Lend me your math!!!

[SethDrebitko]

Hello all,

I am in need of some help with probabilities on a dice mechanic I am working with, and was hoping some folks her could help. I modified m20 so that characters do not increase skill ranks (or have skills), nor do they have varying BAB progression by class. Instead, depending on how good you are at a skill (or combat based on class) you roll between 1-3 d20 keeping the highest result.

For example: a fighter would swing with 3d20 keep highest, while a wizard would swing with just a single d20.

What I would like help figuring out is what the probability of obtaining any given result would be on the roll 2 keep 1, and roll 3 keep one options. Thanks in advance for any help!

 

[GMMichael]

Obtaining a given result is different from obtaining the given result -or higher-. While the math varies, the basic concept is always the same:

Out of all possible outcomes, what percentage of them are acceptable?

It gets tricky in two places: figuring out -all possible outcomes-, and then counting the acceptable ones.

In the 3d20 fighter example, a fighter with bad odds on 1d20 doesn't benefit much from additional rolls. A fighter with good odds on 1d20 gets success basically guaranteed on successive rolls.

That's the qualitative explanation. I will not be offering the quantitative one.

 

[Loonook]

Hello all,

I am in need of some help with probabilities on a dice mechanic I am working with, and was hoping some folks her could help. I modified m20 so that characters do not increase skill ranks (or have skills), nor do they have varying BAB progression by class. Instead, depending on how good you are at a skill (or combat based on class) you roll between 1-3 d20 keeping the highest result.

For example: a fighter would swing with 3d20 keep highest, while a wizard would swing with just a single d20.

What I would like help figuring out is what the probability of obtaining any given result would be on the roll 2 keep 1, and roll 3 keep one options. Thanks in advance for any help!

This can easily be done in any spreadsheet that allows you to run something. For Excel, for instance, copy the following

=RANDBETWEEN($Cell$1, $Cell$2)

Into 3 columns, then copy the equation down. $Cell$2 and $Cell$1 are locked for the minimum and maximum values of your rolls.

Then create a simple IF function checking each set of rows in order:

=IF([A1]>=$Cell$3,1,IF([A2]>=$Cell$3,2,IF([A3]>=$Cell$3,3,0).

$Cell$3, of course, is our DC or TN value.

Then do a set of basic equation that shows you how many of your IF statements ended in 1s, 2s, 3s, or 0s. These will just check for how many have the value you're looking for.

Tada! You now have a way to check your system! It can generate as many random results as you want... Personally I would suggest 10,000 to get a good randomization. This basic setup can be extrapolated into some cool complex stuff, and is flexible for any size of die and any modifier.

Slainte,

-Loonook.

 

[GMMichael]

I am totally gonna try this!

 

[Darkness]

The probabilities should be:

2d20		
result	in 400	in %
1	1	0.25
2	3	0.75
3	5	1.25
4	7	1.75
5	9	2.25
6	11	2.75
7	13	3.25
8	15	3.75
9	17	4.25
10	19	4.75
11	21	5.25
12	23	5.75
13	25	6.25
14	27	6.75
15	29	7.25
16	31	7.75
17	33	8.25
18	35	8.75
19	37	9.25
20	39	9.75

3d20		
result	in 8000	in %
1	1	0.01
2	7	0.09
3	19	0.24
4	37	0.46
5	61	0.76
6	91	1.14
7	127	1.59
8	169	2.11
9	217	2.71
10	271	3.39
11	331	4.14
12	397	4.96
13	469	5.86
14	547	6.84
15	631	7.89
16	721	9.01
17	817	10.21
18	919	11.49
19	1027	12.84
20	1141	14.26

Note: 3d20 probabilities in % are rounded.

I did this by making a spreadsheet display every single possible combination.

 

[SethDrebitko]

Thanks for all the help folks! John Payne over at the facebook group posted a link to an awesome dice resource http://anydice.com/program/1e0a.

The results look great from a difficulty standpoint though we'll see how it works in practice. With the roll keep deal the average intelligence person will be able to accomplish a tough task (DC 15) in an area that they are an expert in. I think the trick will be to clearly define what would constitute a roll of the extra dice.

I have the feeling this will make combat far more quick and deadly which should be interesting.