Need a statistic major's help here...

[Darkness]

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?

Fair enough - and funny, too.

 

[kreynolds]

Fair enough - and funny, too.

Nah. The more I think about it, it really wasn't funny. Ah well. I'lll come up with some that's actually funny later.

 

[hong]

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.

You are not comparing 1d4 to 2d10. 2d10 means you take the result of the two d10s and add them together, giving a result between 2 and 20. You are comparing 1d4 to d10 * 10, + d10 (except that two 0's = 100, not zero). This result has a uniform distribution on the range 1-100 inclusive, namely all numbers between 1 and 100 are equally likely.

Because of this uniform distribution, your chance of rolling any number between 1 and 25 inclusive is simply the number of desired outcomes (25) divided by the total number of possible outcomes (100). That's 25/100, which reduces to 1/4.


Hong "trust me, I'm a statistician" Ooi

 

[Caliber]

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.

First let me gloat over starwolf. Mwahahahaha! Now that that is out of my system ...

The problem is you AREN'T doing 2d10. You're rolling a d100. It doesn't matter whether or not you are rolling two d10s or are using one of those massive d100s.

The differences noted in the article you linked are there because despite 2d6 and 1d8+1d4 both having the same range (2-12) there possible combinations are different.

2d6 can add up to a 7 in a multidue of ways. 1-6, 2-5, 3-4, 4-3, 5-2, 6-1. 1d8+1d4 only has 6-1, 3-4, 4-3, 6-1.

See the difference?

When you roll 2d10 as percentile you don't have this problem because you aren't summing the two rolls. You have a linear distribution (ie, each number from 1-100 occurs exactly once.)

Better?

Edit: Curses! In the process of my gloating, Hong beat me to the post!

 

[nameless]

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.

Okay, I see the problem you're having, and the page kind of adresses it under the triangular probability. With two dice, you get a triangular probability if you sum them, but a linear probability if you read them sequentially. Here's a layman's explanation for the triangular probability principle though:

When you chuck one die, assuming its a fair die (all sides equally likely to land), then no result it more likely than another. When you chuck two dice and add them together, the numbers aren't all equally likely. Since each total can be reached by more than one distinct throw of the dice, the ones in the middle end up being more common.

When you don't sum the dice, however, this doesn't apply. Each possible outcome for each die is unique. Since a designated die always represents the 10's and another one always represents the 1's, each numerical outcome physically matches one literal die combination. Since they all match exactly one die outcome, they all have the same likelyhood (1 in 100), and that's the definition of a linear distribution.

1d4 is exactly the same as 1d100 if you're checking percentile, and both are linear distribution. Adding a d50 to d51 and then subtracting 1 (for example) would give you a number 1 to 100, but not distributed linearly.

If you don't believe me, just reread that paragraph on triangular distributions, and you'll see the thing about adding dice versus sequencing them.

edit: geez, two people beat me to the post!

-nameless

 

[RigaMortus]

Ok, I'll take another stab at what I am trying to get at here, but please remember, I am not statistics major =) Let's assume that you have a 25% chance of something BAD happening to you in game. So you do NOT want to roll that 25%.

If you roll a 1d4, a 1 will come up 25% of the time.

If you roll 2d10, you have a 30% chance of a 0, 1 or 2 coming out for your first roll.

If the 0 comes out (10% chance of that happening) then you need to roll another 0 on the other die to be safe (that would be another 10% chance you have to roll for to be safe).

If the 1 comes out (another 10% chance) it won't matter what your next roll is, you will fail (so that would be equal to 0% because anything you roll will make you fail at this point 100% of the time).

If a 2 comes out (another 10% chance), then you need to roll a 6 - 9 to be safe (this is another 40% chance you have to roll in order to be safe).

The point??? I don't know the point. It's 2AM and I can't comprehend any point I am trying to make. Good night.

 

[RigaMortus]

Bah, I get it now =)

Well how about this then...

A 1d4 has less "bounce" then 2d10, therefore it is easier to "drop" the d4 on the desired number then it is for the 2d10, therefore you have a greater chance of rolling a 25% chance on a d4 then you do with 2d10.

 

[Vinyafod]

For such things it is best to write down the chances/ combinations of possible die rolls and simply start counting then:

possible outcomes of 2d10 (not summed up!! but percentile roll)

    0    1    2    3    4    5    6    7    8    9 
0   00   [b][color=red]01   02   03   04   05   06   07   08   09[/color]
1[color=red]   10   11   12   12   14   15   16   17   18   19[/color]
2[color=red]   20   21   22   23   24   25[/b][/color]   26   27   28   29 
3   30   31   32   33   34   35   36   37   38   38
4   40   41   42   43   44   45   46   47   48   49 
5   50   51   52   53   54   55   56   57   58   59
6   60   61   62   63   64   65   66   67   68   69
7   70   71   72   73   74   75   76   77   78   79
8   80   81   82   83   84   85   86   87   88   89
9   90   91   92   93   94   95   96   97   98   99

We have a hundred different combinations here. 25 of those gives scores of 25 or lower. 25 out of 100 =25/100 = 1/4 = 25%

d4:

1
2
3
4

We have 4 "combinations". One of those gives a 1. 1 out of 4 = 1/4 = 25%

That is absolutely correct and nothing to argue about. Chances are exactly the same. Believe it or not. if that won't convice you, nothing will.

To take the approach you tried in your last post:

Assuming numbers 1 to 25 are not wanted...
The first die always displays the 10-digit, the second the 1-digit.
First roll = 0 (chance to happen: 10%), second roll must be 0 in order to succeed (chance to happen: 10%) -> 0.1*0,1=0.01 -> 1% chance to succed on a first roll of a 0

First die shows a 1 (10% chance), nothing can save you now -> plain 0% chance to suceed -> 0%

First die shows a 2 (10% chance), 6 to 9 will succeed (40% chance) -> 0.1*0.4=0.04 -> 4% chance to succeed on a first roll of a 2

First die show 3 to 9 (70% chance), all those will automatically succeed -> plain 70% chance

1% + 4% + 70% = 75% 3 out of 4 succeed 75% chance to succeed.

Thats the maths whith which you calculate it!
Hope that will convince you.

 

[Berk]

*places 20 down on 8 the hard way and another 15 on 54 on the hop* =o)

sorry, the 2d6 reply and the amount of chances to roll a 7 just make me miss craps so bad. been ages since I went to a casino.

 

[Caliber]

Its amazing how much gambling and/or DnD can teach you about dicing ...

Yes its easier to cheat with a d4. Thats why rat bastard DMs always demand d100s for weird rolls.