Dice Probability

[HellHound]

In another thread, we were discussing some rules, and I had a question for someone who has a clue about probabilities (I am so non-math-inclined that it hurts).

What are the odds of rolling lower or equal on a d% than on a d20.

ie: If I rolled both at once, what are the odds that the d100 roll will be lower than or equal to the d20 roll?

 

[diaglo]

if we use coins. say heads = 1. tails = 0.

1 in 2 chance of heads
1 in 2 chance of tails.

so total outcomes 4.

0,0 = 0
0,1 = 1
1,0 = 1
1,1 = 2

0, 2 are your equal outcomes. and 1,0 is where the first coin beats second... in this case 75% of the time the first coin will equal or beat the second.

 

[Thanee]

You have 20 possible outcomes for the d20 (1, 2, 3, ..., 20). Each have the same chance of occurance (5% chance for each number to turn up).

Each such result has a cumulative 1% probability (1%, 2%, 3%, ..., 20%), that if you roll a d%, you will roll equal to or lower than that number (rolling a 1 or lower on a d% is a 1% chance, rolling a 2 or lower on a d% is a 2% chance, and so on).

To get the average probability, you simply add up the these probabilities for all possibilities (20 total for the d20 roll, each number from 1 to 20 is one possible result) and then divide by the total number of possibilities (which is 20, obviously).

Therefore the average probability to have a d% roll equal to or lower than the result of a d20 roll is ((1+2+3+...+20)/20)% = (210/20)% = 10.5%

Bye
Thanee

 

[Beholder Bob]

My initial thought - there is a 20% chance the d100 generates a number 1-20.

The chance that you generate a number equal or lower on 1 d20 vs another - I believe is 11/20. So, 11/20*1/5 or 11/100 or 11%.

I'm just running numbers in my head, so this may not be exact

this is a disclaimer

BB

 

[diaglo]

change coin 1 to 1, 2 for outcome. and change coin 2 to a d4.

total outcomes changes to 8

1,1
1,2
1,3
1,4
2,1
2,2
2,3
2,4

now we see only 3 of 8 meet the proper parameter


change d4 to d6
total outcomes jumps to 12.
but 3 of 12 meet the proper parameter

change d6 to d20
total outcomes jumps to 40
so 3 of 40 meet the proper parameter...

 

[HellHound]

Thanks!

 

[Thanee]

Of course, you could also take the shortcut...

The average result on a d20 is 10.5, the chance to roll equal to or below that number on a d% is 10.5%, therefore the average probability for a d% to roll equal to or lower than a d20 is 10.5%.

Bye
Thanee