Need a statistic major's help here...

[RigaMortus]

First off, let me say that I could be completely wrong here and I'm willing to accept that. But...

Got into a slight tiff with a groupmate today when I tried to explain the difference between a 25% chance by rolling a 1d4 and a 25% chance by rolling 1d100.

Now, like I said, I am not a statistics major so I could be completely off (coincidentally enough, the person I had the dispute with is a math major of some sort). I can remember numerous times on this site where people who were really good with statistics would be able to break down average damage (for example).

Anyway, we had a 25% chance to succeed at something. My arguement (although I couldn't articulate that well) was that rolling a 1 on a 1d4 is not the same as rolling 1-25 on a 1d100. The reason being, there is a larger margin. All things equal, it would take you 1 out of 4 tries to roll a 1 on a 1d4 and 1 out of 25 tried to roll anything between a 1 to 25 on a 1d100. That is a lot more rolls. Anyway, I was hoping someone here can prove or disprove (hopefully prove) my theory here.

 

[Kraedin]

OK.

A d4 die has a range of 1-4, while a d% has a range of 1-100. A "1" comes up 1/4 of the time on a d4. A number between 1-25 (inclusive) on a d% comes up 25/100 times. The fraction 25/100 reduces to 1/4.

The last time I checked, 1/4 == 1/4, so, sorry, you're wrong.

(One caveat: I'm a computer science major, not a math major. Close enough, right?)

 

[RigaMortus]

I know that fractionally they are the same thing, but the chances a 1 will come up on a d4 will be more then any number between 1 to 25 (including 1 and 25 of course) coming up on a d100.

 

[kreynolds]

I know that fractionally they are the same thing, but the chances a 1 will come up on a d4 will be more then any number between 1 to 25 (including 1 and 25 of course) coming up on a d100.

If you are rolling a d100 for a 25%, you only need to get any number between 1 and 25. Any of those numbers will do, so I would think the chances are the same. Basically, whether you're rolling a d4 or a d100, there's a 25% chance that you'll roll a 25% on either one. I could definately be wrong though. If you're rolling for a miss chance, that's different.

Now, the really important question is this: when you say d100, do you really mean a d100, or do you actually mean 2d10's (with one being the percentile die)?

 

[RigaMortus]

Good catch! I do in fact mean two 10 sided die (one being a percentile die).

There just seems to be a bigger margin between rolling a 1-25 using percentile rather then a 1 on a d4. If the margin is bigger, then so is the chance of not rolling a 1 to 25, I would think.

I guess I am looking at it like this. All things being equal, if I roll a 4 sided die 4 times, a 1 should theoretically come out at least once.

If I roll a percentile 25 times, a 1 to 25 won't theoretically come out because there are more combinations to roll. I'd need to roll 76 times to ensure a 1 to 25 came out (because the first 75 rolls could be any number of 26 to 100). Again, all things being equal.

 

[Darkness]

Now, the really important question is this: when you say d100, do you really mean a d100, or do you actually mean 2d10's (with one being the percentile die)?

Why is that so important

If the percentile die comes up 0, your 25% roll succeeds if the other die comes up any number but 0.

If the percentile die comes up 1, your roll succeeds regardless of what you roll on the second die.

If the percentile die comes up 2, your roll succeeds if you roll 0-5.

If the percentile die comes up 3-9, you are the weakest link - goodbye.

Which, all taken together, means a success 25% of the time...

 

[Caliber]

If I roll a percentile 25 times, a 1 to 25 won't theoretically come out because there are more combinations to roll. I'd need to roll 76 times to ensure a 1 to 25 came out (because the first 75 rolls could be any number of 26 to 100). Again, all things being equal.

Herein lies your problem.

Even if you rolled four d4s, you aren't ensured you will get a 1. Nor are you ensured to get a number under 25 (inclusive) by rolling a d100 76 times.

Mathmatically, your chances are indeed the same. Yes, the range of possible failure is bigger, but so is the range of possible success.

Think of it this way. On a 1d4, you can succeed on 1 out of 4 sides, and fail on 3 out of 4 sides.

On a d100 you can succeed on 25 out of 100 sides, and fail on 75 out of 100 sides. Either way you are three times more likely to fail than to succeed.

I am not sure what to say to convice you since you already accept that both come out to a 1 in 4 chance.

Hope I could help.

 

[starwolf]

Ok, lets look at the odds shall we,

on a d4 you have 1 side that will save you and 3 side that will kill you. thats a 25% chance of winning.

on a percentile dice roll you have 25 combinations that will save you and 75 combinations that will kill you. that is still a 25% chance of winning.


edit: too slow on the draw..see Caliber's answer

 

[RigaMortus]

Here is a good site that may help show what I am trying to prove:

http://205.200.64.249/GC/scrolls/2000/feb/dice.html

Look under the Triangular Probability Distributions part in particular. The only problem is, I'm trying to compare a 1d4 to 2d10 and they are comparind 2d6 vs 1d8+1d4. Kinda sorta what I am trying to do, but with different dice.

Now, if only someone could punch in my numbers to their formulas I might be able to show the point I am trying to make on this.

 

[kreynolds]

Why is that so important

It's not. I found it funny, and it only matters if I found it funny. You don't have to find it funny to be funny. Funny, isn't it?