of +5 and my target has an athletics of +1 then there is a +4 difference

 

2.  Subtract that value from 20

For exmaple 20 - 4 = 16.  Let this nubmer = x

 

3.  Use this formula: x(x-1) / 2

For example: 16*15 / 2 = 120

*120 = the ways for the  +1 to end up greater than the +5 after rolling.

 

4.  Determine who wins ties

 

5.  If the person with the lower +bonus wins ties add x to it

For example: 120 + 16 = 136 

***If the person with the lower bonus doesn't win ties then do nothing.

 

6.  Subtract the final result from 400.

400 - 120 = 280 (if the larger + value wins ties)

400 - 136 = 264 (if the lower +value wins ties)

 

My chance of winning is 280/400 = 70% if I win ties

My chance of winning is 264/400 = 66% if my opponent wins ties.

#2

FrogReaver

Mar 12, 2015 0:21:04

Another example.

 

Assume I have +7 athletics and the enemy has 0 athletics.

 

Difference is +7

 

20-7 = 13

 

13*12/2 = 78 ways to lower athletics wins

 

13 ways they tie

 

400 - 78 = 322 ways the +7 wins if the +7 wins ties

400 - 91 = 309 ways the +7 wins if the 0 wins ties.

 

322/400 = 80.5%

309/400 = 77.25%

 

 

#3

FrogReaver

Mar 12, 2015 0:23:42

Even with a +10 difference on opposed rolls:

 

10*9/2 = 45

 

10 ways to tie

 

355/ 400 = 88.75%

345/400 = 86.25%